Munich Mathematical CalendarCalendar with mathematical talks near Munich2021-10-18T06:01:05Ztag:mathcal.ma.tum.de,2013-04-10:/feed/filter2/year2021/month1011.10.2021 15:00 Daniela Schlager: Stability Analysis of Multiplayer Games on Simplicial Complexes in Adaptive Networks2021-09-30T10:52:21ZDaniela Schlagertag:mathcal.ma.tum.de,2013-04-10:/talk/created/20210930125034We develop models of multiplayer games based on cooperation, the Snowdrift game and the Prisoner’s Dilemma, on adaptive networks. They contain explicit interactions of multiple players on simplicial complexes. All operations of and on the network are based on game theoretical properties of the respective games. The evolution of the models over time is described by moment equations and is closed by pair approximation. The stability of equilibria is examined when irrational decisions in simplices are added into the models.
11.10.2021 16:30 Detlef Kreß (LMU; MSc presentation): A percolation model without positiv correlattion2021-09-30T06:45:13ZDetlef Kreß (LMU; MSc presentation)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20210930084200We introduce a bond-percolation model that is a modification of the corrupted compass model introduced by Christian Hirsch, Mark Holmes and Victor Kleptsyn (2021).On a given graph we start in each vertex independent with probability p a random walk of length L. We make an edge occupied if it was used by a random walk. This model does not exhibit positive correlation.If L is choosen such that there is percolation for p=1, we have a sharp phase transition for p. We discuss the question of percolation on the hypercubic lattice and show that on the square lattice percolation occurs for L=2.
18.10.2021 14:00 Bernd Sturmfels (MPI Leipzig) : Algebraic Statistics with a View towards Physics2021-10-06T12:05:56ZBernd Sturmfels (MPI Leipzig) tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20211006134341We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding example is the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.
18.10.2021 15:00 Eric Lucon & Christophe Poquet, part 1: Periodic behavior of mean-field systems2021-10-07T07:35:16ZEric Lucon & Christophe Poquet, part 1tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20210930125238We will study non-linear mean-field Fokker-Planck equations describing the infinite population limit of interacting excitable particles subject
to noise. Taking a slow-fast dynamics approach we will describe the emergence of periodic behaviors induced by the noise and the
interaction, considering in particular the case in which each unit evolves according to the FitzHugh Nagumo model.
This talk is linked to the one given by my co-author Eric Luçon the following week, in which he will speak about the long time behavior of
the population of particles when the population is finite.
25.10.2021 15:00 Eric Lucon & Christophe Poquet, part 2: Large-time dynamics of mean-field interacting diffusions along a limit cycle2021-10-08T09:58:36ZEric Lucon & Christophe Poquet, part 2tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20210930125332This talk is the natural continuation of the previous talk of Christophe Poquet which concerned the existence of periodic solutions to nonlinear Fokker-Planck equations. We are here interested in the microscopic counterpart of the same problem: nonlinear Fokker-Planck equations are natural limits of the empirical measure of N mean-field interacting diffusions as N goes to infinity. Standard propagation of chaos estimates show that this limit remains relevant only up to times that remains bounded in N. A natural question is then to ask about the dynamics of the empirical measure of the system on a larger time scale. We answer to this question in the case the FP limit possess a smooth and stable limit cycle. The main result of the talk will be to show that, on a time scale of order N, the empirical measure remains with high probability close to the periodic orbit with a diffusive dynamics along the limit cycle.
25.10.2021 16:30 Wolfgang Löhr (Universität Duisburg-Essen): TBA2021-10-18T06:01:05ZWolfgang Löhr (Universität Duisburg-Essen)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20211018075422TBA