The metric measure boundary of spaces with Ricci curvature bounded below
Bruè, E
Mondino, A
Semola, D
(21 May 2022)
Scaling laws for properties of random graphs that grow via successive combination
Grindrod, P
Journal of Complex Networks
volume 10
issue 3
(21 Jun 2022)
The universal program of nonlinear hyperelasticity
Yavari, A
Goriely, A
Journal of Elasticity
volume 154
issue 1
91-146
(20 Jul 2022)
Fri, 10 Jun 2022
13:30 -
17:00
Lecture Theatre 5
Groups and Geometry in the South East
(Mathematical Institute)
Further Information
Property (T) and random quotients of hyperbolic groups
1:30
Calum Ashcroft (Cambridge)
In his original manuscript on hyperbolic groups, Gromov asked whether random quotients of non-elementary hyperbolic groups have Property (T). This question was later refined by Ollivier, and then answered in the case of random quotients of free groups by Zuk (and Kotowski--Kotowski).
In this talk we answer the Gromov--Ollivier question in the affirmative. We will discuss random quotients and some of their properties, in particular with relation to Property (T).
Connections between hyperbolic geometry and median geometry
2:45
Cornelia Drutu (Oxford)
In this talk I shall explain how groups endowed with various forms of hyperbolic geometry, from lattices in rank one simple groups to acylindrically hyperbolic groups, present various degrees of compatibility with the median geometry. This is joint work with Indira Chatterji, and with John Mackay.
TEA
3:45
Division, group rings, and negative curvature
4:00
Grigori Avramidi (Bonn)
In 1997 Delzant observed that fundamental groups of hyperbolic manifolds with large injectivity radius have nicely behaved group rings. In particular, these rings have no zero divisors and only the trivial units. In this talk I will explain how to extend this observation to show such rings have a division algorithm (generalizing the division algorithm for group rings of free groups discovered by Cohn) and that these group rings have``freedom theorems’’ showing that all of their ideals that are generated by few elements are free, where the specific value of `few’ depends on the injectivity radius of the manifold (which can be viewed as generalizations from subgroups to ideals of some freedom theorems of Delzant and Gromov). This has geometric consequences to the homotopy classification of 2-complexes with surface fundamental groups and to complexity of cell structures on hyperbolic manifolds.
Notes on Resonances and Unitarity from Celestial Amplitudes
García-Sepúlveda, D
Guevara, A
Kulp, J
Wu, J
(29 May 2022)
http://arxiv.org/abs/2205.14633v1
Hedging Option Books Using Neural-SDE Market Models
Cohen, S
Reisinger, C
Wang, S
(01 Jan 2022)
Oxford Mathematician Jared Duker Lichtman explains his fascination and frustration with a conjecture that has puzzled mathematicians for years.
Tue, 21 Jun 2022
14:00 -
15:00
L6
The orbit method and normality of closures of nilpotent orbits
Dan Barbasch
(Cornell University, USA)
Abstract
The work of Kraft-Procesi classifies closures of nilpotent orbits that are normal in the cases of classical complex Lie algebras. Subsequent work of Ranee Brylinsky combines this work with the Theta correspondence as defined by Howe to attach a representation of the corresponding complex group. It provides a quantization of the closure of a nilpotent orbit. In joint work with Daniel Wong, we carry out a detailed analysis of these representations viewed as (\g,K)-modules of the complex group viewed as a real group. One consequence is a "representation theoretic" proof of the classification of Kraft-Procesi.
Tue, 07 Jun 2022
03:00 -
04:00
Online
Infinite-bin model and the longest increasing path in an Erdős-Rényi graph
Bastien Mallein
(Sorbonne Université - Université de Paris)
Further Information
Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.
Abstract
We consider an oriented acyclic version of the Erdős-Rényi random graph: the set of vertices is {1,...,n}, and for each pair i < j, an edge from i to j is independently added to the graph with probability p. The length of the longest path in such a graph grows linearly with the number of vertices in the graph, and its growth rate is a deterministic function C of the probability p of presence of an edge.
Foss and Konstantopoulos introduced a coupling between these graphs and a particle system called the "Infinite-bin model". By using this coupling, we prove some properties of C, that it is analytic on (0,1], its development in series at point 1 and its asymptotic behaviour as p goes to 0.