Jing Tao (University of Oklahoma/Fields Institute)
Big Torelli groups
4:00PM, Fri Oct 19 2018, 122 Math
A surface S is of finite-type if its fundamental group is finitely generated; otherwise, it is of infinite type. The mapping class group MCG(S) of S is the group of isotopy classes of orientation-preserving homeomorphisms of S. This is a well-studied group when S has finite type, but big mapping class groups, i.e. MCG(S) of infinite-type surfaces, remain quite mysterious. But big mapping class groups arise naturally in various areas of mathematics and recently there has been a surge of interests in studying them. In this talk, I will discuss some recent results about the Torelli subgroup of MCG(S). This is joint with Aramayona, Ghaswala, Kent, McLeay, and Winarski.
Algebra Seminar-Vasu Tewari, University of Pennsylvania
Divided symmetrization and generalized permutahedra
4:00PM, Mon Nov 5 2018, 150 Mathematics Bldg
Generalized permutahedra are an important class of polytopes which
show up in many areas in mathematics. The volume and number of lattice
points of these polytopes are given by certain multivariate
polynomials that were introduced and +studied by Alex Postnikov, who
further established various remarkable combinatorial properties
thereof. In this talk, I will discuss in depth the procedure of
divided symmetrization that allows one to compute volumes of
generalized +permutahedra. Along the way, we will encounter familiar
combinatorial objects such as standard Young tableaux, reduced pipe
dreams, P-partitions and various Catalan objects.
This is joint work with Philippe Nadeau
Algebra Seminar- Naihuan Jing, North Carolina State University
Presentation of Yangian algebras in BCD types.
4:00PM, Mon Nov 12 2018, 150 Mathematics Bldg
It is well-known that the R-matrix presentation of the Yangian in type A yields generators of
its Drinfeld presentation. It has been an open problem since Drinfeld's pioneering work
to extend this result to the remaining types.
We will provide a solution for the classical types of BCD
by constructing an explicit isomorphism between
the R-matrix and Drinfeld presentations of the Yangian.
It is based on an embedding theorem which allows us to consider
the Yangian of rank n-1 as a subalgebra of the Yangian of rank n of the same type.
This is joint work with A. Molev and M. Liu.
Bülent Tosun (Alabama)
4:00PM, Fri Nov 16 2018, 122 Math
Jacob Russell (CUNY)
4:00PM, Fri Nov 30 2018, 122 Math