Events

Jesse Huang, University of Waterloo

Birational coherent constructible correspondence

A major progress towards the Homological Mirror Symmetry (HMS) conjecture of Kontsevich is a version of HMS for toric varieties proved by Fang-Liu-Treumann-Zaslow and Kuwagaki using constructible sheaves, following an approach originally introduced by Bondal. These results suggest that Bondal's approach can be reinvested as a powerful tool to investigate fundamental algebraic questions pertaining to the birational geometry of toric varieties, and have inspired recent works of Hanlon-Hicks-Lazarev and my works with Favero, both used Bondal's map to obtain short resolutions of the diagonal by a specific collection of line bundles. In this talk, I will discuss these results and their connections to noncommutative resolutions of toric singularities and the broader goal to establish birational toric HMS.

MC 5417

Riley Thornton, Carnegie Mellon University

Topological weak containment

Weak containment is a notion from ergodic theory with a wide variety of applications-- in dynamics, combinatorics, group theory, model theory, and beyond-- and a correspondingly wide variety of equivalent definitions. In this talk, I'll report on a project to adapt the theory to topological dynamics.

MC 5479

Viktor Majewski, Humboldt University Berlin

Resolutions of Spin(7)-Orbifolds

In Joyce’s seminal work, he constructed the first examples of compact manifolds with exceptional holonomy by resolving flat orbifolds. Recently, Joyce and Karigiannis generalised these ideas in the G2 setting to orbifolds with Z2-singular strata. In this talk I will present a generalisation of these ideas to Spin(7) orbifolds and more general isotropy types. I will highlight the main aspects of the construction and the analytical difficulties.

MC 5479

Candace Bethea, Duke University

The local equivariant degree and equivariant rational curve counting

I will talk about joint work with Kirsten Wickelgren on defining a global and local degree in stable equivariant homotopy theory. We construct the degree of a proper G-map between smooth G-manifolds and show a local to global property holds. This allows one to use the degree to compute topological invariants, such as the equivariant Euler characteristic and Euler number. I will discuss the construction of the equivariant degree and local degree, and I will give an application to counting orbits of rational plane cubics through 8 general points invariant under a finite group action on CP^2. This gives the first equivariantly enriched rational curve count, valued in the representation ring and Burnside ring. I will also show this equivariant enrichment recovers a Welchinger invariant in the case when Z/2 acts on CP^2 by conjugation.

MC 5417