University of York Geometry, Analysis and Mathematical Physics seminar 2023-24

All are welcome to attend the seminar, which usually takes place at 2pm on Tuesdays in the Topos during term time.

Autumn Semester 2023

Date	Speaker	Title
26 September	Jakob Stein (UCL)	\(G_2\) instantons bubbling at infinity on \(S^3 \times \mathbb{R}^4\)
3 October
10 October 3:30pm in the Topos Note the time!	Fernando Galaz-Garcia (Durham)	Topology and geometry of 3-dimensional Alexandrov spaces
17 October	Ruadhai Dervan (Glasgow)	TBA
24 October	Tathagata Ghosh (Leeds)	Instantons on Asymptotically Conical Spin(7)-Manifolds
31 October
7 November
8 November Lewis Fry Richardson seminar	David Tong (Cambridge)	TBA
14 November
21 November
28 November	Ronald Zúñiga-Rojas (Universidad de Costa Rica)	TBA
5 December	Ana Peon-Nieto (Birmingham)	TBA
12 December	Dave Smith (Yale-NUS)	Fokas Diagonalization

Spring Semester 2024

Date	Speaker	Title
16 January
23 January
30 January
6 February
13 February	Ilyas Khan (Duke)	TBA

Previous years' seminars

2022-23
2021-22
2020-21
2019-20

Abstracts

26 September Jakob Stein (UCL)
Title. \(G_2\) instantons bubbling at infinity on \(S^3 \times \mathbb{R}^4\)
Abstract. In this talk, we will discuss two sorts of bubbling for Yang-Mills instantons on a \(G_2\)-manifold, with some explicit examples arising from solutions to an ODE. The first describes bubbling off instantons on a fixed asymptotic model space, in this case, the asymptotic cone of the Bryant-Salamon \(S^3 \times \mathbb{R}^4\). The second describes the limiting behaviour of instantons as one varies the asymptotic geometry in family of Taub-NUT-type metrics.

This is joint work with Matt Turner (Bath).

10 October Fernando Galaz-Garcia (Durham)
Title. Topology and geometry of 3-dimensional Alexandrov spaces
Abstract. Alexandrov spaces (with curvature bounded below) are metric generalizations of complete Riemannian manifolds with a uniform lower sectional curvature bound. Instances of Alexandrov spaces include compact Riemannian orbifolds and orbit spaces of isometric compact Lie group actions on compact Riemannian manifolds. In addition to being objects of intrinsic interest, Alexandrov spaces play an important role in Riemannian geometry, for example, in Perelman's proof of the Poincaré Conjecture. In this talk, I will discuss the topology and geometry of 3-dimensional Alexandrov spaces, focusing on their classification and structure under certain geometric constraints (for example, positive or non-negative curvature and collapse).

17 October Ruadhai Dervan (Glasgow)
Title. TBA
Abstract. TBA

24 October Tathagata Ghosh (Leeds)
Title. Instantons on Asymptotically Conical Spin(7)-Manifolds
Abstract. TBA

28 November Ronald Zúñiga-Rojas (Universidad de Costa Rica)
Title. TBA
Abstract. TBA

5 December Ana Peon-Nieto (Birmingham)
Title. TBA
Abstract. TBA

12 December Dave Smith (Yale-NUS)
Title. Fokas Diagonalization
Abstract. We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP whose spatial parts are described by such operators. We argue that the method described may be viewed as a reimplementation of the Fokas transform method for linear evolution equations on the finite interval. The results are extended to multipoint and interface operators, including operators defined on networks of finite intervals, in which the coefficients of the differential operator may vary between subintervals, and arbitrary interface and boundary conditions may be imposed; differential operators with piecewise constant coefficients are thus included.

13 February Ilyas Khan (Duke)
Title. TBA
Abstract. TBA

Last updated 2 October, 2023