Events for 11/19/2021 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Laura Shou, Princeton University

Title: Pointwise Weyl law for graphs from quantized interval maps

Abstract: In this talk I will discuss the eigenvectors of families of unitary matrices obtained from quantization of one-dimensional interval maps. This quantization for interval maps was introduced by Pakoński et al. [J. Phys. A: Math. Gen. 34 9303 (2001)] as a model for quantum chaos on graphs. The resulting unitary matrices are sparse, yet numerically exhibit CUE random matrix behavior. To analyze the eigenvectors, I prove a pointwise Weyl law with shrinking spectral windows. This implies a stronger version of the quantum ergodic theorem for these models, and shows in the semiclassical limit that a family of randomly perturbed quantizations has approximately Gaussian eigenvectors.

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: ZOOM

Speaker: Gilles de Castro , Federal University of Santa Catarina

Title: C*-algebras and Leavitt path algebras for labelled graphs

Abstract: Since the work of Cuntz and Krieger in 1980, there has been an interest in studying C*–algebras associated with subshifts and combinatorial objects, such as 0-1 matrices and graphs. Bates and Pask introduced a class of algebras associated with labelled graphs that generalised several of the previously mentioned algebras. A couple of decades before the work of Cuntz and Krieger, Leavitt studied a class of rings that do not satisfy the IBN. In the early 2000s, Ara et al. studied a purely algebraic analogue of the Cuntz-Krieger algebras, and they observed that when considering the matrix consisting only of 1’s (which in the C*-algebra are the Cuntz algebras), we obtain a subclass of Leavitt rings. Motivated by this work, Abrams and Pino introduced an algebraic analogue of C*-algebras of graphs, which they called Leavitt path algebras. These algebras share several properties and a way of proving this is by considering them as groupoid algebras/C*-algebras. In this talk, I will present the C*-algebras of labelled graphs and their algebraic counterpart and I will explain how we can obtain groupoid models for these algebras. I will also talk about the approach using partial actions and give some conditions on partial actions of the free group such that they can be modelled using labelled graphs.

URL: Event link

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Anna Pun, University of Virginia

Title: A Note on the Higher order Tur\'{a}n inequalities for k-regular partitions

Abstract: Nicolas and DeSalvo and Pak proved that the partition function $p(n)$ is log concave for $n \geq 25$. Chen, Jia and Wang proved that $p(n)$ satisfies the third order Tur\'{a}n inequality, and that the associated degree 3 Jensen polynomials are hyperbolic for $n \geq 94$. Recently, Griffin, Ono, Rolen and Zagier proved more generally that for all $d$, the degree $d$ Jensen polynomials associated to $p(n)$ are hyperbolic for sufficiently large $n$. In this talk, we will see that the same result holds for the $k$-regular partition function $p_k(n)$ for $k \geq 2$. In particular, for any positive integers $d$ and $k$, the order $d$ Tur\'{a}n inequalities hold for $p_k(n)$ for sufficiently large $n$. The case when $d = k = 2$ proves a conjecture by Neil Sloane that $p_2(n)$ is log concave. This is a joint work with William Craig.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: zoom

Speaker: Gleb Smirnov, ETH, Zurich

Title: Symplectic mapping class groups of K3 surfaces

Abstract: I will briefly introduce symplectic mapping class groups and explain how to use Seiberg-Witten theory to get information about them. In particular, I will prove that the symplectic mapping class groups of many K3 surfaces are infinitely generated, thus extending a recent result of Sheridan and Smith. Time permitting, we will also discuss the elliptic version of the story, where K3 is replaced with a blow-up of the complex torus.