The seminar on differential geometry will continue on October 22 in the lecture room M5 by the lecture:

Ilya Kossovskiy:

Real analytic coordinates for smoothly embedded CR hypersurfaces.

Prof. Javier Esparza

TU Munich, an ERC advanced grant holder, and a Honorary doctor of Masaryk University (among his many other distinguished honors).

The lecture will be in the Mendel Museum (not FI!) on * Wednesday Oct 10, since 16:00.

Black Ninjas in the Dark: Analyzing Population Protocols

Abstract:

Population protocols are a mathematical model of distributed computation introduced by Angluin et al. in 2004. The original purpose of Angluin et al. was the theoretical study of systems consisting of identical, cheap mobile devices with tiny computational resources, like sensor networks. However, since its introduction, the model has also been used to analyze the behavior of chemical systems and people in social networks. Population protocols help us to pose and study many fundamental questions about distributed systems: What can be computed by agents wishing to remain anonymous? Are leader processes necessary for optimal speed? Can macroscopic "phase transitions" be "programmed" at a microscopic level? Is it possible to check automatically that a protocol works correctly? Is it possible to automatically synthesize a protocol for a given task?

In the talk, I will introduce the population protocol model with the help of several examples. More precisely, I will present the problem of the Black Ninjas in the Dark, and the different solutions given to it by their Senseis. I will also show animated simulations of some protocols.

We will continue on Thursday, October 11, in M5 at 13.00 by the talk of:

A. Tokarčík

The aim of this lecture is to present the main results of van den Berg's paper "Path categories and propositional identity types," discussing an approach to providing a categorical model for perhaps the most intriguing aspect of intensional Martin-Löf type theory, (a variant of) the inductively defined family of identity types. In particular, a precise link between the syntactic category of a type theory with propositional identity types, (Joyal's) tribes with propositional identity types, path tribes and path categories is established. The material will be accompanied by a short introduction to the rules of the type theory and its categorical semantics.

The seminar on differential geometry will continue on October 8 from 10am in lecture room M5 by the lecture

Katharina Neusser:

C-projective equivalence in Kähler geometry

Abstract:
While a projective structure on a manifold is given by a class of affine connections that have the same (unparametrised) geodesics, a c-projective structure on a complex manifold is given by a class of affine complex connections that have the same ``J-planar'' curves. In this talk we will be mainly concerned with c-projective structures induced by Kähler metrics (via their Levi-Civita connections). We will present some work on the geometric and topological consequences of the existence of at least two c-projectively equivalent Kähler metrics, and on c-projective automorphism groups of Kähler manifolds. This talk is based on joint work with Calderbank--Eastwood--Matveev, and with Matveev.

I will try to balance the talk well so that those, who are unfamiliar with the topic, can follow well, but I also want to use the opportunity to give some more details about the proofs for those, who are and have already heard some short talks by me on the topic.