uk: Комп'ютерні науки

description: Die Train-the-Trainer-Workshops für Open-Access-Multiplikator:innen stellen eine wichtige Säule des Kompetenzvermittlungs- und Vernetzungsangebotes von open-access.network dar. Seit dem erstmaligen Angebot im November 2020 konnte die zwölfteilige Reihe verschiedene Institutionen adressieren. Gemein ist den Teilnehmer:innen jedoch ihre Tätigkeit als Open-Access-Beauftragte bzw. publikationsunterstützendem Personal. Auf einer Gratwanderung zwischen der Vermittlung von didaktischen Methoden und Open Access relevanten Themen, bietet die Veranstaltungsreihe Ideen zur Umsetzung von Schulungen, Workshops, usw. an der eigenen Einrichtung. Das Format unterstützt die Schulenden bei der Sensibilisierung für die Bedürfnisse Ihrer Zielgruppen. Gleichsam erhalten die Teilnehmer:innen selbst Informationen und Tipps zu aktuellen Entwicklungen im Bereich Open Access. Die Auswahl der zu behandelnden, Open Access relevanten Themen erfolgt durch Abfrage im Vorfeld. Ob „Transformation“, „Repositorien“, „Finanzierung“: Die Teilnehmer:innen entscheiden, worüber sie miteinander in Gespräch kommen. Neben einem Input-Vortrag bzw. einem Good-Practice-Beispiel, welcher*s auf den Adressatenkreis zugeschnitten ist, gelingt der gemeinsame Wissens- und Erfahrungsaustausch mithilfe von Arbeitsaufträgen und Fragestellungen. Diese greifen zuvor benannte, um Open Access konzentrierte Bereiche auf und ermöglichen eine zielorientierte Diskussion in Kleingruppen und Plenum. Die Relevanz der Train-the-Trainer-Workshops bemisst sich an der Schlüsselfunktion Ihrer Mitwirkenden: Sie unterstützen Wissenschaftler:innen bei der Publikation ihrer Forschungsergebnisse und stehen diesen mit (den neu gewonnenen) Informationen beratend zur Seite. Gleichzeitig ermöglichen erworbene Kenntnisse über interaktive Schulungsmethoden den Workshop-Absolvent:innen, an der eigenen Einrichtung für Open Access zu begeistern. Das Publikationsverhalten der Forscher:innen soll auf Basis eines eigenen Schulungsangebotes nachhaltig verändert werden. Darüber hinaus tragen der gemeinsame Wissens- und Erfahrungsaustausch der Open-Access-Beauftragten zur Schaffung einer Community of Practice bei. Der Vortrag möchte die Stimmen der Teilnehmer:innen abbilden: Treten wiederkehrende Fragen und Erfahrungswerte bezüglich Veranstaltungs- und Beratungsangeboten rund um Open Access auf? Gilt es vielleicht mehr, als nur die Wissenschaftler:innen zu begeistern?

uk: вхід без авторизації

name: Nachhaltig für Open Access begeistern – Oder: Wie erreiche ich die Wissenschaftler:innen meiner Einrichtung?


Jasmin Schmitz

type: Person

cs: Informatika

de: Informatik

fi: tietojenkäsittelytiede

uk: Комп'ютерні науки

en: Computer Science

fr: Informatique

da: Datalogi

es: Ciencias de la Computación

nl: Informatica

cs: Technické vědy

de: Ingenieurwissenschaften

fi: tekniikka

uk: Інженерія

en: Engineering Sciences

fr: Ingénierie

da: Ingeniørvidenskab

es: Ingeniería

nl: Engineering

description: Das Projekt open-access.network verfolgt drei wesentliche Ziele: Das Informieren, Vernetzen und Fortbilden der Open-Access-Community. Zu diesem Zweck wurde die Informationsplattform open-access.net im Rahmen des Projekts umgestaltet zum Kompetenz- und Vernetzungsportal open-access.network. Der Relaunch findet im Rahmen der Open-Access-Tage am Abend des 27. September im Rahmen einer Relaunch-Party statt. In diesem Vortrag stellen die Projektmitarbeiter Maximilian Heber und Andreas Kirchner die neue Website vor und geben dabei eine kleine Einführung in die Grundlagen des Open Access. Des Weiteren geben sie praktische Tipps zur Umsetzung von Open Access und stellen die Services vor, welche das Portal allen Interessierten bietet.

TIB AV-Portal

type: Service

type: WebContent

type: MediaObject

@language: de

cs: přihlášení není vyžadováno

de: keine Anmeldung erforderlich

uk: вхід без авторизації

en: no login required

nl: geen login vereist

name: Preprints als „besondere Form“ der Open-Access-Veröffentlichung – Herausforderungen und Umgang damit

Universität Konstanz

addressCountry: DE

addressLocality: Konstanz

addressRegion: Baden-Wurttemberg

type: Organization

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


uk: Комп'ютерні науки

description: Das Museum für Naturkunde Berlin ist ein integriertes Forschungsmuseum in der Leibniz-Gemeinschaft. Es ist ein Ort, an dem sich Wissenschaft und Gesellschaft treffen und stärkt die Wissensgesellschaft durch den freien Zugang zu Informationen und Forschungsinfrastrukturen, sowie durch die Öffnung seiner Forschung im Sinne von Open Science. Die Bibliothek des Museums trägt dazu bei, indem sie Open Access (OA) innerhalb und außerhalb der Institution fördert. Dies ist nicht zuletzt ein Verdienst der Koordinierungsstelle für wissenschaftliches Publizieren. Die Stelle wurde 2017 in der Bibliothek eingerichtet und unterstützt bei Fragen rund um den wissenschaftlichen Publikationsprozess, beim Reporting zum wissenschaftlichen Output, beim Lizenzmanagement sowie den Transformationsverträgen und in der Erstellung bzw. Erneuerung der Open Access Leitlinie. Darüber hinaus ist die Koordinationsstelle für das Article Approving Management und die interne Koordination der Publikationskosten zuständig. All diese Aufgabenbereiche sowie die zukünftigen Aktivitäten zur Umsetzung und Förderung von Open Access in der Einrichtung, wie beispielsweise die Einrichtung eines hauseigenen Publikationsfonds, sind Herausforderungen, die in großen wissenschaftlichen Bibliotheken längst umgesetzt sind. Dies wirft die Frage auf, wie groß die Kluft bei der Umsetzung von Open Access zwischen großen und kleinen Bibliotheken ist. Was sind die größten Hindernisse, mit denen kleinere Einrichtungen wie Spezial- und Museumsbibliotheken konfrontiert sind? Gibt es Best Practices, die in anderen Einrichtungen übernommen werden könnten? Um dies herauszufinden, wurde im Frühjahr 2021 eine Umfrage unter Museumsbibliotheken durchgeführt, deren Ergebnisse bei den Open Access Tagen 2021 vorgestellt werden. Wir hoffen aus den Ergebnissen heraus Möglichkeiten zu identifizieren, um die Kluft zwischen den verschiedenen Bibliotheken zu verringern und im besten Fall Strukturen zu schaffen, die kleineren Bibliotheken helfen, Open Access und Open Science in ihren Einrichtungen zu fördern.

uk: вхід без авторизації

name: Open Access - Eine Herausforderung für kleinere Bibliotheken?


uk: Комп'ютерні науки

description: Nach DOIs für wissenschaftliche Werke und ORCID iDs für wissenschaftliche Autor*inInnen sind Persistent Identifier (PID) für wissenschaftliche Organisationen das entscheidende Puzzlestück im wissenschaftlichen Publikationsprozess. Erst durch Organizations-IDs wird das volle Potential der Automatisierung und Verknüpfung von PIDs ausgeschöpft. Dadurch werden Ressourcen von wissenschaftlichen Einrichtungen und ihre Forschenden bei der Erfassung, Erstellung und Pflege von Publikationsmetadaten geschont. Darüber hinaus sind PIDs elementare Bestandteile zur Umsetzung von Open Access bzw. Open Science. Gerade bei der Analyse von Publikationen und Kosten für die Open-Access-Transformation einer Einrichtung kommt der Schaffung eines PID für wissenschaftlichen Einrichtungen und Förderorganisationen einen zentrale Bedeitung zu. Wichtige PID-Service-Infrastrukturanbieter, wie DataCite und Crossref, unterstützen bereits die Angabe von Organisations-IDs in ihren Metadatenschemata und tragen so maßgeblich zu ihrer Verbreitung bei. Um mehr über den Status quo der Nutzung und Verbreitung von Organisations-IDs in Deutschland zu erfahren, wurde im Rahmen des DFG-geförderten Projekts ORCID DE Ende 2020 eine "Umfrage zum Bedarf und Nutzung von Organisations-IDs an Hochschulen und außeruniversitären Forschungseinrichtungen in Deutschland" unter 548 wissenschaftlichen Einrichtungen in Deutschland durchgeführt. Bestandteil der Studie waren unter anderem Fragen zur Kenntnis, Verbreitung und Nutzung von Organisations-IDs an wissenschaftlichen Einrichtungen. Darüber hinaus wurden Anforderungen an Organisations-IDs bzw. ihre Metadaten (z. B. Relationen und Hierarchie-Ebenen) erfragt. Die finalen Ergebnisse dieser Erhebung sollen erstmals öffentlich präsentiert und diskutiert werden und stellen einen Beitrag zur Förderung und Aufklärung über Organisations-IDs dar.

