Oxford Mathematics Public Lecture
Four Ways of Thinking: Statistical, Interactive, Chaotic and Complex - David Sumpter
Wednesday 13 September 2023, 5 - 6pm Andrew Wiles Building
Mathematics is about finding better ways of reasoning. But for many applied mathematicians, the primary mission is to shape their minds in a way that gets them closer to the truth. The calculations are secondary, the real question is: how we can better understand the world around us?
14:00
Microlocal sheaves and affine Springer fibers
Abstract
The resolutions of Slodowy slices S͂e are symplectic varieties that contain the Springer fiber (G/B)e as a Lagrangian subvariety. In joint work with R. Bezrukavnikov, M. McBreen, and Z. Yun, we construct analogues of these spaces for homogeneous affine Springer fibers. We further understand the categories of microlocal sheaves in these symplectic spaces supported on the affine Springer fiber as some categories of coherent sheaves.
In this talk I will mostly focus on the case of the homogeneous element ts for s a regular semisimple element and will discuss some relations of these categories with the small quantum group providing a categorification of joint work with R.Bezrukavnikov, P. Shan and E. Vasserot.
13:00
Double scaled SYK and the quantum geometry of 3D de Sitter space
Abstract
In this talk, I describe an exact duality between the double scaling limit of the SYK model and quantum geometry of de Sitter spacetime in three dimensions. The duality maps the so-called chord rules that specify the exact SYK correlations functions to the skein relations that govern the topological interactions between world-line operators in 3D de Sitter gravity.
This talk is part of the series of Willis Lamb Lectures in Theoretical Physics. Herman Verlinde is the Lamb Lecturer of 2024.
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