I will describe how the large charge limit of extremal correlators in N=2 superconformal field theories is captured by a dual description which is a random matrix model of the Wishart-Laguerre type. This gives a new analytic handle on the physics in some particular excited states. The random matrix model also admits a 't Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge.

# Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Conical Symplectic Resolutions form a broad family of holomorphic symplectic manifolds that are of interest to mathematical physicists, algebraic geometers, and representation theorists; Nakajima Quiver Varieties and Hypertoric Varieties are known as their special cases. In this talk, I will be focused on the Symplectic Geometry of Conical Symplectic Resolutions, and its non-symplectic applications. More precisely, I will talk about my work on finding Exact Lagrangian Submanifolds inside CSRs, and work in progress (joint with Alexander Ritter) about the construction of Symplectic Cohomology on CSRs.

We exhibit a new martingale coupling between two probability measures $\mu$ and $\nu$ in convex order on the real line. This coupling is explicit in terms of the integrals of the positive and negative parts of the difference between the quantile functions of $\mu$ and $\nu$. The integral of $|y-x|$ with respect to this coupling is smaller than twice the Wasserstein distance with index one between $\mu$ and $\nu$. When the comonotonous coupling between $\mu$ and $\nu$ is given by a map $T$, it minimizes the integral of $|y-T(x)|$ among all martingales coupling.

(joint work with William Margheriti)

In this talk we will survey a novel domain of computational group theory: computing with linear groups over infinite fields. We will provide an introduction to the area, and will discuss available methods and algorithms. Special consideration is given to algorithms for Zariski dense subgroups. This includes a computer realization of the strong approximation theorem, and algorithms for arithmetic groups. We illustrate applications of our methods to the solution of problems further afield by computer experimentation.

We discuss the models of random geometry that are derived

from scaling limits of large graphs embedded in the sphere and

chosen uniformly at random in a suitable class. The case of

quadrangulations with a boundary leads to the so-called

Brownian disk, which has been studied in a number of recent works.

We present a new construction of the Brownian

disk from excursion theory for Brownian motion indexed

by the Brownian tree. We also explain how the structure

of connected components of the Brownian disk above a

given height gives rise to a remarkable connection with

growth-fragmentation processes.

I will explain what the Willmore Morse Index of unbranched Willmore spheres in Euclidean three-space is and how to compute it. It turns out that several geometric properties at the ends of complete minimal surfaces with embedded planar ends are related to the mentioned Morse index.

One consequence of that computation is that all unbranched Willmore spheres are unstable (except for the round sphere). This talk is based on work with Jonas Hirsch.

Cities are now central to addressing global changes, ranging from climate change to economic resilience. There is a growing concern of how to measure and quantify urban phenomena, and one of the biggest challenges in quantifying different aspects of cities and creating meaningful indicators lie in our ability to extract relevant features that characterize the topological and spatial patterns of urban form. Many different models that can reproduce large-scale statistical properties observed in systems of streets have been proposed, from spatial random graphs to economical models of network growth. However, existing models fail to capture the diversity observed in street networks around the world. The increased availability of street network datasets and advancements in deep learning models present a new opportunity to create more accurate and flexible models of urban street networks, as well as capture important characteristics that could be used in downstream tasks. We propose a simple approach called Convolutional-PCA (ConvPCA) for both creating low-dimensional representations of street networks that can be used for street network classification and other downstream tasks, as well as a generating new street networks that preserve visual and statistical similarity to observed street networks.

Vandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem.

In this talk, we consider the random version of some classical extremal problems in the context of long cycles. This type of problems can also be seen as random analogues of the Turán number of long cycles, established by Woodall in 1972.

For a graph $G$ on $n$ vertices and a graph $H$, denote by $\text{ex}(G,H)$ the maximal number of edges in an $H$-free subgraph of $G$. We consider a random graph $G\sim G(n,p)$ where $p>C/n$, and determine the asymptotic value of $\text{ex}(G,C_t)$, for every $A\log(n)< t< (1- \varepsilon)n$. The behaviour of $\text{ex}(G,C_t)$ can depend substantially on the parity of $t$. In particular, our results match the classical result of Woodall, and demonstrate the transference principle in the context of long cycles.

Using similar techniques, we also prove a robustness-type result, showing the likely existence of cycles of prescribed lengths in a random subgraph of a graph with a nearly optimal density (a nearly ''Woodall graph"). If time permits, we will present some connections to size-Ramsey numbers of long cycles.

Based on joint works with Michael Krivelevich and Adva Mond.