uk: вхід без авторизації

name: Organisations-IDs: integraler Bestandteil der OA-Transformation? Umfrageergebnisse zur Verbreitung und Nutzung an wissenschaftlichen Einrichtungen in Deutschland


uk: Комп'ютерні науки

uk: вхід без авторизації

name: Building human and financial capacity for Diamond OA


uk: Комп'ютерні науки

description: Die Open-Access-Transformation unterstützt in erster Linie die Veröffentlichung in kommerziellen Open-Access-Zeitschriften, bei denen Article Processing Charges (APCs) anfallen. Im Gegensatz dazu werden APC-freie Diamond-Zeitschriften in der Regel nur während der Migrations- und Gründungsphase gefördert; eine längerfristige Perspektive lässt sich dadurch jedoch häufig nicht gewährleisten. Wissenschaftliche Einrichtungen können durch institutionelle Publikationsdienste die dringend benötigte Nachhaltigkeit schaffen. Insbesondere Angebote für das Hosting von wissenschaftlichen Fachzeitschriften ermöglichen den langfristigen Betrieb von Publikationsplattformen nach aktuellen Standards und Kriterien einer offenen Wissenschaft (u. A. Transparenz, persistente Idenfifikatoren, Metriken, Mehrsprachigkeit, Multimedia). Die Umsetzung dieser Standards und die langfristige Sichtbarmachung von Inhalten sorgen für eine nachhaltige Verbreitung und Nachnutzung. Herausgebende Wissenschaftler:innen können auf dieser formalen und technischen Basis eigenverantwortlich publizieren. Die Ausrichtung des Angebots an internationalen Standards ermöglicht, die jeweilige Zeitschrift unabhängig von kommerziellen Angeboten als fachliche Marke auf- oder auszubauen. Dies schafft Alternativen bzw. Ergänzungen im Sinne einer wissenschaftlichen Publikationsvielfalt. Am Beispiel des Open-Access-Zeitschriften-Hostingangebots der SUB Hamburg wollen wir zeigen, wie eine wissenschaftliche Bibliothek einen professionellen Publikationsdienst nachhaltig gestalten kann. Im Fokus liegen dabei sowohl die Anforderungen an wissenschaftliche Erstveröffentlichungen wie auch die Berücksichtigung der Ressourcen der Einrichtung. Darüber hinaus wollen wir den Aspekt der Skalierbarkeit beleuchten und mit den Teilnehmenden Szenarien der Vernetzung und Interaktion diskutieren. Perspektivisch können alle Akteure von den dabei entstehenden Synergien profitieren.

uk: вхід без авторизації

name: "Shine bright like a diamond" - wie institutionelle Publikationsdienste offene Wissenschaft fördern


uk: Комп'ютерні науки

description: Ein Problem zahlreicher APC-freier Open-Access-Zeitschriften aus dem akademischen Umfeld ist, dass verlegerische Standards nicht oder nicht vollständig beachtet werden. Besonders für wissenschaftsnahe Open-Access-Zeitschriften ist es aber wichtig, sich mit diesen Standards zu befassen, um mit Zeitschriften bei kommerziellen Anbietern mithalten zu können. Verschiedene Organisationen aus dem Open-Access-Umfeld haben Kriterien entwickelt, die eine hohe formale Qualität von Open-Access-Zeitschriften garantieren. Zu nennen sind hier v.a. die technical implementation guidelines von Plan S, die Kriterien zur Erreichung des DOAJ Seal sowie die Mitgliedschaftskriterien der Open Access Scholarly Publishing Association (OASPA). Einige der von diesen Organisationen und Initiativen angewendeten Kriterien überschneiden sich, andere sind komplementär. Die Kriterien können verschiedenen Bereichen zugeordnet werden, wie z. B. Open-Access-Standards, Identifier, Metadaten und Richtlinien bzw. Webseiteninhalte. Für TIB Open Publishing, die neue Open-Access-Publikationsplattform der Technischen Informationsbibliothek (TIB), haben diese formalen Qualitätskriterien hohe Relevanz, da Zeitschriften und Konferenzpublikationen, die mit TIB Open Publishing veröffentlichen, von vorne herein konform mit aktuellen Förderrichtlinien (z.B. Plan S) und Datenbanken (z.B. DOAJ) sein sollen, um ein möglichst große Reichweite und Sichtbarkeit zu erreichen. Im Rahmen des Aufbaus von TIB Open Publishing sind diese Kriterien daher zusammengetragen worden und sollen im Vortrag anhand einiger Beispiele veranschaulicht werden. Dabei wird auch die Übertragbarkeit auf andere Plattformen und Zeitschriften analysiert und aufbereitet.

uk: вхід без авторизації

name: Nicht-kommerziell ist nicht genug. Warum formale Standards auch für IHRE Publikation eine Rolle spielen (sollten)


uk: Комп'ютерні науки

description: Hintergrund: Open-Access-Publizieren verändert die Publikationslandschaft. Erhöhte potentielle Sichtbarkeit, Wettbewerbsfähigkeit und beschleunigter Austausch von Forschungsergebnissen sind nur einige von vielen Vorteilen. Hier stellt sich die Frage, ob von diesem Wandel der Publikationslandschaft bestimmte Personengruppen unterschiedlich stark profitieren. Die Analyse von Open-Access-Publikationen und der benötigten Infrastruktur für Open Access lassen die Frage aufkommen, ob es einen Gender-Open-Access-Publication-Gap gibt. Methodik: Im Rahmen der empirischen Erhebungen des vom Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg geförderten Projekts „Implementierung von Open Access an HAWen und PHen in Baden-Württemberg“ (Befragung von 563 Wissenschaftler:innen aus 11 Hochschulen für Angewandte Wissenschaften (HAW) und Pädagogischen Hochschulen (PH) im Herbst 2020) zeigte sich, dass sich die Quantität von Publikationen, auch von Open-Access-Publikationen, zwischen den Geschlechtern an HAWen und PHen unterscheidet. Ergebnisse: Näher beleuchtet werden die Fragen, ob die Unterschiede in der Häufigkeit der OA-Publikationen durch Faktoren wie Fachbereich, Erwerbsumfang (Vollzeit vs. Teilzeit), berufliche Stellung (Professor:in vs. Wissenschaftliche:r Mitarbeiter:in), Alter und Hochschultyp erklärt werden können, oder ob das Geschlecht im Publikationsverhalten eine Rolle spielt. Darüber hinaus werden weitere „weiche“ Faktoren wie die Motivation zu publizieren, Motivation OA zu publizieren, Hemmnisse, Wahrnehmung von Vorteilen und Nachteilen der OA-Publikationen untersucht und Unterschiede zwischen den Geschlechtern dargestellt. Diskussion: Es gibt Unterschiede in der Häufigkeit der OA-Publikationen und in den „weichen Faktoren“. Profitieren die Geschlechter unterschiedlich stark von dem Trend hin zu mehr Open-Access-Publikationen? Sind diese Ergebnisse auch für universitäre Forschung gültig oder eine Besonderheit der HAWen und PHen?

uk: вхід без авторизації

name: Open Access: Diversität oder Chancenungleichheit?


Open-Access-Tage 2021 - Q&A-Panel

uk: Комп'ютерні науки

@language: en

uk: вхід без авторизації


cs: Matematika

de: Mathematik

fi: matematiikka

uk: Математика

en: Mathematics

fr: Mathématiques

da: Matematik

es: Matemáticas

nl: Wiskunde

de: Mathematik, Naturwissenschaften

uk: Математика, природничі науки

en: Mathematics, Natural Sciences

description: This talk will introduce the field of rigorous computing and explain some of the problems it solves and tools it requires in a classical fixed grid context. We will then consider continuation problems where moving meshes are particularly useful. r-adaptive methods provide numerical efficiency and also simplify some of the topological technicalities in this approach.

uk: вхід без авторизації

name: Applications of adaptivity in verified numerics

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: In the first part of this talk, I discuss the generation of meshes adapted to a prescribed scalar 'monitor' function. This is done through equidistribution, so that the volume of a cell is inversely proportional to the monitor function. We supplement this with an optimal transport condition, which aids with mesh regularity, and guarantees existence and uniqueness of such a mesh. The resulting mesh can be obtained by solving a Monge-Ampère equation, a scalar nonlinear elliptic PDE. This optimal transport also approach generalizes naturally from Euclidean space to manifolds such as the sphere. In the second part of this talk, I discuss the integration of moving mesh adaptivity into a finite element shallow water model, in the wider context of the need for global numerical weather prediction models that can resolve small-scale dynamic features. We do this by modifying the governing fluid equations so they are solved in a frame relative to the moving mesh. The finite element discretization is based on a 'compatible', or 'mimetic', approach, in which the finite element spaces are linked by differential operators. The degrees of freedom correspond not just to point values, but also to fluxes and densities, which complicates the modifications that are required.

uk: вхід без авторизації

name: Mesh adaptivity on the sphere using optimal transport, and a moving mesh scheme for the nonlinear shallow water equations


uk: Математика, природничі науки

description: The moving mesh finite element method of Baines, Hubbard and Jimack [1] determines mesh velocities by building the underlying PDE into a monitor conservation principle and recovering an approximation in a manner which preserves the original monitor distribution (so an equidistributed mesh remains so as time progresses). The first part of this talk will outline this method and show some examples which illustrate its ability to track interfaces accurately for implicit moving boundary problems [2]. In theory, it is possible to drive the mesh movement in this algorithm using other monitors, e.g. arc-length, which could be used to distribute mesh nodes more effectively in the interior of the domain. Initial attempts to implement this as a continuous Galerkin finite element method have lacked robustness, so the second part of the talk will outline a discontinuous Galerkin version of the algorithm, capable of stabilising the approximation of the hyperbolic terms introduced when the mesh nodes no longer move according to a physically meaningful conservation principle. Initial results will be shown to demonstrate the feasibility of the approach and the extension to higher orders of accuracy will be discussed. I would particularly like to acknowledge the contributions to this work by Prof Mike Baines (University of Reading), Prof Peter Jimack (University of Leeds) and Mr Tom Radley (University of Nottingham). References: [1] M.J.Baines, M.E.Hubbard and P.K.Jimack, A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries, Appl. Numer. Math. 54:450--469, 2005. [2] M.J.Baines, M.E.Hubbard and P.K.Jimack, Velocity-based moving mesh methods for nonlinear partial differential equations, Commun. Comput. Phys. 10(3):509--576, 2011.

