Jens Walter Fischer

Jens Walter Fischer

Mathematician with an interest in all quantitative domains.

Talks and presentations

High-dimensional grid exploration using self-avoiding exclusion processes

May 03, 2023

Talk, Universität Potsdam, Potsdam, Germany

I discussed an approach based on self-avoiding exclusion processes inspired by swarm/genetic algorithms to explore high dimensional grids. Those are considered now as one option in post-quantum cryptography and pose interesting problems for self-avoiding exlcusion processes which form a natural extension of a self-avoiding random walk. The possible particle transitions, I discussed, left the next neighbor structure of graphs behind them and focused on transitions based on a given lattice basis and geometrically distributed jump lengths in one randomly picked direction. This talk used many notions from my thesis but applied in a completely different field.

Absorption times for generalized exclusion processes in random absorbing environments

November 25, 2021

Talk, College Doctorale Université Franco-Allemande UFA, Online

I presented a theoretical framework for absorption times for generalized exclusion processes in random absorbing environments on a graph motivated by the Echo Chamber Model as an example. I discussed the dependency on the underlying graph structure relativ to the structure of the induced subgraph of the absorbing sites. I gave a general upper bound, combining the quasi-stationary distribution of the processes with an extended notion of Token graphs and quantified its quality for a special case of the Echo Chamber Model.

Random Network Dynamics - A reduced Echo Chamber model

September 08, 2021

Talk, Online, Paris, France

The content of this talk was a summary of my research work of my PhD up to this point with a focus on the necessity to employ algebraic, combinatoric and graph theoretic techniques to answer questions regarding generalized exclusion processes associated to opinions dynamics. I explained the difficulties one might encounter while using functional analytical technqiues based on Eigenvalues of some associated operator and the trade-off I had to accept between the two points of view.

Social conflict and exclusion processes - a link

March 23, 2021

Talk, Online, Kyiv, Ukraine

I presented a negativ result concerning the reversibility of some generalized exclusion processes due to the strong lokal dependencies on the structure of the underlying discrete state space. Using combinatorical methods I showed that for a fixed transition structure, possible state spaces can be separated into two classes based on the reversibility property of the exclusion process. Both classes are completely defined by solutions of a Diphontine equation of order four in four variables, which encodes cycles of length four of the process.

Day of the PhD Students

February 02, 2021

Talk, Université Toulouse III - Paul Sabatier, Toulouse

I gave an introdution to mathematical modelling of population dynamics based on my work on generalized birth-death processes with catastrophes and opinion dynamics in heterogenous populations. The focus lay on the explanation of the basic assumptions and ideas without too many technical details.

Consensus Dynamics and Exclusion processes

December 02, 2020

Talk, Université Toulouse III - Paul Sabatier, Toulouse, France

I presented a first result linking opinion dynamics with exclusion processes in a random absorbing environment. The lift to token graphs was the central focus of this talk which formed the basis of further discussion regarding the applicability of Markov chain results to complex systems of heterogeneous agents.