Mon, 20 May 2019

15:45 - 16:45
L3

Low degree approximation of real singularities

ANTONIO LERARIO
(SISSA ITALY)
Abstract

In this talk I will discuss some recent results that allow to approximate a real singularity given by polynomial equations of degree d (e.g. the zero set of a polynomial, or the number of its critical points of a given Morse index) with a singularity which is diffeomorphic to the original one, but it is given by polynomials of degree O(d^(1/2)log d).
The approximation procedure is constructive (in the sense that one can read the approximating polynomial from a linear projection of the given one) and quantitative (in the sense that the approximating procedure will hold for a subset of the space of polynomials with measure increasing very quickly to full measure as the degree goes toinfinity).

The talk is based on joint works with P. Breiding, D. N. Diatta and H. Keneshlou      

Mon, 13 May 2019

14:15 - 15:45
L3

Solving nonlinear PDE's in the presence of singular randomness.

NIKOLAY TZETKOB
(University of Clergy France)
Abstract

We will start by presenting two basic probabilistic effects for questions concerning the regularity of functions and nonlinear operations on functions. We will then overview well-posedenss results for the nonlinear wave equation, the nonlinear Schr\"odinger equation and the nonlinear heat equation, in the presence of singular randomness.

Mon, 29 Apr 2019

15:45 - 16:45
L3

Inference of a large rank-one matrix and Hamilton-Jacobi equations

JEAN-CHRISTOPHE MOURRAT
(ENS FRANCE)
Abstract

We observe a noisy version of a large rank-one matrix. Depending on the strength of the noise, can we recover non-trivial information on the matrix? This problem, interesting on its own, will be motivated by its link with a "spin glass" model, which is a model of statistical mechanics where a large number of variables interact with one another, with random interactions that can be positive or negative. The resolution of the initial question will involve a Hamilton-Jacobi equation

Mon, 29 Apr 2019

14:15 - 15:15
L3

Scaling limits and surface tension for gradient Gibbs measure

WEI WU
(Warwick University)
Abstract

I will discuss new results for the gradient field models with uniformly convex potential (also known as the Ginzburg-Landau field). A connection between the scaling limits of the field and elliptic homogenization was introduced by Naddaf and Spencer in 1997. We quantify the existing central limit theorems in light of recent advances in quantitative homogenization; and positively settle a conjecture of Funaki and Spohn about the surface tension. Joint work with Scott Armstrong. 

 

Tue, 25 Jun 2019

15:30 - 16:30
L4

Global analytic geometry and Hodge theory

Kobi Kremnizer
(Oxford)
Abstract

In this talk I will describe how to make sense of the function $(1+t)^x$ over the integers. I will explain how different rings of analytic functions can be defined over the integers, and how this leads to global analytic geometry and global Hodge theory. If time permits I will also describe an analytic version of lambda-rings and how this can be used to define a cohomology theory for schemes over Z. This is joint work with Federico Bambozzi and Adam Topaz. 

Mon, 09 Sep 2019 12:00 -
Wed, 11 Sep 2019 12:00
L5

Workshop on Higher-order Interaction Networks: Dynamics, Structure, Data

See below for speaker information
(Speakers from several universities)
Further Information

The goal of the research workshop "Higher-order interaction networks: dynamics, structure, data" is to bring together researchers from these different communities with distinct perspectives on network dynamics —- from network science, dynamical systems, and data science/machine learning -- to develop novel approaches to understand networked systems. By cutting across different mathematical communities, this will allow to develop new tools, for example by exploring links between data driven methods (such as machine learning) and dynamics. A particular focus of this workshop will be on the role of non-dyadic dynamical interactions (joint interactions between more than two nodes) whose importance for the modeling, analysis, and control of such networked systems have recently been highlighted.

Expressions of interest are now open with an initial deadline of June 1, 2019, with notification of acceptance no later than June 15, 2019.

Participation in the workshop will cost a nominal fee of £50 which will be used to cover catering during the workshop. Participants will also have the chance to attend the workshop dinner on Wednesday 10th September at the nearby Somerville College, the cost of which will be £30.  

Thanks to generous funding from EU and the London Mathematical Society, there is limited travel support for UK-based early career researchers available. Please indicate whether you wish to apply for support during registration.

For further information including registration please click here.

Confirmed Speakers:

Lou Pecora (Naval Research Labs)
Tanya Berger-Wolf (Illinois)
Santiago Segarra (Rice)
Tiago Pereira (USP Sao Carlos)
Marta Sales-Pardo (Barcelona)
Jacopo Grilli (Santa Fe Institute/ICTP Trieste)
Marya Bazzi (ATI)
Rebecca Hoyle (Southampton)
Ana Paula Dias (Porto)
Laetitia Gauvin (ISI Torino)
Heather Harrington (Oxford)
Rodolphe Sepulchre (Cambridge)
Jess Enright (Stirling)
Peter Ashwin (Exeter)
Pawel Dlotko (Swansea)

Fri, 26 Apr 2019

16:00 - 17:00
L1

Mathematics in developing countries

Federico Danieli and Christian Bick
(University of Oxford)
Abstract

How do you create a self-sustaining, flourishing academic community in a developing country? What kind of challenges need to be overcome to ensure that quality education becomes available? What can we do to help make it happen? In this talk, we will describe our experience visiting the University of Yangon in Myanmar. During the visit, we delivered a course to the academic staff, and discussed future collaborations between Oxford and Yangon, as well as further directions for Mathematical education in Myanmar, all the while marvelling at the wonders of the Burmese culture.

Tue, 21 May 2019

14:30 - 15:30

Intervals in the Hales-Jewett Theorem

Christoph Spiegel
Further Information

The Hales–Jewett Theorem states that any r–colouring of [m]^n contains a monochromatic combinatorial line if n is large enough. Shelah’s proof of the theorem implies that for m = 3 there always exists a monochromatic combinatorial line whose set of active coordinates is the union of at most r intervals. I will present some recent findings relating to this observation. This is joint work with Nina Kamcev.

Tue, 14 May 2019

14:30 - 15:30
L6

Graphs which are expanders both locally and globally

Michael Chapman
Further Information

Expander graphs play a key role in modern mathematics and computer science. Random d-regular graphs are good expanders. Recent developments in PCP theory require families of graphs that are expanders both globally and locally. The meaning of “globally" is the usual one of expansion in graphs, and locally means that for every vertex the subgraph induced by its neighbors is also an expander graph. These requirements are significantly harder to satisfy and no good random model for such (bounded degree) graphs is presently known. In this talk we discuss two new combinatorial constructions of such graphs. We also say something about the limitations of such constructions and provide an Alon-Bopanna type bound for the (global) spectral gap of such a graph. In addition we discuss other notions of high dimensional expansion that our constructions do and do not satisfy, such as coboundary expansion, geometric overlap and mixing of the edge-triangle-edge random walk. This is a joint work with Nati Linial and Yuval Peled.
 

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