uk: вхід без авторизації

name: Continuous and discontinuous approaches to moving mesh finite elements


uk: Математика, природничі науки

description: There are numerous scientific applications which require large and complex meshes. Given the explosive growth in parallel computer architectures, ranging from supercomputers to hybrid CPU/GPU architectures, there has been a corresponding increase in interest in parallel computer simulations. For computational simulations involving the above applications, algorithms, which generate the mesh and manipulate it in parallel, are required. In particular, parallel mesh quality improvement is required whenever meshes of low quality arise in such simulations. In this talk, we describe our parallel variational mesh quality improvement method designed for distributed memory machines. The method is based on the sequential variational mesh quality improvement method of Huang and Kamenski. Although most mesh quality improvement methods directly minimize an objective function that explicitly specifies the mesh quality, Huang and Kamenski use the Moving Mesh PDE (MMPDE) method to discretize and find the minimum/maximum of a meshing functional, which is related to the mesh quality in an implicit manner. We solve the resulting ODE in parallel, which yields a mesh with a better quality. To solve the ODE in parallel, the mesh is first partitioned into regions using METIS. Next, the ODE is solved in parallel on the interior nodes of each mesh sub region. For nodes belonging to partition boundaries, i.e., those that are shared among cores, the algorithm calculates a partial ODE solution. To complete the solution at the shared nodes, a reduction operation using non-blocking MPI collective communication is performed. In order to overlap communication with computation, we experiment with various strategies for data organization. We test the performance of our method for up to 128 cores on tetrahedral meshes with up to 160M elements. Excellent strong scaling results and typical weak scaling results for unstructured meshes are obtained.

uk: вхід без авторизації

name: A parallel variational mesh quality improvement method for distributed memory machines


ton fragezeichnen

uk: Математика, природничі науки

description: We start with a brief introduction to the conforming finite element method on polygonal/polyhedral meshes using the generalized barycentric coordinates. Then we present our recent work in this direction on the construction of a H(div)/H(curl) conforming element and a Crouzeix-Raviart type non-conforming element. Finally, we discuss how to develop an alignment and an equidistribution quality measures for polytopal meshes, and how to build a Moving Mesh PDE (MMPDE) moving mesh method based on these mesh quality measures. The work on H(div)/H(curl) conforming element is done in collaboration with Dr. Wenbin Chen. The work on mesh quality and moving mesh method is done in collaboration with Dr. Weizhang Huang.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Given a mesh on a surface, our goal is to improve the quality of the mesh using a moving mesh method. To this goal, we will construct a surface moving mesh method based on mesh equidistribution and alignment conditions. We will then discuss several proven advantages of this surface moving mesh approach. Finally, we will study various numerical examples using both the Euclidean metric and a Riemannian metric.

uk: вхід без авторизації

name: A surface moving mesh method based on equidistribution and alignment


uk: Математика, природничі науки

description: Error analysis and convergence results for PDE discretization methods are normally based on the assumption, among other, that the PDE coefficients are continuous functions. When PDE discretization methods are applied to PDEs (BVPs or IVPs) with discontinuous coefficients, numerical results indicate that the standard convergence orders are typically not observed, and, even more, convergence is not guaranteed. We consider spline collocation PDE discretization methods and their application to a discontinuous diffusion PDE, modelling brain cancer growth, with the discontinuity of the diffusion coefficient arising from the different properties of the white and grey matters of the brain. We consider techniques based on adaptive grids and the approximation of the discontinuous coefficients by continuous ones, and techniques based on adjusting the basis functions so that they satisfy appropriate discontinuity conditions. We present numerical results highlighting the strengths and weaknesses of different approaches.

uk: вхід без авторизації

name: Adaptive and non-adaptive spline collocation methods for a discontinuous diffusion PDE with application to brain cancer growth


uk: Математика, природничі науки

description: In this talk we consider the impact of discretization on traveling waves of bistable reaction-diffusion equations. Both temporal discretization by Backward Differentiation Formulas (BDF) methods and spatial discretizations by moving mesh methods are analyzed. Special attention is paid to propagation failure in one space dimension and to discretization induced anisotropy in higher space dimensions.

uk: вхід без авторизації

name: Bistable traveling waves under discretization: moving meshes


uk: Математика, природничі науки

description: We present a robust moving mesh finite difference method simulation of fourth order nonlinear PDEs describing elastic-electrostatic interactions in two dimensions. We use and extend the Parabolic Monge-Amp ́ere methods developed by Budd and Williams [1] to solve a fourth order PDE with finite time singularity. A key feature in our implementation is the generation of a high order transformation between computational and physical meshes that can accommodate the high order derivatives in the PDE. The PDE derived from a plate contact problem develops finite time quenching singularities at discrete spatial location(s). The moving mesh method dynamically resolves these temporally forming singularities, while preserving the underlying length scales of the problem. We show that the PMA resolves the singularities to high accuracy and gives strong evidence of self similarity near blow up. We briefly discuss the prediction of the touchdown profile using the skeleton theory from [3]. We numerically predict the skeleton set for a variety of domains, including domains with cutouts and non-convex domains. These predictions and verification of the skeleton theory are made using variational moving mesh methods developed in [2]. Accurately resolving singularities on general domains motivates recent work in extending the parabolic Monge-Amp ́ere equation to problems with curved domains. We utilize the optimal transport methods in [4] paired with the PMA to efficiently solve PDEs on curved domains using finite difference methods on a fixed, uniform computational domain. We present preliminary results of this method for semi-linear blow-up problems, sharp interface and prescribed moving boundary problems in curved two dimensional regions. References [1] C.J. Budd and J.F. Williams. Moving mesh generation using the parabolic Monge-Ampere equation. SIAM Journal on Scientific Computing, 31(5):3438-3465, 2009. [2] W. Huang and L. Kamenski. A geometric discretization and a simple implementation for variational mesh generation and adapation. J. Compt. Phys., 301:322-337. 2015. [3] A.E. Lindsay and J. Lega, Multiple quenching solutions of a fourth order parabolic PDE with a singular nonlinearity modeling a MEMS capacitor. SIAM Journal On Applied Mathematics, 72(3):935-958, 2012. [4] J. Benamou, B. Froese, A. Oberman. Numerical solution of the optimal transportation problem using the Monge Ampere Equation. J. Compt. Phys., 260:107-126,2014.

uk: вхід без авторизації

name: Monge-Ampére methods for fourth order PDEs and applications to elastic interface problems


uk: Математика, природничі науки

description: Our main goal in this talk is to present residual-type a posteriori error estimates in the maximum norm, as well as in the energy norm, on anisotropic meshes, i.e. we allow mesh elements to have extremely high aspect ratios [2, 4]. The error constants in these estimates are independent of the diameters and the aspect ratios of mesh elements. Note also that, in contrast to some a posteriori error estimates on anisotropic meshes in the literature, our error constants do not involve so-called matching functions (that depend on the unknown error and, in general, may be as large as mesh aspect ratios). To deal with anisotropic elements, a number of technical issues have been addressed in [2, 4]. For example, an inspection of standard proofs for shape-regular meshes reveals that one obstacle in extending them to anisotropic meshes lies in the application of a scaled traced theorem when estimating the jump residual terms (this causes the mesh aspect ratios to appear in the estimator). For maximum norm estimates, the analysis also employs sharp bounds on the Green’s function from [1]. For the estimation in the energy norm, a special quasi-interpolation operator is constructed on anisotropic meshes, which may be of independent interest [4]. We shall also touch on that certain perceptions need to be adjusted for the case of anisotropic meshes. In particular, it is not always the case that the computed-solution error in the maximum norm is closely related to the corresponding interpolation error [3]. References: [1] A. Demlow and N. Kopteva, Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems, Numer. Math., 133 (2016), 707-742 [2] N. Kopteva, Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes, SIAM J. Numer. Anal., 53 (2015), 2519-2544 [3] N. Kopteva, Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations, Math. Comp., 83 (2014), 2061-2070 [4] N. Kopteva, Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes Numer. Math., 137 (2017), 607-642. [5] N. Kopteva, Fully computable a posteriori error estimator using anisotropic flux equilibration on anisotropic meshes, (2017).

uk: вхід без авторизації

name: A posteriori error estimation on anisotropic meshes


uk: Математика, природничі науки

description: In this presentation, a moving mesh discontinuous Galerkin (DG) method is developed for the numerical solution of hyperbolic conservation laws. The method combines the DG method and the mesh movement strategy which is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of mesh partial differential equations. The mesh is a nonuniform mesh that is sparse in the regions where the solution is smooth and more concentrated near discontinuities. The method can not only achieve the high order in the smooth region, but also capture the shock well in the discontinuous region. For the same number of grid points, the numerical solution with the moving mesh method is much better than ones with the uniform mesh method. Numerical examples are presented to show the accuracy and shock-capturing of the method.

uk: вхід без авторизації

name: A moving mesh discontinuous Galerkin method for hyperbolic conservation laws


uk: Математика, природничі науки

description: In the last years considerable progress has been made in the development of Large Eddy Simulation (LES) for turbulent flows. The characteristic length scale of the turbulent fluctuation varies substantially over the computational domain and has to be resolved by an appropriate numerical grid. We propose to adjust the grid size in an LES by adaptive moving meshes. The monitor function, which is the main ingredient of a moving mesh method, is determined with respect to a quantity of interest (QoI). These QoIs can be physically motivated, like vorticity, turbulent kinetic energy or enstrophy, as well as mathematically motivated, like solution gradient or some adjoint-based error estimator. The main advantage of mesh moving methods is that during the integration process the mesh topology is preserved and no new degrees of freedom are added and therefore the data structures are preserved as well. We will present results for real-life engineering and meteorological applications.

uk: вхід без авторизації

name: Adaptive moving meshes in large eddy simulation for turbulent flows


uk: Математика, природничі науки

description: Discontinuous (jumping) coefficients often appear in modelling problems where the computational domain represents inhomogeneous media. An example of this is the geophysical electromagnetic (EM) modelling problem, where these jumps occur at interfaces that separate regions with different conductivities. These interfaces, along with other problem features, such as singular EM sources and pointwise solution observations, motivate mesh refinement to achieve good accuracy. The goal of this study is to investigate the combined application of h- and r-refinement to reduce numerical error in the modelling of EM data. For simplicity, aspects of this hr-adaptivity are explored in 1D. The steady-state diffusion and Helmholtz equations (which are commonly solved for the EM scalar and vector potentials, respectively) constitute the physical PDEs (PPDEs) here, while the r-refinement is based on an equidistribution principle. The PPDEs and the mesh PDE are solved alternately in an iterative manner to reduce an error estimate to a desired level. At each iteration, the old mesh is h-refined, the error estimate and its corresponding monitor function are updated and the r-refinement is performed. Various finite-element (FE) a posteriori global and local error estimates were examined: while FE residual-based estimates were cheaper to compute, hierarchical error estimates were found to be better indicators of the true errors. The solutions of adjoint problems of the PPDEs were used to construct local error estimates. These estimates were successfully used for goal-oriented refinement of the FE models.

