Mark Pullins (CU) Generically 2-transitive actions of linear algebraic groups with solvable point stabilizers

Tue, Mar. 10 2pm (MATH 220)

Logic

Michael Wheeler (CU Boulder) Graph-like Types and Good Ultrafilters, Part 3

Tue, Mar. 10 2pm (MATH 350)

Lie Theory

Gabe Feinberg (Washington College)

X

A fully commutative element of a Coxeter group is one for which any reduced word can be obtained from another by applying only commutation relations. For example, in a type A Coxeter group, these are exactly the 321-avoiding permutations, known to be counted by the Catalan numbers. For other types, these fully commutative elements have been studied and enumerated by John Stembridge, and have been found to be related to Temperley-Lieb algebras and Khovanov-Lauda-Rouquier algebras. In this talk, we’ll extend the theory to more general complex reflection groups. We’ll deal with some difficulties in generalizing the notion of full commutativity and see some interesting combinatorial structures, including the related Catalan triangle.

Fully commutative elements of complex reflection groups Sponsored by the Meyer Fund

Tue, Mar. 10 3pm (Math 350)

Algebraic Geometry

Leo Herr (Utah)

X

Costello's Pushforward Formula relates virtual fundamental classes on different spaces. It's useful in enumerative geometry, where the goal is to perform computations on these classes within Cohomology or Chow Groups. More specifically, it's often used to compare different ways of performing curve counts or compare curve counts between related spaces. Tragically, this formula has a missing hypothesis. In joint work with Jonathan Wise, we provide counterexamples, prove a correct version of Costello's result, and check that papers using this formula are correct. We obtain a sort of "generalization" by weakening the hypotheses while correcting them, and then another which pertains to log geometry. Attendees can expect an exposition of virtual fundamental classes, clarification of the state of Costello's Formula, and report on ongoing generalizations.

The Cobordism Hypothesis provides a beautiful interplay between extended topological field theories and dualizability conditions, allowing for a conceptual explanation of certain finiteness conditions appearing in representation theory, and, vice versa, a geometric understanding of algebraic objects. In turn, $E}_{n$-algebras, which are algebras for the little disks operad, (e.g.~associative algebras and quantum groups) provide important examples. I will explain why every $E}_{n$-algebra leads to a categorified topological field theory using dualizability arguments. Furthermore, I will explore extensions and further directions. The main result is joint work with Owen Gwilliam.

E_n-algebras, extended topological field theories, and dualizability