Topology Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
26 November 2018

In this talk I will articulate and contextualize the following sequence of results.

The Bruhat decomposition of the general linear group defines a stratification of the orthogonal group.
Matrix multiplication defines an algebra structure on its exit-path category in a certain Morita category of categories.  
In this Morita category, this algebra acts on the category of n-categories -- this action is given by adjoining adjoints to n-categories. 

This result is extracted from a larger program -- entirely joint with John Francis, some parts joint with Nick Rozenblyum -- which proves the cobordism hypothesis.  

26 November 2018

 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.

Add to My Calendar