uk: вхід без авторизації

name: Combining h- and r-adaptivity for finite-element models with jumping coefficients


Parallel PDE based mesh generators

uk: Математика, природничі науки

description: To reduce the overhead involved with the solution of the coupled system of physical and mesh PDEs, we propose a family of parallel solvers based on domain decomposition approaches. In this short talk I will review theoretical results obtained for the convergence of Schwarz methods for the steady state equidistribution principle at both the continuous and discrete levels and for a particular MMPDE solved by Rothe’s method.

uk: вхід без авторизації


uk: Математика, природничі науки

description: An essential component of a high quality numerical software package is a framework that provides an error-controlled computation of the approximate solution. This means that the package returns a numerical solution such that an associated error estimate satisfies a user-prescribed tolerance. This type of computation has two important advantages: (i) the user can have reasonable confidence that the numerical solution has an error that is consistent with the requested tolerance, and (ii) the cost of the computation will be consistent with the requested accuracy. In this talk, we introduce a new software package, called BACOLRI, for the error-controlled numerical solution of 1D PDEs. This code employs a high order B-spline collocation algorithm to discretize the spatial domain and then uses a high order error control Runge-Kutta package to solve the resulting system of time-dependent Differential-Algebraic Equations. BACOLRI estimates the spatial error of the approximate solution on each time-step using an interpolation-based scheme and employs adaptive mesh refinement to provide control of the spatial error. We will briefly survey the family of solvers from which BACOLRI has evolved, describe the algorithms implemented in BACOLRI, and review numerical results that demonstrate the superior performance of BACOLRI compared to other comparable solvers.

uk: вхід без авторизації

name: B-spline adaptive collocation/Runge-Kutta software with interpolation-based spatial error estimation for the error-controlled numerical solution of PDEs


uk: Математика, природничі науки

description: Multi-scale models are commonly used to mathematically describe the evolution of many interesting and important systems. They attempt to capture dynamics on multiple scales and integrate them into a common framework. One way to do this is via partial differential equations (PDEs) that do not depend on spatial derivatives to represent dynamics on small scales. Upon spatial discretization, these PDEs reduce to sets of ordinary differential equations (ODEs) at each discrete spatial point. eBACOLI is a numerical software package for solving multi-scale models consisting of parabolic PDEs coupled with PDEs that do not depend on spatial derivatives in one spatial dimension. eBACOLI features adaptive error control in the temporal and spatial domains. It uses a B-spline collocation method for the spatial discretization to yield a set of ODEs, which together with the boundary conditions, form a system of differential-algebraic equations (DAEs). These DAEs are then solved using DASSL. We demonstrate this applicability and efficiency of this software package on a number of examples, including the monodomain model of cardiac electrophysiology.

uk: вхід без авторизації

name: Extending BACOLI to solve Multi-Scale Models


uk: Математика, природничі науки

description: Many finite difference methods that involve spatial adaptation employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This constructive strategy has been proven to be extremely effective and easy-to-use in multiphysical computations. However, selections of core monitoring functions are often challenging and crucial to the computational success. This note concerns several different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first a few monitoring designs to be discussed are within the so-called direct regime, the rest belong to a newer category of the indirect type, which requires the priori knowledge of certain important solution features or characteristics. Some simulated examples will be presented to illustrate our study and conclusions. This note is based on recent collaborative work with M. A. Beauregard and J. L. Padgett.

uk: вхід без авторизації

name: Note on Spatial adaptations for the numerical solution of singular reaction-diffusion equations


uk: Математика, природничі науки

description: Linearized (semi)-implicit schemes are the most commonly-used approximations in numerical solution of nonlinear parabolic equations since at each time step, the schemes only require the solution of a linear system. However the time step restriction condition of schemes is always a key issue in analysis and computation. For many nonlinear parabolic systems, error analysis of Galerkin type finite element methods with linearized semi-implicit schemes in the time direction is established usually under certain time step condition τ≤hα for some α>0. Such a time-step condition may result in the use of a very small time step and extremely time-consuming in practical computations. The problem becomes more serious when a non-uniform mesh or adaptive meshing is used. In this talk, we introduce a new approach to unconditional error analysis of linearized semi-implicit Galerkin FEMs for a large class of nonlinear parabolic PDEs.

uk: вхід без авторизації

name: New Analysis of Fully Discrete FEMs for Nonlinear Parabolic PDEs


uk: Математика, природничі науки

description: An adaptive moving mesh finite difference method is presented to solve a modified Buckley Leverett equation with a dynamic capillary pressure term from porous media. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. Special attention is paid to the non-monotonic profiles. The governing equation is discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive time dependent monitor function with directional control is applied to redistribute the mesh grid in every time step, and a diffusive mechanism is used to smooth the monitor function. The behavior of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction is investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, a good mesh quality and a high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experiments is presented to demonstrate the accuracy and effectiveness of the numerical method.

uk: вхід без авторизації

name: Moving mesh finite difference method for non-monotone two-phase flows in porous media


uk: Математика, природничі науки

description: We present a mesh smoothing algorithm based on the MMPDE moving mesh method based on the direct geometric discretization of the underlying meshing functional on simplicial meshes. The nodal mesh velocities are given in a simple, analytical matrix form. We further combine the moving mesh smoothing with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity, and utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical comparison with some publicly available mesh improving software is provided. This work is a collaboration with Weizhang Huang (University of Kansas), Hang Si (Weierstrass Institute), Franco Dassi (Università degli Studi di Milano-Bicocca), and Patricio Farrell (Weierstrass Institute).

uk: вхід без авторизації

name: MMPDE moving mesh smoothing: Tetrahedral mesh improvement using moving mesh smoothing and lazy searching flips

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: Background on cohomological point of view


uk: Математика, природничі науки

uk: вхід без авторизації

name: Sparse High-dimensional Approximation from Highly Noisy Data


Data and Models

uk: Математика, природничі науки

uk: вхід без авторизації


Deep Neural Nets meets ODE's

uk: Математика, природничі науки

uk: вхід без авторизації


Nonconvex Approaches in Data Science

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Compressed sensing approximation of high-dimensional functions via convex and nonconvex regularizations


uk: Математика, природничі науки

uk: вхід без авторизації

name: Asymptotics of objective functionals in semi-supervised learning


uk: Математика, природничі науки

uk: вхід без авторизації

name: Manifold learning by sparse grid methods


The Multivariate Decomposition Method

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Greedy approximation selection with data assimilation


uk: Математика, природничі науки

uk: вхід без авторизації

name: Learning Regularisers: from Shallow to Deep Regularisers in Variational Models


Topological Dimensionality Reduction

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Sparse Appoximation for Nonlinear Dynamics and Stationary Processes


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Game Theoretic Approach to Numerical Approximation and Algorithm Design


uk: Математика, природничі науки

uk: вхід без авторизації

name: Joint Sparse Recovery Through Manifold Optimization


uk: Математика, природничі науки

description: A central problem of microstructure is to develop technologies capable of producing an arrangement, or ordering, of the material, in terms of mesoscopic parameters like geometry and crystallography, appropriate for a given application. Is there such an order in the first place? We describe very briefly the emergence of the grain boundary character distribution (GBCD), a statistic that details texture evolution, and illustrate why it should be considered a material property. Its identification as a gradient flow by our method is tantamount to exhibiting the harvested statistic as the iterates in a mass transport JKO implicit scheme, which we found astonishing. Consequently the GBCD is the solution, in some sense, of a Fokker-Planck Equation. The development exposes the question of how to understand the circumstances under which a harvested empirical statistic is a property of the underlying process. (joint work with P. Bardsley, K. Barmak, E. Eggeling, M. Emelianenko, Y. Epshteyn, X.-Y. Lu and S. Ta'asan).

uk: вхід без авторизації

name: Towards a gradient flow for microstructure: microstructure meets Boltzmann


uk: Математика, природничі науки

description: We are interested in evolutionary biology models for sexual populations. The sexual reproductions are modelled through the so-called Infinitesimal Model, which is similar to an inelastic Boltzmann operator. This kinetic operator is then combined to selection and spatial dispersion operators. In this talk, we will show how the Wasserstein estimates that appear naturally for the kinetic operator can be combined to estimates on the other operators to study the qualitative properties of the solutions. In particular, this approach allows us to recover a well-known (in populations genetics) macroscopic model.

uk: вхід без авторизації

name: Wasserstein estimates and macroscopic limits in a model from ecology


uk: Математика, природничі науки

description: Swelling media (e.g. gels, tumors) are usually described by mechanical constitutive laws (e.g. Hooke or Darcy laws). However, constitutive relations of real swelling media are not well-known. Here, we take an opposite route and consider a simple heuristics relying on the following rule: (i) particles are at packing density; (ii) any two particles cannot swap their position; (iii) motion should be as slow as possible. These heuristics determine the medium velocity uniquely. In general, this velocity cannot be retrieved by a simple Darcy law.

uk: вхід без авторизації

name: A new continuum theory for incompressible swelling materials


uk: Математика, природничі науки

description: We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. Our approach is based on a relative entropy method, where the macroscopic quantities of the kinetic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigourous link between kinetic and reaction-diffusion models.

uk: вхід без авторизації

name: Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system


uk: Математика, природничі науки

description: In this talk, we consider a system of equations arising from reproduction processes in biology, where two densities evolve under diffusion, absorbing reaction and chemotaxis. We prove that chemotaxis plays a crucial role to ensure the efficiency of reaction: Namely, the reaction between the two densities is very slow in the pure diffusion case, while adding a chemotaxis term greatly enhances reaction. While proving our main results we also obtain a weighted Poincare's inequality for the Fokker-Planck equation, which might be of independent interest.

uk: вхід без авторизації

name: Enhancement of biological reaction by chemotaxis


uk: Математика, природничі науки

description: For a range of physical and biological processes—from dynamics of granular media to biological swarming—the evolution of a large number of interacting agents is modeled according to the competing effects of pairwise attraction and (possibly degenerate) diffusion. We prove that, in the slow diffusion limit, the degenerate diffusion becomes a hard height constraint on the density of the population, as arises in models of pedestrian crown motion. We then apply this to develop numerical insight for open conjectures in geometric optimization.

