# Algebra and Number Theory Seminar Winter 2017

**Friday, January 13, 2017**

*"Nearest Points on Toric Varieties*"

**Martin Helmer, University of California, Berkeley
**

We determine a combinitorial expression for the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of local Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point. This also leads to combinatorial expressions for the polar degrees, the degree and codimension of the dual variety, and the Chern-Mather class of a projective toric variety. This is joint work with Bernd Sturmfels.

**January 20, 2017**

**TBA**

**January 27, 2017**

**TBA**

**February 3, 2017
**

**TBA**

**February 10, 2017**

**TBA**

**February 17, 2017**

**"Loewy Lengths of Centers of Blocks"**

**Burkhard Külshammer, University of Jena, Germany**

In my talk I will report on bounds for the Loewy lengths of centers of blocks recently obtained by Y. Otokita, B. Sambale and myself.

**February 24, 2017**

**TBA**

**March 3, 2017**

**TBA**

**March 10, 2017**

**"Coset Construction of W-algebras"**

**Tomoyuki Arakawa, Kyoto University, RIMS**

W-algebras are interesting vertex algebras that can be regarded as cousins of affine Kac-Moody algebras. Despite their importance in integrable systems, conformal field theory, geometric Langlands program, 4d gauge theory, and etc, many problems on W-algebras are still open because of the complexity of the structure. In my talk, I will prove the conjecture of Kac and Wakimoto from 1990 on the coset construction of (principal) W-algebras in full generality. This is joint work with Thomas Creutzig and Andrew Linshaw.

**March 17, 2017**

**TBA**

**March 24, 2017**

**NO SEMINAR**

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