Geometric perspectives; from curved spaces to game theory and its applications

29.10.2014, 14:00 Uhr  –  Universität Potsdam, Am Neuen Palais 10, Haus 9, Raum 1.12
Institutskolloquium

Martina Zähle (Jena), Julie Rowlett (Bonn)

• 14:00 Uhr: Martina Zähle (Jena)
  Geometry past and present; a stroll through curved spaces.
• 15:00 Uhr: Coffee break
• 15:30 Uhr: Julie Rowlett (Bonn)
  Biological applications of algebraic geometry

Abstracts:
Martina Zähle (Jena): Geometry past and present; a stroll through curved spaces
We offer an excursion through geometry and analysis of the last 150 years, focusing on some complete systems of Euclidean invariants - the continuous motion invariant valuations. Convex geometry, differential geometry, geometric measure theory and algebraic geometry provide different approaches to these functionals and their measure theoretic counterparts on various classes of sets. In special situations they are known, e.g., as quermassintegrals or as Lipschitz-Killing curvatures and (lower-dimensional) volumes, including the topological Euler number. We shall also discuss how to describe the geometry of self-similar or self-conformal sets in more detail by means of current fractal versions.
Julie Rowlett (Bonn): Biological applications of algebraic geometry

Julie Rowlett (Bonn): Biological applications of algebraic geometry
In this talk we will first review the basics of non-cooperative game theory and proceed to prove a general result concerning the payoff function of such games and its level sets. It turns out that these level sets are real semi-algebraic varieties and in most cases have Hausdorff dimension at least one. This will be shown to have what appear to be rather unexpected biological implications. This talk is based on joint work with Susanne Menden-Deuer.