uk: вхід без авторизації

name: Minimizers and gradient flows in the slow diffusion limit


uk: Математика, природничі науки

description: Entropic regularization of optimal transport is appealing both from a numerical and theoretical perspective. In this talk we will discuss two applications, one from incompressible fluid dynamics and the other from mean-field games theory.

uk: вхід без авторизації

name: Entropic regularization of optimal transport and applications

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


Entropic concavity and positive energy

uk: Математика, природничі науки

description: On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions also make sense in a (nonsmooth) metric measure setting, where they have found powerful applications. In this talk I describe the development of an analogous theory for lower Ricci curvature bounds in time-like directions on a Lorentzian manifold. In particular, by lifting fractional powers of the Lorentz distance (a.k.a. time separation function) to probability measures on spacetime, I show the strong energy condition of Penrose is equivalent to geodesic concavity of the Boltzmann-Shannon entropy there.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, and we use it to define heat flow on the Wasserstein space. We verify a distinctive smoothing effect of this flow for a particular class of initial conditions. To this end, we will develop a theory of Fourier analysis and conic surfaces in metric spaces. We note that the use of the infinitesimal generators has been instrumental in proving various theorems for Mean Field Games, and we anticipate they will play a key role in future studies of viscosity solutions of PDEs in the Wasserstein space (Joint work with Y. T. Chow).

uk: вхід без авторизації

name: A partial Laplacian as an infinitesimal generator on the Wasserstein space


uk: Математика, природничі науки

description: We explore a dynamic formulation of the optimal transportation problem with the additional freedom to choose the end-time of each trajectory. The dual problem is then posed with a Hamilton-Jacobi variational inequality, which we analyze with the method of viscosity solutions. We find properties that imply the optimal stopping-time is the hitting-time of the free boundary to the variational inequality.

uk: вхід без авторизації

name: From Monge Transport to Skorokhod Embeddings


uk: Математика, природничі науки

description: BGK equations are kinetic transport equations with a relaxation operator that drives the phase space distribution towards the spatially local equilibrium, a Gaussian with the same macroscopic parameters. Due to the absence of dissipation w.r.t. the spatial direction, convergence to the global equilibrium is only possible thanks to the transport term that mixes various positions. Hence, such models are hypocoercive. We shall prove exponential convergence towards the equilibrium with explicit rates for several linear, space periodic BGK-models in dimension 1 and 2. Their BGK-operators differ by the number of conserved macroscopic quantities (like mass, momentum, energy), and hence their hypocoercivity index. Our discussion includes also discrete velocity models, and the local exponential stability of a nonlinear BGK-model. The proof is based, first, on a Fourier decomposition in space and Hermite function decomposition in velocity. Then, the crucial step is to construct a problem adapted Lyapunov functional, by introducing equivalent norms for each mode.

uk: вхід без авторизації

name: Large-time behavior in hypocoercive BGK-models


uk: Математика, природничі науки

description: We will present here two different approaches to study the long time behaviour of the kinetic Langevin equation : 1) hypocoercivity technique for entropic convergence via a new weighted logarithmic Sobolev inequality ; 2) Wasserstein convergence via a particular reflection coupling.

uk: вхід без авторизації

name: Long time behaviour of kinetic Langevin equation


uk: Математика, природничі науки

description: Using a nonlinear parabolic flow, in this talk I will explain why the optimal regions of symmetry and symmetry breaking for the extremals of critical and subcritical Caffarelli-Kohn-Nirenberg inequalities are related to the spectral gap of the linearized problem around the asymptotic Barenblatt solutions. This is a surprising result since it means that a global test yields a global result. The use of the parabolic flow also allows to get improved inequalities with explicit remainder terms.

uk: вхід без авторизації

name: Why in some cases the asymptotic linearized problem yields optimal results for a nonlinear version of the carré du champ


uk: Математика, природничі науки

description: We investigate new functional inequalities for the well-known Kac's Walk, and largely resolve the 'Almost' Cercignani Conjecture on the sphere. A new notion of chaoticity plays an essential role. The results we obtain validate Kac's suggestion that functional inequalities for the Kac walk could be used to quantify the rate of approach to equilibrium for the Kac-Boltzmann equation.

uk: вхід без авторизації

name: Entropy production inequalities for the Kac Walk


uk: Математика, природничі науки

description: As well as results in Hilbert spaces, Villani's memoire on hypocoercivity contains convergence to equilibrium results measured in relative entropy. Since then hypocoercivity in more general Phi entropies has been studied by several authors. These works have mainly been for diffusion equations which can be put in a 'Hormander sum of squares form'. The linear relaxation Boltzmann equation is a simple equation not of this form for which hypocoercivity in Phi entropies can still be shown but with extra terms added to the functional which would not be needed for a diffusion.

uk: вхід без авторизації

name: Hypocoercivity in Phi-entropy for linear relaxation Boltzmann equation


uk: Математика, природничі науки

description: We prove exponential convergence to equilibrium for renormalised solutions to general complex balanced reaction-diffusion systems without boundary equilibria and even for systems with boundary equilibria provided a finite dimensional inequality holds along solutions trajectories. Our proofs are based on the entropy method and represent the most general results on the convergence to equilibrium for complex balanced RD systems currently available.

uk: вхід без авторизації

name: Equilibration of renormalised solutions to nonlinear chemical reaction-diffusion systems


uk: Математика, природничі науки

description: The behavior of solutions to the classical porous medium equation is by now well understood: the support of the solution expands at finite speed, and for large times it behaves as the separate-variable solution. When the Laplacian is replaced by a nonlocal diffusion, completely new and surprising phenomena arise depending on the power of the nonlinearity and the one of the diffusion. The aim of the talk is to give an overview of this theory.

uk: вхід без авторизації

name: Global estimates for local and nonlocal porous medium type equations on bounded domains


Entropy and the Kac Master Equation

uk: Математика, природничі науки

description: The Kac master equation models the behavior of a large number of randomly colliding particles. Due to its simplicity it allows, without too much pain, to investigate a number of issues. E.g., Mark Kac, who invented this model in 1956, used it to give a simple derivation of the spatially inhomogeneous Boltzmann equation. One important issue is the rate of approach to equilibrium, which can be analyzed in various ways, using, e.g., the gap or the entropy. Explicit entropy estimates will be discussed for a Kac type master equation modeling the interaction of a finite system with a large but finite reservoir. This is joint work with Federico Bonetto, Alissa Geisinger and Tobias Ried.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In this talk I would like to present some recent results on the asymptotic behavior of a very fast diffusion PDE with periodic boundary conditions. This equation is motivated by the gradient flow approach to the problem of quantization of measures. I prove exponential convergence to equilibrium under minimal assumptions on the data, and I also provide sufficient conditions for W2-stability of solutions. Moreover, I will present a work in progress with Filippo Santambrogio and Francesco Saverio Patacchini where we use the JKO scheme to relax the hypotheses of my previous convergence result.

uk: вхід без авторизації

name: Asymptotical analysis of a weighted very fast diffusion equation arising in quantization of measures via the JKO scheme


uk: Математика, природничі науки

description: In this talk I will discuss the construction of approximate solutions for the Non-linear Fokker-Planck equation. We utilize the L2-Wasserstein gradient flow structure of this PDEs to perform a semi discretization in time by means of the variational BDF2 method. Our approach can be considered as the natural second order analogue of the Minimizing Movement or JKO scheme. In comparison to our own recent work on constructing solutions to λ-contractive gradient flows in abstract metric spaces, the technique presented here exploits the differential structure of the underlying L2-Wasserstein space. We directly prove that the obtained limit curve is a weak solution of the non-linear Fokker-Planck equation without using the abstract theory of curves of maximal slope. Additionally, we provide strong Lm convergence instead of merely weak convergence in the L2-Wasserstein topology of the time-discrete approximations.

uk: вхід без авторизації

name: A BDF2-Approach for the Non-Linear Fokker-Planck Equation


uk: Математика, природничі науки

description: We discuss two examples of "dynamical optimal transport problems", whose formulations involve a relative entropy functional. The first case is related to the Hellinger-Kantorovich distance and induces an interesting geometric structure on the space of positive measures with finite (but possibly different) mass. In particular, contraction estimates of nonlinear flows are strongly related to geodesic convexity of the generating entropy functionals. In the second example an entropy functional penalizes the density of the connecting measures with respect to a given reference measure (typically the Lebesgue one) and leads to a first order "mean field planning" problem, which is classicaly formulated by a continuity equation and a Hamilton Jacobi equation with a nonlinear coupling. In this case, the variational approach and the displacement convexity of the entropy functionals (in the usual sense of optimal transport) provide crucial tools to give a precise meaning to the PDE system and to prove the existence of a solution.

uk: вхід без авторизації

name: Entropic optimal transport and nonlinear PDE's


uk: Математика, природничі науки

description: For a natural class of discretisations of a convex domain in Rn, we consider the dynamical optimal transport metric for probability measures on the discrete mesh. Although the associated discrete heat flow converges to the continuous heat flow, we show that the transport metric may fail to converge to the 2-Kantorovich metric. Under an additional symmetry condition on the mesh, we show that Gromov-Hausdorff convergence to the 2-Kantorovich metric holds. This is joint work with Peter Gladbach and Eva Kopfer.

uk: вхід без авторизації

name: Gromov-Hausdorff convergence of discrete optimal transport


uk: Математика, природничі науки

description: We study the main consequences of the existence of a Gradient Flow (GF for short), in the form of Evolution Variational Inequalities (EVI), in the very general framework of an abstract metric space. In particular, no volume measure is needed. The hypotheses on the functional associated with the GF are also very mild: we shall require at most completeness of the sublevels (no compactness assumption is made) and, for some convergence and stability results, approximate λ-convexity. The main results include: quantitative regularization properties of the flow (in terms e.g. of slope estimates and energy identities), discrete-approximation estimates of a minimizing-movement scheme and a stability theorem for the GF under suitable gamma-convergence-type hypotheses on a sequence of functionals approaching the limit functional. Existence of the GF itself is a quite delicate issue which requires some concavity-type assumptions on the metric, and will be addressed in a future project.

