Dear Friends of Hikes and Mathematics,

you are invited to our 27th mathematical hike planned on December 14th. Meet at 09:36 at the bus stop "Rozcestí" (bus 57) in Útěchov.

We have planned a short hike (not even 10 km) not following any tourist path towards the ruins of Ronov castle. The end of the hike is in Útěchov.

Snow or mud, doesn't matter, look forward to a Christmas hike.

All information and photos can be found at http://conference.math.muni.cz/vylety/. (in CZ)

Have a nice December,

Jonatan Kolegar and Jana Bartoňová, organizers,
Jan Slovák, Director of the Department of Mathematics and Statistics

The seminar on differential geometry will continue with this lecture:

December 2, 10am, lecture room M5.

Vincent Pecastaing (University of Luxembourg):

Actions of higher-rank lattices on conformal and projective structures

Abstract:

The main idea of Zimmer's program is that in real-rank at least 2, the rigidity of lattices of semi-simple Lie groups makes that their actions on closed manifolds are understandable. After a short survey giving a more precise idea of Zimmer's conjectures and their context, I will give recent results about conformal and projective actions of cocompact lattices. The fact that these geometric structures do not carry a natural invariant volume is one of the main motivations. We will see that the real-rank is bounded above like when the ambient Lie group is acting, and that at the critical value, the manifold is globally isomorphic to a model homogeneous space. The proofs rely in part on an "invariance principle" recently introduced by Brown, Rodriguez-Hertz and Wang, which guarantees the existence of finite invariant measures in some dynamical context.

Seminar of differential equations will continue on December 2, 2019 at 12pm in lecture room M5.

Dr. Rotchana Chieochan (Khon Kaen University, Thajsko)

Floquet theory for q-difference equations

Abstract:

In this talk, we introduce q-periodic functions in quantum calculus and study the first-order linear q-difference vector equation for which its coefficient matrix function is q-periodic and regressive. Based on the new definition of periodic functions, we establish Floquet theory in quantum calculus.

We will continue on Thursday, November 28, in M5 at 1pm by the talk

J. R. Gonzales

Grothendieck categories and their tensor product as filtered colimits

Abstract:
Grothendieck categories are the Ab-enriched Grothendieck topoi. In this talk, we will first show two different ways to obtain a Grothendieck category as a filtered colimit of its representing linear sites: one given by all possible representing linear sites, the other, coarser, given by the representing linear sites induced by the full subcategories of alpha-presentable objects, with varying regular cardinal alpha. Making use of the latter, we show that the tensor product of Grothendieck categories, introduced in previous joint work with Lowen and Shoikhet, is compatible via this construction with Kelly's alpha-cocomplete tensor product. This allows us to translate the functoriality, simmetry and commutativity of Kelly's tensor product to the tensor product of Grothendieck categories.