Erik Carlsson, University of California, Davis, will present a colloquium titled "Combinatorics and Two Geometric Constructions of the Diagonal Coinvariant Algebra" as part of the Mathematics Department Colloquium Lecture series.
The abstract for this lecture is: The diagonal coinvariant algebra $DR_n$ is the quotient ring of the polynomials in 2n variables by the nonconstant symmetric ones, under the simultaneous action of the symmetric group $S_n$. Interestingly, this algebra appears as a central object in different forms in a broad range of topics in geometry and algebra, including the Hilbert scheme of point in the complex plane, Springer theory, Khovanov-Rozansky knot homology, and others. The relationship between these subject leads to very difficult and deep combinatorics. I will explain this, and the next step, which is to "categorify" the combinatorics, with the goal of understanding broader conjectures about how the different geometric topics were related in the first place.
Tuesday, November 12 at 2:30pm to 3:20pm