Random Matrix Theory 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.

Past events in this series
Tomorrow
15:30
Abstract

In recent years, our understanding of the asymptotic behavior of characteristic polynomials of random matrices has seen much progression. A key paradigm in this area is that the asymptotic behavior is often captured by an appropriate family of Gaussian multiplicative chaos (GMC) measures (defined heuristically as the normalized exponential of log-correlated random fields). Indeed, such results have been shown for Harr distributed matrices for U(N), O(N), and Sp(2N), as well as for one-cut Hermitian invariant ensembles (and in particular, GUE(N)). In this talk we explain an extension of these results to GOE(2N) and GSE(N). The key tool is a new asymptotic relation between the moments of the characteristic polynomials of all three classical ensembles. 

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  • Random Matrix Theory Seminars
8 February 2022
15:30
TBA
Alex Little

Further Information: 

Could be upgraded to an in-person seminar depending on Covid restrictions

Abstract

TBA

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  • Random Matrix Theory Seminars
15 February 2022
15:30
Emilia Alvarez
Abstract

I will present a collection of moment computations over the unitary, symplectic and special orthogonal matrix ensembles that I've done throughout my thesis. I will focus on the methods used, the motivation from number theory, the relationship to Painlev\'e equations, and directions for future work.

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  • Random Matrix Theory Seminars
1 March 2022
15:30
Abstract

In this talk, we give an overview of recent results on the fluctuation of the statistic $\sum_{i\neq j} f(L_N(\theta_i-\theta_j))$ for the Circular Beta Ensemble in the global, mesoscopic and local regimes. This work is morally related to Johansson's 1988 CLT for the linear statistic $\sum_i f(\theta_i)$ and Lambert's subsequent 2019 extension to the mesoscopic regime. The special case of the CUE ($\beta=2$) in the local regime $L_N=N$ is motivated by Montgomery's study of pair correlations of the rescaled zeros of the Riemann zeta function. Our techniques are of combinatorial nature for the CUE and analytical for $\beta\neq2$.

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  • Random Matrix Theory Seminars
8 March 2022
15:30
TBA
Stefan Zohren

Further Information: 

Could be upgraded to an in-person seminar depending on Covid restrictions

Abstract

TBA

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  • Random Matrix Theory Seminars
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