Jan Rychtář

Programming projects for Ph.D. (and other) students

Come to see me in person if you need more details or if you would prefer to do a different project under my supervision.
  1. Evolutionary Dynamics on Graphs - solving large and sparse systems of linear equations
  2. Evolutionary Optimization.

Research projects for thesis

Come to see me in person if you need more details or if you did not find what are you looking for. Check the publications to get a feel for the topics.

Mathematical Biology

  • Modeling territorial and raiding behavior
    Brief description: A population of individuals lives in a spatially structured population. Each individual has its own territory and each territory has a certain amount of resources. Each individual also can raid territories of its neighbors (or can stay home, potentially defend its own territory). What is the optimal behavior (i.e. how much should the individuals raid)? How does it depend on the population structure? The tricky part is that the optimal behavior of one individual depends on the behavior of others (that also want to behave individually). The typical approach is to assume that all individuals behave in a same way and only one individual is trying to be "smart" and picking the best behavior; the goal is to find the behavior such that if everybody adopts it, it is optimal even for the smart individual to adopt it. The problem with this approach arises when the situation is not homogeneous (i.e. if the individuals cannot behave in the same way on the first place either because the population structure is not symmetric, or certain territories are richer in resources). Two main goals this project would be to find efficient ways to deal with homogeneous situations and to explore some ways to deal with non-homogeneous ones.
  • Kleptoparasitism (Models of stealing behavior)
  • Evolutionary Dynamics on Graphs (How stucture of the population influences the outcome of different dynamics)
  • Various collaborative projects on mathematical models of biological phenomena

Applied Mathematics

Math models of various things in various fields. See, for example, here.

Game Theory

Evolutionary stable strategies

Functional Analysis

  • Fixed points
  • Smoothness in Banach spaces
  • Convexity in Banach spaces
  • Weak and weak* topology in Banach spaces, compactness