Wed, 27 May 2020
10:00
Virtual

Poincare's Polyhedron Theorem and Applications to Algorithms.

Joe Scull
(University of Oxford)
Abstract

Much progress in the study of 3-manifolds has been made by considering the geometric structures they admit. This is nowhere more true than for 3-manifolds which admit a hyperbolic structure. However, in the land of algorithms a more combinatorial approach is necessary, replacing our charts and isometries with finite simplicial complexes that are defined by a finite amount of data. 

In this talk we'll have a look at how in fact one can combine the two approaches, using the geometry of hyperbolic 3-manifolds to assist in this more combinatorial approach. To do so we'll combine tools from Hyperbolic Geometry, Triangulations, and perhaps suprisingly Polynomial Algebra to find explicit bounds on the runtime of an algorithm for comparing Hyperbolic manifolds.

Wed, 13 May 2020
10:00
Virtual

A Mapping Class Group Presentation from Fatgraphs

Adele Jackson
(University of Oxford)
Abstract

The mapping class group of a surface with boundary acts freely and properly discontinuously on the fatgraph complex, which is a contractible cell complex arising from a cell decomposition of Teichmuller space. We will use this action to get a presentation of the mapping class group in terms of fat graphs, and convert this into one in terms of chord diagrams. This chord slide presentation has potential applications to computing bordered Heegaard Floer invariants for open books with disconnected binding.

Wed, 06 May 2020
10:00
Virtual

Revisiting Leighton's Theorem

Daniel Woodhouse
(University of Oxford)
Abstract

Let X_1 and X_2 be finite graphs with isomorphic universal covers.

Leighton's graph covering theorem states that X_1 and X_2 have a common finite cover.

I will discuss recent work generalizing this theorem and how myself and Sam Shepherd have been applying it to rigidity questions in geometric group theory.

Mon, 25 May 2020
12:45
Virtual

Symplectic duality and implosion -- ZOOM SEMINAR

Andrew Dancer
(University of Oxford)
Abstract

We discuss hyperkahler implosion spaces, their relevance to group actions and why they should fit into the symplectic duality picture. For certain groups we present candidates for the symplectic duals of the associated implosion spaces and provide computational evidence. This is joint work with Amihay Hanany and Frances Kirwan.
 

Fri, 22 May 2020

16:00 - 17:00
Virtual

North Meets South

Lucie Domino and Clemens Koppensteiner
(University of Oxford)
Abstract
Lucie Domino
How to build 3D shapes from flat sheets using a three-centuries old theory
 
In this talk, I’ll present some of our recent work on morphing structures. We start from flat two-dimensional sheets which have been carefully cut and transform them into three-dimensional axisymmetric structures by applying edge-loads. We base our approach on the well-known Elastica theory developed by Euler to create structures with positive, negative, and variable Gaussian curvatures. We illustrate this with famous architectural examples, and verify our theory by both numerical simulations and physical experiments.
 
 
Clemens Koppensteiner
Logarithmic Riemann-Hilbert Correspondences

The classical Riemann-Hilbert correspondence is an elegant statement linking geometry (via flat connections) and topology (via local systems). However, when one allows the connections to have even simple singularities, the naive correspondence breaks down. We will outline some work on understanding this "logarithmic" setting.
Thu, 30 Apr 2020

16:45 - 18:00
Virtual

Inverting a signature of a path

Weijun Xu
(University of Oxford)
Further Information
Abstract

Abstract: The signature of a path is a sequence of iterated coordinate integrals along the path. We aim at reconstructing a path from its signature. In the special case of lattice paths, one can obtain exact recovery based on a simple algebraic observation. For general continuously differentiable curves, we develop an explicit procedure that allows to reconstruct the path via piecewise linear approximations. The errors in the approximation can be quantified in terms of the level of signature used and modulus of continuity of the derivative of the path. The main idea is philosophically close to that for the lattice paths, and this procedure could be viewed as a significant generalisation. A key ingredient is the use of a symmetrisation procedure that separates the behaviour of the path at small and large scales.We will also discuss possible simplifications and improvements that may be potentially significant. Based on joint works with Terry Lyons, and also with Jiawei Chang, Nick Duffield and Hao Ni.

Wed, 08 Apr 2020

17:00 - 18:00

Robin Thompson - How do mathematicians model infectious disease outbreaks? ONLINE LECTURE

Robin Thompson
(University of Oxford)
Further Information

Models. They are dominating our Lockdown lives. But what is a mathematical model? We hear a lot about the end result, but how is it put together? What are the assumptions? And how accurate can they be?

In our first online only lecture Robin Thompson, Research Fellow in Mathematical Epidemiology in Oxford, will explain. Robin is working on the ongoing modelling of Covid-19 and has made many and varied media appearances in the past few weeks. We are happy to take questions after the lecture.

Watch live:

https://twitter.com/oxunimaths?lang=en
https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/Thompson

Oxford Mathematics Public Lectures are generously supported by XTX Markets

Thu, 02 Apr 2020
16:00

What is the Jiang Su algebra (Virtual Seminar)

Sam Evington
(University of Oxford)
Further Information

This is the first meeting of the virtual operator algebra seminar in collaboration with colleagues in Glasgow and UCLan.  The seminar will take place by zoom, and the meeting details will be available here.

Wed, 27 May 2020

17:00 - 18:00
L1

Philip Maini: Squirrels, Turing and Excitability - Mathematical Modelling in Biology, Ecology and Medicine

Philip Maini
(University of Oxford)
Further Information

Mathematical modelling lives a varied life. It links the grey squirrel invasion in the UK to the analysis of how tumour cells invade the body; Alan Turing's model for pattern formation gives insight into animal coat markings and Premier League Football Shirts; and models for Excitability have been used to model the life cycle of the cellular slime mold and heart attacks.

Philip Maini will reveal all in our latest Oxford Mathematics Public Lecture.

Philip Maini is Professor of Mathematical Biology in the University of Oxford.

Watch live:
https://twitter.com/OxUniMaths
https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/Maini

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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