Boston Algebraic Geometry Day

Speakers: Xin Jin, Eric Jovinelly, Daniel Litt, Eyal Markman

Location: University Hall Y02-2110, UMass Boston.  See Visitor Resources for directions, parking, and transportation. 

Schedule: 

9:30-10  Check-in and refreshments

10-11  Xin Jin: Around the multiplicative universal centralizer

11-11:30  Coffee break

11:30-12:30  Eric Jovinelly

12:30-2  Lunch (not provided; lunch is available for purchase at the Dining Commons in Residence Hall East)

2-3  Daniel Litt: Tuples of matrices (after Charlie Wu)

3-3:30  Coffee break

3:30-4:30  Eyal Markman  

Abstracts:

Xin Jin (Boston College): Around the multiplicative universal centralizer

The multiplicative universal centralizer $J$ of a complex reductive group $G$ plays an important role in geometric representation theory. For $G=GL_n$, $J$ is a transverse Hilbert scheme of $n$ points on $\mathbb{C}^\times\times \mathbb{C}^\times$. For $G$ of ADE type, $J$ is the K-theoretic Coulomb branch of pure gauge theory. I will present joint work with Ben Webster (to appear) establishing two remarkable structures on $J$: a (toric-like) Bruhat stratification and a cluster structure. Time permitting, I will discuss applications of these structures, including a partial resolution of a conjecture of Cautis–Williams, applications to the cohomology of $J$, and the determination of the Donaldson–Thomas transformation on $J$.

Daniel Litt (University of Toronto): Tuples of matrices (after Charlie Wu)

Consider the space of n-tuples of matrices whose product is the identity, up to simultaneous conjugation, and where the matrices are constrained to lie in some collection of fixed conjugacy classes. This is an example of a "relative character variety," in this case of the projective line minus n points. I'll discuss work of Charlie Wu (in his PhD thesis) describing some of the topology of these spaces, as well as relative character varieties of higher genus curves, and in particular a classification of the compact components of the real points of these spaces. I'll also discuss joint work in progress that further studies the rich geometry of these compact components and their mapping class group dynamics.