# 2012 Lafayette-Lehigh Geometry-Topology Seminar

The Lafayette-Lehigh Geometry-Topology Seminar will be held Saturday March 24 at Lafayette College. The Mathematics Department is located in Pardee Hall (building # 37 on the Campus Map). The Directions on the Lafayette Website direct you to the Visitor Parking Deck behind Markle Hall. You may be able to park near Pardee Hall—there are spots adjacent to the building, between Pardee and Watson Courts, and along the Quad. Please refer to the the Campus Map.

The talks will be held in Pardee Hall 217. We will gather for coffee and bagels, etc., around 10:00 AM, across the hall in Pardee 218 (the Saalfrank Common Room).

** Schedule **

10:30-11:30: **Radmila Sazdanovic ** (University of Pennsylvania)

** Categorification in knot and graph theory **

*Abstract*: We review homology theories of links and graphs, focusing on Khovanov link and chromatic graph homology, as well as relations between them. We will start with a brief introduction to categorification and proceed with Khovanov homology, the categorification of the famous Jones polynomial. Khovanov homology is related to a categorification of the chromatic polynomial for graphs, via Hochschild homology. We use this beautiful relation to address the conjecture by A. Shumakovich about torsion in Khovanov homology. Finally, we prove M. Khovanov’s conjecture relating the algebraic and topological categorifications of the chromatic polynomial.

11:45-12:45: **Adam Pigott** (Bucknell University)

** Automorphisms of free products of finite groups **

* Abstract *: A free product G of finite groups acts geometrically on a tree. We

shall discuss two constructions—the first due to McCullough and

Miller, the second to Krstic and Vogtmann—which encode in simplicial

complexes the ways in which G acts on trees. In each case, the result

is a simplicial complex upon which Aut(G) acts.

1:00-2:00: Lunch Break: **Light lunch ** in Pardee 218.

2:00-3:00: **Valentino Tosatti ** (Columbia University)

** Degenerations of Calabi-Yau manifolds and mirror symmetry **

*Abstract*: We will discuss the problem of understanding how Ricci-flat

Calabi-Yau manifolds can degenerate, and how this can be used in the

context of the Strominger-Yau-Zaslow picture of mirror symmetry for

hyperkahler manifolds. Joint work with Mark Gross and Yuguang Zhang.

March 6, 2012 at 6:34 pm

I will mention this to students, and try to give you an idea of how many are coming from Lehigh.

March 6, 2012 at 8:07 pm

Thanks, David! FYI: I did send an email to some folks (Aydin, Cuneyt, and the folks from my fall course), but I don’t know if there may be others interested.