Please join us for pre-seminar Tea

For discrete subgroups of semisimple Lie groups, the limit cone serves as a key invariant in studying asymptotic properties. Anosov subgroups, well-known for their rich geometric and dynamical features, form an important class of these discrete subgroups. A natural question arises: does the limit cone vary continuously along deformations of Anosov subgroups? In this talk, we discuss a sufficient condition for such continuity, along with applications like the continuity of the growth indicators along deformations. Based on joint work with Hee Oh.

The Jones polynomial of a link can be computed diagrammatically by using skein relations which encode the representation theory of SL(2). By considering the vector space spanned by links drawn on a surface and imposing these skein relations, we obtain an algebra known as the Kauffman bracket skein algebra of the surface. Replacing SL(2) by SL(3) or any other higher rank Lie group gives rise to a new skein algebra involving not only links but also certain graphs called webs. In this talk, we will discuss some of the complications involved with studying skein algebras built from webs on surfaces and then discuss how the use of stated skein algebras helps us get around these.