Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|October 2020||December 2020|
Events for 20 November 2020
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The Gaussian \beta-ensemble is one of the central model in random matrix theory. Because of its integrable structure, it allows to describe several universal limiting laws of the eigenvalues of random matrices. For instance, in a seminal work, Ramirez, Rider and Virag constructed the Airy-\beta process, the scaling limit of the eigenvalues near the spectral edge of the Gaussian \beta-ensemble and gave a new representation for the Tracy-Widom distributions.
In this talk, I intend to review this construction and present recent results on the asymptotics for the characteristic polynomial of the Gaussian beta-ensemble obtained jointly with Elliot Paquette (McGill University). Our results rely on a new approach to study the characteristic polynomial based on its recurrence. My goal is to report on the behavior of the characteristic away from the eigenvalues and near the spectral edge and to explain how this relates to a log-correlated Gaussian process and to the Airy-\beta process.
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Confinement is one of the most important but basic features of non-Abelian gauge theories, and an intuitive and interesting scenario of its dynamics is condensation of magnetic monopoles. When we add the topological theta term to it, more exotic condensations may appear, which are called oblique confinement phases. In a 4d lattice model proposed by Cardy and Rabinovici, such interesting phases can be explicitly realized. In this talk, I will uncover its topological nature based on the recent applications of 't Hooft anomaly matching. Moreover, it has been known that the local dynamics of Cardy-Rabinovici model shows the SL(2,Z) self-duality, but it turns out that the self-duality does not extend to the global aspect of the original theory. We cooked up a SL(2,Z) self-dual theory by gauging a part of the 1-form symmetry of the Cardy-Rabinovici model, and the self-duality has a mixed gravitational anomaly. These data give useful constraints to discuss the phase diagram.
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