uk: вхід без авторизації

name: Gradient Flows in Abstract Metric Spaces: Evolution Variational Inequalities and Stability


uk: Математика, природничі науки

description: Nonlinear convection and nonlocal aggregation equations are known to feature a "formal" gradient flow structure in presence of a "nonlinear mobility", in terms of the generalized Wasserstein distance "à la" Dolbeault-Nazaret-Savaré. Such a structure is inherited by the discrete Lagrangian approximations of those equations in a quite natural way in one space dimension, and this simple remark allows to formulate a discrete-to-continuum "many particle" approximation. I will describe some recent results in this direction, which include the discrete (deterministic) particle approximation for scalar conservation laws and (more recently) a large class of nonlocal aggregation equations as main examples.

uk: вхід без авторизації

name: Deterministic particle approximations for transport models with nonlinear mobility


uk: Математика, природничі науки

description: One of the archetypical aggregation-diffusion models is the so-called classical parabolic-elliptic Patlak-Keller-Segel (PKS for short) model. This model was classically introduced as the simplest description for chemotatic bacteria movement in which linear diffusion tendency to spread fights the attraction due to the logarithmic kernel interaction in two dimensions. For this model there is a well-defined critical mass. In fact, here a clear dichotomy arises: if the total mass of the system is less than the critical mass, then the long time asymptotics are described by a self-similar solution, while for a mass larger than the critical one, there is finite time blow-up.

uk: вхід без авторизації

name: Recent results on nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics


uk: Математика, природничі науки

description: We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the functional making it energetically favorable to spread, while the attraction is modeled through nonlocal forces. We give conditions on general entropies and interaction potentials for which neither ground states nor local minimizers exist. We show that these results are sharp for homogeneous functionals with entropies leading to degenerate diffusions while they are not sharp for fast diffusions. The particular relevant case of linear diffusion is totally clarified giving a sharp condition on the interaction potential under which the corresponding free energy functional has ground states or not.

uk: вхід без авторизації

name: Existence of ground states for aggregation-diffusion equations

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: We propose a generalization of the Schr\"odinger problem by replacing the usual entropy with a functional F which approaches the Wasserstein distance along the gradient of F. From an heuristic point of view by using Otto calculus, we show that interpolations satisfy a Newton equation, extending the recent result of Giovani Conforti. Various inequalities as Evolutional-Variational-inequalities are also established from a heuristic point of view. As a rigorous result we prove a new and general contraction inequality for the usual Schr\"odinger problem under Ricci bound on a smooth and compact Riemannian manifold. This is a joint work with L. Ripani and C. L\'eonard.

uk: вхід без авторизації

name: When Otto meets Newton and Schrödinger, an heuristic point of view


uk: Математика, природничі науки

description: Stein kernels are a way of measuring distance between probability measures, defined via integration by parts formulas. I will present a connection between these kernels and optimal transport. The main result is a way of deriving rates of convergence in the classical central limit theorem using regularity estimates for a variant of the Monge-Ampere PDE. As an application, we obtain new rates of convergence for the multi-dimensional CLT, with explicit dependence on the dimension.

uk: вхід без авторизації

name: Stein kernels, optimal transport and the CLT


uk: Математика, природничі науки

description: I will present a discrete notion of super Ricci flow that applies to time dependent Markov chains or weighted graphs. This notion can be characterized equivalently in terms of a discrete time-dependent Bochner inequality, gradient estimates for the heat propagator on the evolving graph, contraction estimates in discrete transport distances, or dynamic convexity of the entropy. I will also discuss several examples.

uk: вхід без авторизації

name: Super Ricci flows for weighted graphs and Markov chains


uk: Математика, природничі науки

description: We revisit a result in probability known as the Harris theorem and give a simple proof which is well-suited for some applications in PDE. The proof is not far from the ideas of Hairer \& Mattingly (2011) but avoids the use of mass transport metrics and can be readily extended to cases where there is no spectral gap and exponential relaxation to equilibrium does not hold. We will also discuss some contexts where this result can be useful, particularly in a model for neuron populations structured by the elapsed time since the last discharge.

uk: вхід без авторизації

name: On a new proof of the Harris ergodic theorem and related subexponential convergence results


uk: Математика, природничі науки

description: In the talk, the McKean-Vlasov equation on the flat torus is studied. The model is obtained as the mean field limit of a system of interacting diffusion processes enclosed in a periodic box. The system acts as a model for several real-world phenomena from statistical physics, opinion dynamics, collective behaviour, and stellar dynamics. This work provides a systematic approach to the qualitative and quantitative analysis of the McKean-Vlasov equation. We comment on the longtime behaviour and convergence to equilibrium, for which we introduce a notion of H-stability. The main part of the talk considers the stationary problem. We show that the system exhibits multiple equilibria which arise from the uniform state through continuous bifurcations, under certain assumptions on the interaction potential. Finally, criteria for the classification of continuous and discontinuous transitions of this system are provided. This classification is based on a fine analysis of the free energy. The results are illustrated by proving and extending results for a wide range of models, including the noisy Kuramoto model, Hegselmann-Krause model, and Keller-Segel model.

uk: вхід без авторизації

name: Phase transitions for the McKean-Vlasov equation on the torus


keywords:
Open Access
Journal Flipping
Geschäftsmodell

uk: Комп'ютерні науки

description: Immer mehr wissenschaftliche Zeitschriften entscheiden sich für Open Access. Das bedeutet, ein neues Geschäftsmodell muss umgesetzt werden. Dieses Video erklärt welche Optionen es dafür gibt und welche Konsequenzen diese haben. Es ist Auftakt für eine Interviewreihe mit Beispielen aus der Praxis.

uk: вхід без авторизації

name: Ab jetzt Open Access: Wie Zeitschriften ihr Geschäftsmodell umstellen können

Technische Informationsbibliothek (TIB)

addressLocality: Hanover

addressRegion: Lower Saxony


keywords:
Open Access
Journal Flipping
business model

uk: Комп'ютерні науки

description: More and more scientific journals are opting for open access. This means a new business model has to be implemented. This video explains what options are available and what consequences they have. It is the start of a series of interviews with practical examples.

uk: вхід без авторизації

name: From now on Open Access: How journals can change their business model


Koszul modules and the Green conjecture

uk: Математика, природничі науки

description: I will discuss the basic theory of Koszul modules, which were originally introduced by Papadima and Suciu as a tool to study topological invariants of groups. A special instance of Koszul modules had previously appeared in David Eisenbud's "Green's conjecture: an orientation for algebraists", where he proposed several programs for proving the Green conjecture for generic canonical curves. I will explain a vanishing theorem for Koszul modules that completes one of these programs, providing an alternative approach to the original proof of Voisin for the generic Green conjecture. Joint work with M. Aprodu, G. Farkas, S. Papadima, and J. Weyman.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In ongoing joint work with Christine Berkesch and Daniel Erman we study the minimal resolution conjecture up to scaling. For Hilbert functions corresponding to modules of low regularity there always exist corresponding Betti tables with no consecutive cancellations up to scaling. For Hilbert functions of many naturally occurring modules, like coordinate rings of Veronese varieties, the Betti table can be semi-pure, even though the region of Hilbert functions corresponding to such tables is a tiny part of the cone of Hilbert functions.

uk: вхід без авторизації

name: Variations on the minimal resolution conjecture


uk: Математика, природничі науки

description: We construct an explicit local duality map for codimension 2 toric ideals, thanks in part to the explicit free resolutions of Peeva--Sturmfels for such ideals. We then combine this with our work on the parametric behavior of the series solutions of an A-hypergeometric system to explain how local cohomology causes rank jumps.

uk: вхід без авторизації

name: A-hypergeometric rank jumps from local cohomology in codimension 2


Cohomologically full rings

uk: Математика, природничі науки

description: Inspired by a question raised by Eisenbud-Musta\c{t}\u{a}-Stillman regarding the injectivity of maps from Ext modules to local cohomology modules, we introduce a class of rings which we call cohomologically full rings. In positive characteristic, this notion coincides with that of F-full rings studied by Pham and Ma, while in characteristic 0, they include Du Bois singularities. We prove many basic properties of cohomologically full rings, including their behavior under flat base change. We show that ideals defining these rings satisfy many desirable properties, in particular they have small cohomological and projective dimension. Furthermore, we obtain Kodaira-type vanishing and strong bounds on the regularity of cohomologically full graded algebras. Joint work with Alessandro De Stefani and Linquan Ma.

uk: вхід без авторизації


uk: Математика, природничі науки

description: A well-known formula expresses the socle of an Artinian complete intersection of characteristic zero in terms of a Jacobian determinant. We generalize this formula to rings that are neither Artinian nor complete intersections. We deduce our formula from an explicit description of the Dedekind complementary module of residual intersections.

uk: вхід без авторизації

name: Residual Intersections: Socles and Duality


uk: Математика, природничі науки

description: In 1891, Poincaré asked if it is possible to bound the degree of a projective plane curve that is left invariant by a vector field in terms of the degree of the vector field. In joint work with Chardin, Hassenzadeh, Simis, and Ulrich we address this question. The question can be restated as a problem about the initial degree of the module of derivations of the coordinate ring R of the curve modulo the Euler derivation in terms of invariants of R. We exhibit lower and upper bounds for this initial degree and in several instances we are able to determine the initial degree. Examples will be given to illustrate the situation.

uk: вхід без авторизації

name: On a problem of Poincaré: Bounds on degrees of vector fields


uk: Математика, природничі науки

description: Ananyan-Hochster's recent proof of Stillman's conjecture crucially uses the notion of strength of a polynomial. Inspired by this, we present two results which capture the idea that collections of polynomials of sufficiently high strength behave like regular sequences. Both of these results state that suitable limits (ultraproduct and inverse limit, respectively) of polynomial rings are themselves polynomial rings. I will discuss how the first result leads to a different proof of Stillman's conjecture. Time permitting, I will also discuss the inverse limit version and how it connects to recent work of Draisma on GL_infinity-noetherianity of polynomial functors.

