Mon, 05 Feb 2024
14:15
L4

Infinite-time Singularities of Lagrangian Mean Curvature Flow

Albert Wood
(Kings College London)
Abstract
Lagrangian mean curvature flow is the name given to the phenomenon that, in a Calabi-Yau manifold, the class of Lagrangian submanifolds is preserved under mean curvature flow. An influential conjecture of Thomas and Yau, refined since by Joyce, proposes to utilise the Lagrangian mean curvature flow to prove that certain Lagrangian submanifolds may be expressed as a connect sum of volume minimising 'special Lagrangians'.
 
This talk is an exposition of recent joint work with Wei-Bo Su and Chung-Jun Tsai, in which we exhibit a Lagrangian mean curvature flow which exists for infinite time and converges to an immersed special Lagrangian. This demonstrates one mechanism by which the above decomposition into special Lagrangians may occur, and is also the first example of an infinite -time singularity of Lagrangian mean curvature flow. The work is a parabolic analogue of work of Dominic Joyce and Yng-Ing Lee on desingularisation of special Lagrangians with conical singularities, and is inspired by the work of Simon Brendle and Nikolaos Kapouleas on ancient solutions of the Ricci flow.
Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local
fields
 Andrew, N Conder, M Markowitz, A Schillewaert, J (10 Jan 2024) http://arxiv.org/abs/2401.05192v1
Fri, 02 Feb 2024

12:00 - 13:00
Quillen Room

Standard Majorana representations of 3-transposition groups

Albert Gevorgyan
(Imperial College, London)
Abstract

The Monster group M is the largest sporadic simple group. It is also the group of automorphisms of 196, 884-dimensional Fischer-Norton-Griess algebra V_M. In 2009, A. A. Ivanov offered an axiomatic approach to studying the structure of V_M by introducing the notions of Majorana algebra and Majorana representation. Later, the theory developed, and Majorana representations of several groups were constructed. Our talk is dedicated to the existence of standard Majorana representations of 3-transposition groups for the Fischer list. The main result is that the groups from the Fischer list which admit a standard Majorana representation can be embedded into the Monster group.

Tue, 30 Apr 2024
13:00
L2

Determinants in self-dual N = 4 SYM and twistor space

Frank Coronado
(McGill)
Abstract
Self-dual Yang-Mills famously have a description in terms of twistors; one of the outstanding questions is how to promote it to full (non-self-dual) Yang-Mills and learn about its dynamics. In this talk, I will present some progress in this direction in the "most symmetric" Yang-Mills theory; namely N=4 super Yang-Mills in four dimensions. I will express the full Yang-Mills theory as a deformation of self-dual Yang-Mills. By treating the deformation perturbatively and using the formalism of twistors, I will write down the loop-integrands of correlation functions of determinant operators in the planar limit at any order in the 't Hooft coupling. Interestingly, the final expression is given by a partition function of a "dual" matrix model. This in turn manifests a ten-dimensional structure that combines spacetime and R-charge symmetries of SYM.
 


 

Tue, 30 Jan 2024
12:30
L4

Towards the large-charge sector of the critical O(N) model with an interface defect

Vito Pellizzani
(Bern)
Further Information

In conformal field theories, special classes of operators, such as defects and local operators carrying large quantum numbers, have received a lot of attention in recent years. In this talk, I will present some work in progress regarding the extraction of CFT data in the critical O(N) model with a codimension-one flat defect (interface), paying special attention to the case where local operators in large traceless symmetric representations of O(N) (the so-called 'large-charge operators' in this context) are inserted in the bulk. The talk will include a discussion of certain general features of codimension-one defect CFTs, a small review of the large-charge bootstrap, as well as an overview of the current understanding of the phase diagram of the boundary/interface critical O(N) model.

Preface
 Málek, J Suli, E Birkhauser Nečas Center Series v-vii (21 Jan 2022)

University of Edinburgh: PhD in Probability Theory

The School of Mathematics at the University of Edinburgh invites applications for a PhD position in Probability Theory. Accepted candidates receive full funding and are not required to take on teaching responsibilities. However, students have the choice to engage in teaching (tutoring) if they wish to, and they will receive compensation for their efforts.

Tue, 30 Jan 2024

14:00 - 15:00
L4

Kneser graphs are Hamiltonian

Torsten Mütze
(University of Warwick)
Abstract

For integers $k \ge 1$ and $n \ge 2k+1$, the Kneser graph $K(n,k)$ has as vertices all $k$-element subsets of an $n$-element ground set, and an edge between any two disjoint sets. It has been conjectured since the 1970s that all Kneser graphs admit a Hamilton cycle, with one notable exception, namely the Petersen graph $K(5,2)$. This problem received considerable attention in the literature, including a recent solution for the sparsest case $n=2k+1$. The main contribution of our work is to prove the conjecture in full generality. We also extend this Hamiltonicity result to all connected generalized Johnson graphs (except the Petersen graph). The generalized Johnson graph $J(n,k,s)$ has as vertices all $k$-element subsets of an $n$-element ground set, and an edge between any two sets whose intersection has size exactly $s$. Clearly, we have $K(n,k)=J(n,k,0)$, i.e., generalized Johnson graphs include Kneser graphs as a special case. Our results imply that all known families of vertex-transitive graphs defined by intersecting set systems have a Hamilton cycle, which settles an interesting special case of Lovász' conjecture on Hamilton cycles in vertex-transitive graphs from 1970. Our main technical innovation is to study cycles in Kneser graphs by a kinetic system of multiple gliders that move at different speeds and that interact over time, reminiscent of the gliders in Conway’s Game of Life, and to analyze this system combinatorially and via linear algebra.

This is joint work with my students Arturo Merino (TU Berlin) and Namrata (Warwick).

Subscribe to