Variational methods on graphs and networks

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WG4 - Variational methods on graphs and networks

Overview

Proceeding from classical variational methods for the analysis of Laplace-type operators, the aim of this Working Group is twofold: on the one hand, classic spectral geometry applies to elliptic operators generating semigroups that are Markovian (i.e., they describe the time evolution of expectation with respect to a Markov process); the plan is to investigate possible generalizations to generators of semigroups that have such a probabilistic interpretation only after a suitable transient; nonlinear contexts will also be studied. On the other hand, insights that have recently allowed the extension of gradient systems with respect to Wasserstein metric in spaces of measures will be extended to nonlinear dynamical systems on further discrete structures. A particular challenge is that the implementation of boundary conditions, which is a central issue in the theory of networks, is not yet well understood in the context of flows on metric spaces.

Tasks

  1. Develop variational methods for nonlinear dynamical systems on graphs (in collaboration with W3).
  2. Prove suitable isoperimetric inequalities for contexts that lack maximum principles.
  3. Exploit spectral geometric information to settle questions related to the long-time behaviour of the dynamical system on graphs.
  4. In collaboration with WG5 develop appropriate numerical methods for applications.

Members

Leader

Delio MUGNOLO Germany

University of Hagen
Universitätstraße 11
Hagen
Germany
No additional info
Vice Leader

Pavel KURASOV Sweden

Institute of Mathematics, Stockholm University
Kräftriket hus 6
Stockholm
Sweden
No additional info

Working Group Participants

Jan MAAS

Austria


Austria
Austria

Noema NICOLUSSI

Austria

Ivica

Croatia
Uni Zagreb
Work Address
Zagreb
Croatia

Tereza KURIMAIOVÁ

Czech Republic


Prague
Czech Republic

Michal TICHÝ

Czech Republic


Prague
Czech Republic

Matěj TUŠEK

Czech Republic


Prague
Czech Republic

David KREJCIRIK

Czech Republic
Czech Technical University in Prague
Trojanova 13
Prague
Czech Republic

Felix Ali MEHMETI

France


Valenciennes
France

Matthias ERBAR

Germany


Bielefeld
Germany

Amru HUSSEIN

Germany


Kaiserslautern
Germany

Joachim KERNER

Germany

Marvin PLÜMER

Germany

Olaf POST

Germany


Trier
Germany

Christian SEIFERT

Germany
Technische Universität Hamburg
Am Schwarzenberg-Campus 3, 21073, Hamburg
Hamburg
Germany

Delio MUGNOLO

Germany
University of Hagen
Universitätstraße 11
Hagen
Germany

Helena Mihaljević

Germany
Hochschule für Technik und Wirtschaft Berlin
Wilhelminenhofstraße 75A
12459 Berlin
Germany

Harun Siljak

Ireland
Trinity College Dublin, CONNECT Centre
34 Westland Row, Dunlop Oriel House
Dublin
Ireland

Sebastian Egger

Israel
Technion
622 Amado Building
Haifa
Israel

Claudio CACCIAPUOTI

Italy


Insubria-Como
Italy

Raffaele CARLONE

Italy

Giuseppe COCLITE

Italy

Simone Dovetta

Italy

Maria Rosaria LANCIA

Italy

Diego NOJA

Italy


Milano-Bicocca
Italy

Andrea POSILICANO

Italy


Insubria-Como
Italy

James KENNEDY

Portugal
Faculdade de Ciencias da Universidade de Lisboa Campo Grande
Edificio C6
Lisboa
Portugal

Liviu IGNAT

Romania
Romanian Academy of Sciences


Romania

Aleksey KOSTENKO

Slovenia
University of Ljubljana
Jadranska 19
Ljubljana
Slovenia

Mojca Vilfan

Slovenia
UL FGG
Jamova 2
Ljubljana
Slovenia

Marjeta Kramar Fijavž

Slovenia
UL FGG
Jamova 2
Ljubljana
Slovenia

José M. MAZÓN

Spain
Universitat de Valencia
Dr. Moliner 50
Burjassot
Spain

Corentin LÉNA

Sweden


Stockholm
Sweden

Andrea SERIO

Sweden


Stockholm
Sweden

Jonathan ROHLEDER

Sweden
Stockholm University Matematiska institutionen

Stockholm
Sweden

Petr SIEGL

United Kingdom


Belfast
United Kingdom

Sven GNUTZMANN

United Kingdom
University of Nottingham
University Park
Nottingham
United Kingdom

Jens BOLTE

United Kingdom
Department of Mathematics, Royal Holloway, University of London
TW20 0EX
Egham
United Kingdom

Matthias Täufer

United Kingdom
Queen Mary University of London
Mile End Road E1 4NS
London
United Kingdom
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