# Events for 11/18/2022 from all calendars

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 09:00AM - 10:00AM

**Location: ** ZOOM

**Speaker: **Alexey Kostenko, University of Lubljana

**Title: ***Laplacians of infinite graphs*

**Abstract: **There are two different notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a venerable history as they are related to several diverse branches of mathematics and mathematical physics.

The existing literature usually treats these two Laplacian operators separately. In this talk, I will focus on the relationship between them (spectral, parabolic and geometric properties). One of our main conceptual messages is that these two settings should be regarded as complementary (rather than opposite) and exactly their interplay leads to important further insight on both sides.

Based on joint work with N. Nicolussi.

## Probability and Mathematical Physics

**Time: ** 09:00AM - 10:00AM

**Location: ** Zoom

**Speaker: **Aleksey Kostenko, University of Ljublajana

**Title: ***Laplacians of infinite graphs*

**Abstract: **There are two different notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a venerable history as they are related to several diverse branches of mathematics and mathematical physics. The existing literature usually treats these two Laplacian operators separately. In this talk, I will focus on the relationship between them (spectral, parabolic and geometric properties). One of our main conceptual messages is that these two settings should be regarded as complementary (rather than opposite) and exactly their interplay leads to important further insight on both sides. Based on joint work with N. Nicolussi.

## Student/Postdoc Working Geometry Seminar

**Time: ** 1:00PM - 2:00PM

**Location: ** BLOC 628

**Speaker: **H. Huang, Auburn

**Title: ***Hopf ring structures and spaces of symmetric tensors*

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 1:50PM - 2:50PM

**Location: ** BLOC 306

**Speaker: **Jorge Villalobos, LSU

**Title: ***Embedded eigenvalues for discrete magnetic Schrodinger operators *

**Abstract: **Reducibility of the Fermi surface for a periodic operator is a key for the existence of embedded eigenvalues caused by a local defect. We consider a discrete model for a multilayer quantum system, such as stacked graphene, subject to a perpendicular magnetic field. Some techniques for constructing embedded eigenvalues extend from non-magnetic operators to magnetic ones, but the magnetic case is more complex because a typical magnetic operator on a periodic graph is merely quasi-periodic.

## Algebra and Combinatorics Seminar

**Time: ** 3:00PM - 3:50PM

**Location: ** BLOC 302

**Speaker: **Frank Sottile, TAMU

**Title: ***A Murnaghan-Nakayama formula in quantum Schubert calculus*

**Abstract: **The Murnaghan-Nakayama formula expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. In geometry, a Murnaghan-Nakayama formula computes the intersection of Schubert cycles with tautological classes coming from the Chern character. In previous work with Morrison, we establshed a Murnaghan-Nakayama formula in the cohomology of a flag variety and conjectured a version for the quantum cohomology ring of the flag variety. In this talk, I will discuss some background, and then some recent work proving this conjecture. This is joint work with Benedetti, Bergeron, Colmenarejo, and Saliola.

## Geometry Seminar

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 302

**Speaker: **Amy (Hang) Huang, Auburn

**Title: ***Vanishing Hessian and Wild Polynomials*

**Abstract: **Notions of ranks and border rank abounds in the literature. Polynomials with vanishing hessian and their classification is also a classical problem. Motivated by an observation of Ottaviani, we will discuss why when looking at concise polynomials of minimal border rank, being wild, i.e. their smoothable rank is strictly larger than their border rank, is the same as having vanishing Hessian. The main tool we are using here is the recent work of Buczynska and Buczynski relating the border rank of polynomials and tensors to the multi-graded Hilbert scheme. From here, we found two infinite series of wild polynomials and we will try to describe their border varieties of sums of powers, which is an analog of the variety of sums of powers.

## Free Probability and Operators

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 306

**Speaker: **Zhiyuan Yang, TAMU

**Title: ***Free Poisson von Neumann algebras*

**Abstract: **We would like to introduce a free Poisson type functor for left Hilbert algebras similar to the Voiculescu's free Gaussian functor and the free Araki-Woods functor. For any left Hilbert algebra A, we consider the von Neumann algebra Γ(A) generated by the operators X(a)=l^*(a)+l(a)+p(a) acting on the full Fock space F(A), where a is in A, l^*(a), l(a) are the creation and annihilation operators, and p(a) is an preservation operator. Using a simple combinatorial method, we will show that when A is a W^* algebra with a finite weight, Γ(A) is isomorphic to the free product of L(Z) and an algebra determined by A (with a possible extra atom). In particular, this implies that the filtration W^* algebras of a free Poisson process (over a time interval) are the interpolated free group factors. We will also describe the behavior of completely positive maps under this functor.