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