uk: вхід без авторизації

name: Big polynomial rings and Stillman's conjecture


uk: Математика, природничі науки

description: We study rational maps from a projective space of dimension two to another of dimension three, both over the same field. We will start by giving the general framework and first results obtained on this question by Botbol, Busé and myself. Then I will turn to questions concerning the fibers of dimension one that such a map can have and present two way to address this question, the first by Tran Quang Hoa, and the second by the same author together with Dale Cutkosky and myself. Examples show that our estimates are pretty sharp, but leave possibilities for improvement.

uk: вхід без авторизації

name: Fibers of rational maps and Jacobian matrices


uk: Математика, природничі науки

description: Let S=k[x1,…,xn] be a polynomial ring and R=S/P a complete intersection defined by pure powers of the variables. In this talk we discuss upper bounds for the Betti numbers of ideals of R with fixed Hilbert function or Hilbert polynomial. We will consider both finite free resolutions over S and infinite free resolutions over R. This is a joint work with Giulio Caviglia.

uk: вхід без авторизації

name: Maximal syzygies in Hilbert schemes of monomial complete intersections


uk: Математика, природничі науки

uk: вхід без авторизації

name: The absolutely Koszul and Backelin-Roos properties for spaces of quadrics of small codimension


uk: Математика, природничі науки

description: Residual intersections of licci ideals behave well in a sense that residual intersection of ideals of 2x2 minors of a 2xn matrix, for n at least 4, do not. Recently Craig Huneke and Bernd Ulrich and I have been studying a way in which these residual intersections, and a certain wider class of ideals whose powers have linear presentations do behave well after all. I'll review the background and discuss what we've learned.

uk: вхід без авторизації

name: An unexpected property of some residual intersections


uk: Математика, природничі науки

description: We present a generalization of Macaulay’s Inverse System to higher dimensions. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. We extend Macaulay's correspondence characterizing the submodules of the divided powers ring in one-to-one correspondence with Gorenstein d-dimensional k-algebras. We present effective methods for constructing Gorenstein graded rings with given numerical invariants fixed by their minimal free resolution. Recent generalizations by S. Masuti, M. Schulze and L. Tozzo will be presented. Possible applications are discussed.

uk: вхід без авторизації

name: A generalization of Macaulay’s correspondence for Gorenstein k-algebras and applications

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: Regularity and h-polynomials of monomial ideals


Square-free Groebner degenerations

uk: Математика, природничі науки

description: Let S be a polynomial ring, I a homogeneous ideal and denote by in(I) the initial ideal of I w.r.t. some term order on S. It is well-known that depth(S/I) >= depth(S/in(I)) and reg(S/I) <= reg(S/in(I)), and it is easy to produce examples for which these inequalities are strict. On the other hand, in generic coordinates equalities hold for a degrevlex term order, by a celebrated result of Bayer and Stillman. In a joint paper with Aldo Conca, we prove that the equalities hold as well under the assumption that in(I) is a square-free monomial ideal (for any term order), solving a conjecture of Herzog. In this talk, after discussing where this conjecture came from, I will sketch the proof of its solution.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Let R be a standard graded Gorenstein algebra over a field presented by quadrics. Conca-Rossi-Valla showed that such a ring is Koszul if reg (R)<= 2 or if reg(R)= 3 and codim(R)<= 4, and asked if this is true for reg(R)= 3 in general. We give a negative answer to their question by finding suitable conditions on a non-Koszul quadratic Cohen-Macaulay ring R that guarantee the Nagata idealization of R with the (twisted) canonical module is a non-Koszul quadratic Gorenstein ring.

uk: вхід без авторизації

name: Non-Koszul Quadratic Gorenstein rings via Idealization


uk: Математика, природничі науки

description: A (d−1)-dimensional simplicial complex is called balanced, if its 1-skeleton is d-colorable. In this talk, I will discuss upper bounds for the graded Betti numbers of the Stanley-Reisner rings of this class of simplicial complexes. Our results include both, bounds for the Cohen-Macaulay case and for the general situation. Previously, upper bounds have been shown by Migliore and Nagel, and Murai for simplicial polytopes, Cohen-Macaulay complexes and normal pseudomanifolds. If time permits, I will also mention, what can be said for balanced normal pseudomanifolds. This is joint work with Lorenzo Venturello.

uk: вхід без авторизації

name: Graded Betti numbers of balanced simplicial complexes


uk: Математика, природничі науки

description: The Lefschetz properties are desirable algebraic properties of graded artinian algebras inspired by the Hard Lefschetz Theorem for cohomology rings of complex projective varieties. A standard way to create new varieties from old is by forming connected sums. This corresponds at the level of their cohomology rings to an algebraic operation also termed a connected sum, which has recently started to be investigated in commutative algebra by Ananthnarayan-Avramov-Moore. It is natural to ask whether abstract algebraic connected sums of graded Gorenstein artinian algebras enjoy the Lefschetz properties in the absence of any underlying topological information. We investigate this question as well as the analogous question concerning a closely related construction, the fibered product.

uk: вхід без авторизації

name: Lefschetz properties of fiber products and connected sums


uk: Математика, природничі науки

uk: вхід без авторизації

name: O_X regularity bound for smooth varieties with classification of extremal and next to extremal examples


uk: Математика, природничі науки

description: Hochster's results tell that homology groups of a simplicial complex have a nice relation to algebraic properties of its Stanley-Reisner ring. On the other hand, it is unknown that how fundamental groups affect to Stanley-Reisner rings. In this talk, we present lower bounds of the second h-number of simplicial complexes in terms of the number of generators of fundamental groups. Our proof is based on recent results about PL Morse inequality and graded Betti numbers.

uk: вхід без авторизації

name: h-vectors and the number of generators of fundamental groups


uk: Математика, природничі науки

description: We discuss a ramification of Arnold’s group-theoretic approach to ideal hydrodynamics as the geodesic flow for a right-invariant metric on the group of volume-preserving diffeomorphisms. We show such problems of mathematical physics as the motion of vortex sheets or fluids with moving boundary, have Lie groupoid, rather than Lie group, symmetries, and describe the corresponding geometry and equations. (This is a joint work with Anton Izosimov.)

uk: вхід без авторизації

name: Beyond Arnold’s geodesic framework of an ideal hydrodynamics


uk: Математика, природничі науки

description: In the 1960's V. Arnold showed how solutions of the incompressible Euler equations can be viewed as geodesics on the group of diffeomorphisms of the fluid domain equipped with a metric given by fluid's kinetic energy. The study of the exponential map of this metric is of particular interest and I will describe recent results concerning its properties as well as some necessary background.

uk: вхід без авторизації

name: The L2 exponential map in 2D and 3D hydrodynamics


uk: Математика, природничі науки

description: We investigate a generalization of cubic splines to Riemannian manifolds. Spline curves are defined as minimizers of the spline energy-a combination of the Riemannian path energy and the time integral of the squared covariant derivative of the path velocity-under suitable interpolation conditions. A variational time discretization for the spline energy leads to a constrained optimization problem over discrete paths on the manifold. Existence of continuous and discrete spline curves is established using the direct method in the calculus of variations. Furthermore, the convergence of discrete spline paths to a continuous spline curve follows from the Γ-convergence of the discrete to the continuous spline energy. Finally, selected example settings are discussed, including splines on embedded finite-dimensional manifolds, on a high-dimensional manifold of discrete shells with applications in surface processing, and on the infinite-dimensional shape manifold of viscous rods.

uk: вхід без авторизації

name: Semi-invariant metrics on groups of diffeomorphisms


uk: Математика, природничі науки

description: We formulate the so-called Schrodinger problem in Optimal Transport on lie group and derive the corresponding Euler-Poincaré equations.

uk: вхід без авторизації

name: On some relations between Optimal Transport and Stochastic Geometric Mechanics


uk: Математика, природничі науки

description: In several situations, the empirical measure of a large number of random particles evolving in a heat bath is an approximation of the solution of a dissipative PDE. The evaluation of the probabilities of large deviations of this empirical measure suggests a way of defining a natural ``large deviation cost'' for these fluctuations, very much in the spirit of optimal transport. Some standard Wasserstein gradient flow evolutions are revisited in this perspective, both in terms of heuristic results and a few rigorous ones. This talk gathers several joint works with Julio Backhoff, Giovanni Conforti, Ivan Gentil, Luigia Ripani and Johannes Zimmer.

uk: вхід без авторизації

name: Gradient flows, interpolations and large deviations


uk: Математика, природничі науки

description: "Continuous time Feynman-Kac measures on path spaces are central in applied probability, partial differential equation theory, as well as in quantum physics. I will present a new duality formula between normalized Feynman-Kac distribution and their mean field particle interpretations. Among others, this formula will allow to design a reversible particle Gibbs-Glauber sampler for continuous time Feynman-Kac integration on path spaces. This result extends the particle Gibbs samplers introduced by Andrieu-Doucet-Holenstein in the context of discrete generation models to continuous time Feynman-Kac models and their interacting jump particle interpretations. I will also provide new propagation of chaos estimates for continuous time genealogical tree based particle models with respect to the time horizon and the size of the systems. These results allow to obtain sharp quantitative estimates of the convergence rate to equilibrium of particle Gibbs-Glauber samplers."

uk: вхід без авторизації

name: A particle Gibbs sampler for Feynman-Kac measures Stability and propagation of chaos


Geometric modelling of uncertainties

uk: Математика, природничі науки

description: In mechanics, and in particular in shape analysis, taking into account the underlying geometric properties of a problem to model it is often crucial to understand and solve it. This approach has mostly been applied for isolated systems, or for systems interacting with a well-defined, deterministic environment. In this talk, I want to discuss how to go beyond this deterministic description of isolated systems to include random interactions with an environment, while retaining as much as possible the geometric properties of the isolated systems. I will discuss examples from geometric mechanics to shape analysis, ranging from interacting rigid bodies with a heath bath to uncertainties quantification in computational anatomy.

uk: вхід без авторизації


uk: Математика, природничі науки

description: "Semi-discrete optimal transport between a discrete source and a continuous target has intriguing geometric properties and applications in modelling and numerical methods. Unbalanced transport, which allows the comparison of measures with unequal mass, has recently been studied in great detail by various authors. In this talk we consider the combination of both concepts. The tessellation structure of semi-discrete transport survives and there is an interplay between the length scales of the discrete source and unbalanced transport which leads to qualitatively new regimes in the crystallization limit."

