Mon, 26 Nov 2018
17:00
L6

Lattices and correction terms

Kyle Larsson
(Alfréd Rényi Institute of Mathematics)
Abstract

 I will introduce two obstructions for a rational homology 3-sphere to smoothly bound a rational homology 4-ball- one coming from Donaldson's theorem on intersection forms of definite 4-manifolds, and the other coming from correction terms in Heegaard Floer homology. If L is a nonunimodular definite lattice, then using a theorem of Elkies we will show that whether L embeds in the standard definite lattice of the same rank is completely determined by a collection of lattice correction terms, one for each metabolizing subgroup of the discriminant group. As a topological application this gives a rephrasing of the obstruction coming from Donaldson's theorem. Furthermore, from this perspective it is easy to see that if the obstruction to bounding a rational homology ball coming from Heegaard Floer correction terms vanishes, then (under some mild hypotheses) the obstruction from Donaldson's theorem vanishes too.

Tue, 28 Nov 2017
17:00
C1

Extension of suboperators and the generalized Schur complement

Tamas Titkos
(Alfréd Rényi Institute of Mathematics)
Abstract

Our long term plan is to develop a unified approach to prove decomposition theorems in different structures. In our anti-dual pair setting, it would be useful to have a tool which is analogous to the so-called Schur complementation. To this aim, I will present a suitable generalization of the classical known Krein - von Neumann extension.

Fri, 29 Apr 2016

11:00 - 13:00
C2

Introduction to Beilinson's approach to p-adic Hodge theory

Tamas Szamuely
(Alfréd Rényi Institute of Mathematics)
Abstract

This is an introduction to the article 

A. Beilinson, p-adic periods and derived de Rham cohomology, J. Amer. Math. Soc. 25 (2012), no. 3, 715--738.

 

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