Algebra Day 2014

Feb 22-23, 2014

at the

Department of Mathematics, University of Kansas,

organized by

Hailong Dao

This mini-workshop, partially sponsored by NSF and the University of Kansas, will feature talks on several topics of (non)commutative algebra/algebraic geometry and plenty of discussion among participants. Some previous versions can be found here .

Location: Department of Mathematics, University of Kansas. The talks will be held at 306 Snow Hall.

Speakers and schedule:

Yunfeng Jiang (University of Kansas) 2:00pm-3:00pm, Feb 22, 306 Snow

Title: On the Behrend function and its relation to Donaldson-Thomas invariants.

Abstract: I will introduce what is Behrend function for a scheme or a DM stack, which is very important to define Donaldson-Thomas invariants. I will also talk about how it is related to primary decomposition in commutative algebra.

Coffee and snacks: 3:00-3:30 pm, 306 Snow

Ilya Smirnov (University of Virginia) 3:30pm - 4:30pm, Feb 22, 306 Snow

Title: Hilbert-Kunz multiplicity.

Abstract: Hilbert-Kunz multiplicity is an invariant of a local ring of positive characteristic introduced by Paul Monsky. In the last 15 years, the Hilbert-Kunz theory became an active subject of research driven by its connection to tight closure, singularity theory and comparison to the classical theory of Hilbert-Samuel multiplicity. In this talk, I will compare these multiplicity theories focusing on their use to study singularities.

Gufang Zhao (Northeastern University) 4:30 - 5:30pm, Feb 22, 306 Snow

Title: Examples of noncommutative resolutions

Abstract: We will begin with the concepts of noncommutative crepant resolutions (NCCR). After the classical example of McKay correspondence, we will discuss varies generalizations: 3-dimensional rational Gorenstein singularities, symplectic quotient singularities, and some determinantal varieties. In each case I will focus on the construction of the NCCR, as well as some very basic properties of their module categories.