uk: вхід без авторизації

name: Semi-discrete unbalanced optimal transport and quantization


uk: Математика, природничі науки

description: In this talk we will discuss the use of a Wasserstein loss function for learning regularisers in an adversarial manner. This talk is based on joint work with Sebastian Lunz and Ozan Öktem.

uk: вхід без авторизації

name: Wasserstein for learning image regularisers


uk: Математика, природничі науки

uk: вхід без авторизації

name: Interpolation of Gaussian mixture models, and other directions in OMT


uk: Математика, природничі науки

uk: вхід без авторизації

name: Normal coordinates and equivolumic layers estimation in the cortex (tentative)


uk: Математика, природничі науки

description: I will present how shape registration via constrained deformations can help understanding the variability within a population of shapes.

uk: вхід без авторизації

name: Analyze shape variability via deformations: Incorporation of a physical model

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


Solar models for Euler-Arnold equations

uk: Математика, природничі науки

description: Many one-dimensional Euler-Arnold equations can be recast in the form of a central-force problem Γtt(t,x)=−F(t,x)Γ(t,x), where Γ is a vector in R2 and F is a nonlocal function possibly depending on Γ and Γt. Angular momentum of this system is precisely the conserved momentum for the Euler-Arnold equation. In particular this picture works for the Camassa-Holm equation, the Hunter-Saxton equation, and the Okamoto-Sakajo-Wunsch family of equations. In the solar model, breakdown comes from a particle hitting the origin in finite time, which is only possible with zero angular momentum. Results due to McKean (for Camassa-Holm), Lenells (for Hunter-Saxton), and Bauer-Kolev-Preston/Washabaugh (for the Wunsch equation) show that breakdown of smooth solutions occurs exactly when momentum changes from positive to negative. I will discuss some conjectures and numerical evidence for the generalization of this picture to other equations such as the μ-Camassa-Holm equation or the DeGregorio equation.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We show that the functional calculus, which maps operators A to functionals f(A), is holomorphic for a certain class of operators A and holomorphic functions f. Using this result we are able to prove that fractional Laplacians depend real analytically on the underlying Riemannian metric in suitable Sobolev topologies. As an application we obtain local well-posedness of the geodesic equation for fractional Sobolev metrics on the space of all Riemannian metrics. (Joint work with Martins Bruveris, Martin Bauer, and Peter W. Michor)

uk: вхід без авторизації

name: Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics


uk: Математика, природничі науки

description: When studying flocking/swarming behaviors in animals one is interested in quantifying and comparing the dynamics of the clustering induced by the coalescence and disbanding of groups of animals. In a similar vein, when attempting to classify motion capture data according to action one is confronted with having to match/compare shapes that evolve with time. Motivated by these applications, we study the question of suitably metrizing the collection of all dynamic metric spaces (DMSs). We construct a suitable metric on this collection and prove the stability of several natural invariants of DMSs under this metric. In particular, we prove that certain zigzag persistent homology invariants related to dynamic clustering are stable w.r.t. this distance. These lower bounds permit the efficient classification of dynamic shape data in applications. We will show computational experiments on dynamic data generated via distributed behavioral models.

uk: вхід без авторизації

name: Metrics on Dynamic Graphs (and lower bounds via Zigzag Persistence)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Robust shape matching with optimal transport


uk: Математика, природничі науки

uk: вхід без авторизації

name: Generalized H(div) geodesics and solutions of the Camassa-Holm equation


uk: Математика, природничі науки

uk: вхід без авторизації

name: Quantization on a Riemannian manifold with application to air traffic control


uk: Математика, природничі науки

uk: вхід без авторизації

name: Geometric quantization and the equivariant Verlinde formula


uk: Математика, природничі науки

uk: вхід без авторизації

name: Semi-classical limits and the graded equivariant Todd class


uk: Математика, природничі науки

description: I will describe a map from `D-cycles' for the twisted K-homology of a compact, connected, simply connected Lie group to the Verlinde ring. The induced map on K-homology is inverse to the Freed-Hopkins-Teleman isomorphism. An application is to show that two options for `quantizing' a Hamiltonian loop group space are compatible with each other. This talk is partly based on joint work with Eckhard Meinrenken and Yanli Song.

uk: вхід без авторизації

name: Quantization of Hamiltonian loop group spaces


Fusion in loop spaces

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

description: Complex line bundles are classified naturally up to isomorphism by degree two integer cohomology H2, and it is of interest to find geometric objects which are similarly associated to higher degree cohomology. Gerbes (of which there are various versions, due respectively to Giraud, Brylinski, Hitchin and Chattergee, and Murray) provide a such theory associated to H3. Various notions of"higher gerbes" have also been defined, though these tend to run into technicalities and complicted bookkeeping associated with higher categories. We propose a new geometric version of higher gerbes in the form of "multi simplicial line bundles", a pleasantly concrete theory which avoids many of the higher categorical difficulties, yet still captures key examples including the string (aka loop spin) obstruction associated to 12 p1 in H4. In fact, every integral cohomology class is represented by one of these objects in the guise of a line bundle on the iterated free loop space equipped with a "fusion product" (as defined by Stolz and Teichner and further developed by Waldorf) for each loop factor.

uk: вхід без авторизації

name: Multigerbes: a new theory of higher gerbes


uk: Математика, природничі науки

description: In the classical geometric quantization procedure with the "half-form correction", one cannot quantize a complex projective space of even complex dimension (there is no "half form bundle"), and one cannot equivariantly quantize any symplectic toric manifold (there is no "equivariant half form bundle"). I will describe a geometric quantization procedure that uses metaplectic-c structures to incorporate the "half form correction" into the prequantization stage and that does apply to these examples. This follows work of Harald Hess from the late 1970s, with recent contributions of Jennifer Vaughan.

uk: вхід без авторизації

name: Geometric quantization with metaplectic-c structures


uk: Математика, природничі науки

description: This is an expository talk about C*-algebra K-theory for reductive groups. I’ll try to explain what it is, what it actually says about representation theory, and what else it suggests about representation theory, at least to a willing mind. The story begins with Harish-Chandra’s parametrization of the discrete series representations, and the realization of discrete series representations using the Dirac operator. I’ll discuss these things, and then touch on other parts of Harish-Chandra’s theory of tempered representations that are prominent from the K-theoretic point of view.

uk: вхід без авторизації

name: Discrete series representations, the Dirac operator and C*-algebra K-theory


uk: Математика, природничі науки

description: In 1980s, Connes and Moscovici studied index theory of G-invariant elliptic pseudo-differential operators acting on non-compact homogeneous spaces. They proved a L2 -index formula using the heat kernel method, which is related to the discrete series representation of Lie groups. In this talk, I will discuss the orbital integral of heat kernel and its relation with Plancherel formula. This is a generalization of the analytic index studied by Connes-Moscovici to the limit of discrete series case. In a recent work by Hochs-Wang, they obained a fixed point theorem for the topogical side of the index.

uk: вхід без авторизації

name: Orbital integral and character of representations


uk: Математика, природничі науки

description: K-theory of reduced group C∗-algebras and their trace maps can be used to study tempered representations of a semisimple Lie group from the point of view of index theory. For a semisimple Lie group, every K-theory generator can be viewed as the equivariant index of some Dirac operator, but also interpreted as a (family of) representation(s) parametrised by A in the Levi component of a cuspidal parabolic subgroup. In particular, if the group has discrete series representations, the corresponding K-theory classes can be realised as equivariant geometric quantisations of the associated coadjoint orbits. Applying orbital traces to the K-theory group, we obtain a fixed point formula which, when applied to this realisation of discrete series, recovers Harish-Chandra's character formula for the discrete series on the representation theory side. This is a noncompact analogue of Atiyah-Segal-Singer fixed point theorem in relation to the Weyl character formula. This is joint work with Peter Hochs.

uk: вхід без авторизації

name: K-theory, fixed point theorem and representation of semisimple Lie groups


uk: Математика, природничі науки

description: Consider an action of a connected compact Lie group on a compact complex manifold M, and two equivariant vector bundles L and E on M, with L of rank 1. The purpose of this talk is to establish holomorphic Morse inequalities, analogous to Demailly's one, for the invariant part of the Dolbeault cohomology of tensor powers of L, twisted by E. To do so, we define a moment map μ by the Kostant formula and then the reduction of M under a natural hypothesis on μ−1(0). Our inequalities are given in term of the curvature of the bundle induced by L on this reduction, in the spirit of "quantization commutes with reduction".

uk: вхід без авторизації

name: G-invariant holomorphic Morse inequalities


uk: Математика, природничі науки

uk: вхід без авторизації

name: From factorization algebras to functorial field theories


K-types of tempered representations

uk: Математика, природничі науки

description: Let G be a real semisimple Lie group, and K<G a maximal compact subgroup. A tempered representation π of G is an irreducible representation that occurs in the Plancherel decomposition of L2(G). The restriction π|K of π to K contains a substantial amount of information about π. (This is roughly analogous to the fact that an irreducible representation of K is determined by its restriction to a maximal torus.) By realising this restriction as the geometric quantisation of a suitable space, which is a coadjoint orbit under a regularity assumption on π, we can apply a suitable version of the quantisation commutes with reduction principle to obtain geometric expressions for the multiplicities of the irreducible representations of K in π|K (the K-types of π). This was done for the discrete series by Paradan in 2003. In recent joint work with Song and Yu, we extended this to arbitrary tempered representation. The resulting multiplicity formula was obtained in a different way for tempered representations with regular parameters by Duflo and Vergne in 2011. In independent work in progress with Higson and Song, we give a new proof of Blattner's formula for multiplicities of K-types of discrete series representations using geometric quantisation. This formula was first proved by Hecht and Schmid in 1975, and later by Duflo, Heckman and Vergne in 1984.

uk: вхід без авторизації


uk: Математика, природничі науки

description: For manifolds including metric-contact manifolds with non-resonant Reeb flow, we prove a Gutzwiller type trace formula for the associated magnetic Dirac operator involving contributions from Reeb orbits on the base. As an application, we prove a semiclassical limit formula for the eta invariant.

uk: вхід без авторизації

name: A Gutzwiller type trace formula for the magnetic Dirac operator