## University of Toledo

## Department of Mathematics and Statistics

# Algebra Seminar

**M 4:00-5:00pm****UH 4170**

## Next Talk

- December 4, 2017
- Mihai D. Staic, (BGSU)
*Secondary Hochschild Cohomology*- Abstract: In this talk I will give an introduction to secondary Hochschild Cohomology, discussing the initial motivation and the main properties for this construction.

## Talks This Semester

- December 4, 2017
- Mihai D. Staic, (BGSU)
*Secondary Hochschild Cohomology*- Abstract: In this talk I will give an introduction to secondary Hochschild Cohomology, discussing the initial motivation and the main properties for this construction.
- November 27, 2017
- Alimjon Eshmatov
*On quivers and their representations II*- Abstract: We continue our discusson of Gabriel's theorem and related things.
- November 6, 2017
- Alimjon Eshmatov
*On quivers and their representations*- Abstract: A quiver is a directed graph. A representation of a quiver is an assignment of a vector space to each vertex and a linear map to each arrow. One of the most fundamental theorems in this theory is Gabriel's theorem. In this talk I will state this theorem and outline its proof.
- October 23, 2017
- Nate Iverson
*Quadratic forms over finite fields*- Abstract: Will define quadratic form and prove the equivalency of the 2 rival definitions for any field. Discuss non-degeneracy (in arbitrary characteristic), equivalence of forms, and classify all non-degenerate quadratic forms over a finite field (up to change of variable). We will explicitly cover the characteristic 2 case and mention the Chevalley-Warning theorem and Witt's theorem (for extending isometries).
- September 25, 2017
- Alimjon Eshmatov
*Noncommutative deformation of Kleinian singularities*- Abstract: Associated to a finite subgroup $G$ of $SL_2 (\mathbb{C})$, there is a family of noncommutative algebras representing a deformation of the coordinate ring of the classical Kleinian singularity $\mathbb{C}^2//G$. These algebras found to be related to many areas of mathematics: mathematical physics, algebraic geometry, symplectic geometry to name few. In the talk, we will give overview of these algebras and related results.