M. Birkner, L. Hartung, A. Klenke
Dienstag, 14 Uhr, Institut für Mathematik, Gebäude 2413, Raum 05-136
Termine im Wintersemester 2025/26
| 25.11.2025 |
Louis Chataignier (Université Toulouse III) Upper moderate deviation probabilities for the maximum of a branching random walk In 2013, Elie Aı̈dékon obtained the convergence in distribution, as time n goes to infinity, of the maximum of a supercritical branching random walk, once recentered by an explicit function m(n). More recently, Lianghui Luo gave an asymptotic equivalent for the upper large deviation probabilities of this maximum. In this talk, I will present a joint work with Lianghui Luo in which we study an intermediate regime. We obtain an asymptotic equivalent for the probability that the maximum arrives at distance x(n) above m(n), where 1 << x(n) = O(sqrt(n)). |
| 02.12.2025 |
Lars Schroeder (Universität Twente) Stationary distribution of node2vec random walks node2vec random walks are tuneable random walks that come from the popular algorithm node2vec which is used for network embedding. The transition probabilities of the random walks depend on the previous visited node and on the triangles that contain the current and the previous node. Even though the algorithm is widely used in practice, mathematical properties of node2vec random walks almost have not been investigated. We present results on the stationary distribution for household models (graphs with clique-structured communities) by studying a coupling to a random walk that jumps in between communities and results on regular graphs by going to a higher-order space. Joint work with Clara Stegehuis, Gianmarco Bet and Luca Avena. |
| 13.01.2026 | Janine Piesold (JGU) - TBD |
| 27.01.2026 | Flavio Dalessi (Uni Basel) - TBD |
| 04.11.2025 |
ENTFÄLLT LEIDER KURZFRISTIG !!! Noela Müller (Universität Eindhoven) Sharp thresholds and hitting times for factors in the Binomial random graph |
Termine im Sommersemester 2025
| 08.07.2025 | Réka Szabó (University of Groningen) Percolation on the stationary distributions of the voter model with stirring The voter model with stirring is a variant of the classical voter model with two possible opinions, 0 and 1. Each site updates its opinion at rate 1 by choosing a neighbour uniformly at random and adopting their opinion. In addition, each pair of neighbouring sites exchanges their opinions at rate v≥ 0, called the stirring parameter. This model was introduced in [Astoquillca '24], where the set of extremal stationary measures on the d-dimensional lattice were described. For d≥3 we consider a site percolation model on configurations sampled from the stationary measures, where the set of occupied sites is the set of voters with opinion 1. We show that the family of (extremal) stationary measures exhibits a non-trivial percolation phase transition in the density of 1s for large stirring parameters. Furthermore, as the stirring parameter approaches infinity, the critical density of this phase transition converges to the critical density for Bernoulli site percolation. Joint work with Jhon Astoquillca and Daniel Valesin.Einladung und Abstract |
| 15.04.2025 | Janina Hesse (Leibniz-Institut für Resilienzforschung, Mainz) How single cell properties can change network synchronization: The saddle-node loop bifurcation in neuron modelsNeurons have traditionally been classified into two types depending on their frequency-input curve. Both types are associated with a particular dynamic transition from rest to spiking. Our work highlights a third transition, for which we found experimental evidence in hippocampal slices. For typical Hodgkin-Huxley-like neuron model, we present a universal bifurcation structure, with the separation of timescale between voltage and ion channel dynamics as one of the bifurcation parameters. We predict that the strongest changes in synchronization with small parameter changes occur at a particular co-dimension two bifurcation, the saddle-node loop bifurcation, and we present characteristics of this transition, from changes in firing rate to phase response curve and synchronization. We will conclude with a short overview over our current research on stress resilience. |
Termine im Wintersemester 2024/25
|
04.02.2025 |
Fabio Frommer (JGU Mainz) Solutions of the Kirkwood-Salsburg equations at negative activity It is well-known that the correlation functions of grand-canonical Gibbs measures satisfy the Kirkwood-Salsburg equations. If the activity is small enough it can be shown that this solution is unique and an analytic function of the activity. We show that in this case the solution of the Kirkwood-Salsburg equations at negative activity correspond to the Janossy densities of the so-called Kirkwood-closure process. This is an extension of the existence result of Kuna et al.
|
| 19.11.2024 | Sascha Franck (Universität zu Lübeck) On the spread of an infection in a spatially distributed host population with host immunity Einladung und Abstract |
| 26.11.2024 | Reinhard Höpfner (JGU Mainz, em.) Circuts von Hodgkin-Huxley-Neuronen Einladung und Abstract |
| 03.12.2024 | Sebastian Hummel (ETH Zürich) Multi-Type Birth-Death Processes with Mean-Field Interactions for B-cell PhylodynamicsEinladung und Abstract |
| 21.01.2025 | Mareike Fischer (Universität Greifswald)
On the reliability of Maximum Parsimony for encoding and reconstructing phylogenetic treesPhylogenetic trees play a major role in the reconstruction and representation of evolutionary relationships among different species. Maximum parsimony (MP) is one of the oldest and simplest phylogenetic tree reconstruction criteria. While it is not based on a nucleotide substitution model but works in a purely combinatorial fashion, it is "folklore knowledge" amongst biologists that it works well whenever the number of substitutions is relatively small. Proving this assertion, which in some regard can be viewed as an extension of the famous Buneman theorem in mathematical phylogenetics, is mathematically quite intriguing. In my talk, I will provide some first steps in this regard, and I will make use of some beautiful combinatorial properties of MP. The results presented in my talk can be regarded as an important step towards proving that MP is justified whenever the number of substitutions is sufficiently small. I will also highlight how these findings on MP impact Maximum Likelihood, another famous tree reconstruction criterion. I will conclude my talk by pointing out some areas of ongoing and future research.
|
| vorangegangene Termine | ||
Sommersemester 2024 |
||
| 07.05.2024 | ||
| 28.05.2024 | ||
| 04.06.2024 |
Samuel Modee (University of Bergen) Einladung und Abstract |
|
| 25.06.2024 | ||
Wintersemester 2023/24 |
||
| 07.11.2023 |