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22.01.2021  Rhein-Main-Kolloquium

Maria Deijfen (Stockholm University)
Siva Athreya (Indian Statistical Institute, Bengaluru)

RMK Darmstadt

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11.06.2021  Rhein-Main-Kolloquium

Gaultier Lambert (Universität Zürich)
Christian Brennecke (Harvard University)

RMK Frankfurt - ONLINE

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09.07.2021  Rhein-Main-Kolloquium

Pascal Maillard (Université de Toulouse)
Markus Heydenreich (LMU München)


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29.01.2021  Rhein-Main-Kolloquium

Gábor Lugosi (Department of Economics, Pompeu Fabra University Barcelona)
Po-Ling Loh (University of Cambridge)

RMK Frankfurt - ONLINE

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03.12.2021  Rhein-Main-Kolloquium

Nina Gantert (Technische Universität München)
Paolo Dai Pra (Università degli Studi di Verona)


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01.07.2022  Rhein-Main-Kolloquium

Julian Gerstenberg (Goethe-Universität Frankfurt)
Jonathan Warren (University of Warwick)

RMKS Frankfurt 01.07.2022

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03.02.2023  Rhein-Main-Kolloquium

Amaury Lambert (Collège de France und École Normale Supérieure, Paris)
Emmanuel Schertzer (Universität Wien)

RMKS Mainz 03.02.2023

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23.06.2023  Rhein-Main-Kolloquium

Mark Sellke (Harvard University)
Steffen Polzer (Université de Genève)

RMKS Darmstadt 23. Juni 2023

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07.07.2023  Rhein-Main-Kolloquium

Christoph Czichowsky (London School of Economics and Political Science)
David Prömel (Universität Mannheim)

RMKS Frankfurt 7. Juli 2023

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02.02.2024  Rhein-Main-Kolloquium

Peter Mörters (Universität Köln)
Alessandra Bianchi (Università degli Studi di Padova)

RMKS Frankfurt/Main 02.02.2024

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12.07.2024  Rhein-Main-Kolloquium

Nicolas Champagnat (Nancy)
Anita Winter (Duisburg-Essen)

RMK Frankfurt

The grapheme-valued Wright-Fisher Diffusion with mutation --- In Athreya, den Hollander and Röllin (2021) models from population genetics were used to de fine stochastic dynamics in the space of graphons that arise as continuum limits of dense graph sequencess. In this talk we extend this framework to a model with mutation. In particular, we define a finite graph valued Markov chain that can be associated with the infinite many alleles model, and establish a diffusion limit as the number of vertices goes to infinity. For that we encode finite graphs as graphemes. Graphems are those graphons that can be represented as a triple consisting of a topological vertex space, an adjacency matrix and a sampling measure. The space of graphons is equipped with convergence of sample subgraph densities. (joint work with Andreas Greven, Frank den Hollander and Anton Klimovsky) -------------------------------------------------------------------- Scaling limits of individual-based models in adaptive dynamics and local extinction of populations (N. Champagnat) --- Starting from an individual-based birth-death-mutation-selection model of adaptive dynamics with three scaling parameters (population size, mutation rate, mutation steps size), we will describe several scaling limits that can be applied to this model to obtain macroscopic models of different natures (PDE, Hamilton-Jacobi equation, stochastic adaptive walks, canonical equation of adaptive dynamics), which allow to characterize the long-term evolution of the population. Motivated by biological criticisms on the time-scale of evolution and the absence of local extinctions in the obtained macroscopic models, we propose new parameter scalings under which we can characterize the evolution of population sizes of the order of $K^\beta$, where $K$ is the order of magnitude of the total population size, and which allows for local extinction of subpopulations. This presentation will gather results obtained with several collaborators: Régis Ferrière, Sylvie Méléard, Amaury Lambert, Viet Chi Tran, Sepideh Mirrahimi, Vincent Hass. Read more

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