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.

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.