Events for 02/17/2023 from all calendars

Student/Postdoc Working Geometry Seminar

Time: 1:00PM - 2:30PM

Location: BLOC 628

Speaker: Liena Colarte Gómez, IPAM (Warsaw)

Title: Hyperplane arrangements and their module of logarithmic derivations

Abstract: A hyperplane arrangement A in the projective space is a finite collection of hyperplanes. To this variety, we attach a submodule Der(A) of the classical module of derivations, called the module of logarithmic derivations of A. In this talk, we approach the problem of understanding the algebraic structure of Der(A) and its freeness towards the so called Terao's conjecture.

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: ZOOM

Speaker: Jesus Sanchez Jr, Washington University in St Louis

Title: Equivariant Local Index Theory for Lie Groupoids

Abstract: In recent work, Higson and Yi developed a new perspective on Getzler’s symbol calculus, reinterpreting the latter in terms of a convolution algebra of sections of a multiplicative vector bundle over the tangent groupoid of a spin manifold. In joint work with S. Liu, Y. Loizides, and A.R.H.S. Sadegh we generalize the construction in two directions; to the equivariant setting, and to the adiabatic groupoid of any Lie groupoid. We discuss applications including an equivariant longitudinal local index theorem for Lie groupoids with a closed space of units.

URL: Event link

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Mahrud Sayrafi, University of Minnesota

Title: Bounding the Multigraded Regularity of Powers of Ideals

Abstract: Building on a result of Swanson, Cutkosky--Herzog--Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e. Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.

Free Probability and Operators

Time: 4:00PM - 5:00PM

Location: BLOC 306

Speaker: Michael Anshelevich, TAMU

Title: Hermite trace polynomials

Abstract: We consider the algebra of trace polynomials with the state induced by the GUE random matrices. In addition to the monomial basis, another natural basis for this algebra consists of the Hermite trace polynomials. They satisfy several properties familiar for the ordinary trace polynomials. The algebra structure can be extended from polynomials to a larger family of stochastic integrals. While the Hermite trace polynomials are not orthogonal, they can be modified to obtain several versions of the chaos decomposition. The simplest of these is related to the Hermite polynomials of matrix argument. This is joint work with David Buzinski.