Bertrand Remy - Wave equations on affine buildings and application to entropy lower bounds

Abstract

This talk will deal with (harmonic) analysis of affine buildings. We will discuss the construction of kernels associated with discrete multitemporal wave equations on these spaces. One motivation is to contribute to progress in arithmetic quantum unique ergodicity, following a general strategy due to Brooks and Lindenstrauss.
This is joint work with Jean-Philippe Anker and Bartosz Trojan.

Talk

Affine Buildings, Combinatorial complements

Let $A$ be an euclidiean tiling. A building $X$ of type $A$ is cp/covered by subcomplexes $\cong A$ called apartments s.t.

• any two cells are contained in an apartment (copy of $A$)
• For any two adjacent apartment there is a isomorphism fixing the common boundary.

If I understand correctlz Bruhat-Tits showed that for every group, there is a maximal building acted upon by the group.

Root-theoretic-notions

We define objects called:

• Weyl sectors
• Highest roots
• Coweight lattices
• root half-spaces

Vectorial distance

In a building $x\in X$ is called a special vertex, if some root properties are given. Then we define a vectorial distance and using this we define a vectorial radius sphere.

Remy hat Gallerien erwähnt!

Harmonic analysis

Algebras of Averaging operators

For more information check out J.Pakinsons PhD. We define the McDonalds polynomials.

About