Monday, October 12, 2015 at 3:00 PM in SAS 4201

Natasha Rozhkovskaya, Kansas State UniversityShifted symmetric functions

The focus of this talk is the properties of so-called shifted Schur functions, in particular their vertex operator presentation. Shifted Schur functions appear in representation theory of classical Lie algebras as eigenvalues of the elements of a certain linear basis of a center of the corresponding universal enveloping algebra. The methods used to construct this linear basis can be extended further to construct explicitly generators of maximal commutative subalgebras in enveloping algebras, and even more, similar techniques were used recently to describe explicitly generators of Feigin-Frenkel centers of classical Lie algebras. The talk is based on a joint project with N. Jing.

Monday, October 19, 2015 at 3:00 PM in SAS 4201

David Penneys, UCLAClassifying quantum symmetries

Quantum symmetries are non-commutative analogs of the representation

categories of finite groups. There is no single best axiomatization;

choices include fusion categories and standard invariants of finite

index subfactors. In one sense, subfactors of small index give the

simplest examples of quantum symmetries. I will discuss recent joint

work with Afzaly and Morrison which gives the complete classification

of subfactor standard invariants to index 5+1/4, which includes

3+sqrt{5}, the first interesting composite index.

Friday, October 30, 2015 at 3:00 PM in SAS 2102

Lindsay Piechnik, High Point UniversityTBA

Monday, November 2, 2015 at 3:00 PM in SAS 4201

Tri Lai, Institute for Mathematics and its ApplicationsTBA

Monday, November 9, 2015 at 3:00 PM in SAS 4201

Emily Barnard, NC State Mathematics Graduate StudentTBA

Monday, November 16, 2015 at 3:00 PM in SAS 4201

Andrei Minchenko, Weizmann Institute, IsraelTBA

Monday, November 23, 2015 at 3:00 PM in SAS 4201

Ezra Miller, Duke UniversityTBA

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Seminar Organizers: Bojko Bakalov and Ricky Liu