Mon, 04 Nov 2013
14:00
L5

4D Einstein equations as a gauge theory

Joel Fine
(UL Brussels)
Abstract

I will explain a new formulation of Einstein’s equations in 4-dimensions using the language of gauge theory. This was also discovered independently, and with advances, by Kirill Krasnov. I will discuss the advantages and disadvantages of this new point of view over the traditional "Einstein-Hilbert" description of Einstein manifolds. In particular, it leads to natural "sphere conjectures" and also suggests ways to find new Einstein 4-manifolds. I will describe some first steps in these directions. Time permitting, I will explain how this set-up can also be seen via 6-dimensional symplectic topology and the additional benefits that brings.

Mon, 04 Nov 2013

12:00 - 13:00
L5

Global Properties of Supergravity Solutions

Jan Gutowski
(Surrey)
Abstract
Recent progress has been made in the analysis of supergravity solutions. It can be shown that for a large class of solutions, the conditions imposed by supersymmetry are equivalent to determining the zero modes of various types of Dirac operators, by an extension of the classical Lichnerowicz theorem. Hence the number of supersymmetries are constrained by index theory. For near-horizon black hole geometries, this mechanism produces symmetry enhancement.
Fri, 01 Nov 2013

14:00 - 15:00
L5

Design principles and dynamics in clocks, cell cycles and signals

Professor David Rand
(University of Warwick)
Abstract

I will discuss two topics. Firstly, coupling of the circadian clock and cell cycle in mammalian cells. Together with the labs of Franck Delaunay (Nice) and Bert van der Horst (Rotterdam) we have developed a pipeline involving experimental and mathematical tools that enables us to track through time the phase of the circadian clock and cell cycle in the same single cell and to extend this to whole lineages. We show that for mouse fibroblast cell cultures under natural conditions, the clock and cell cycle phase-lock in a 1:1 fashion. We show that certain perturbations knock this coupled system onto another periodic state, phase-locked but with a different winding number. We use this understanding to explain previous results. Thus our study unravels novel phase dynamics of 2 key mammalian biological oscillators. Secondly, I present a radical revision of the Nrf2 signalling system. Stress responsive signalling coordinated by Nrf2 provides an adaptive response for protection against toxic insults, oxidative stress and metabolic dysfunction. We discover that the system is an autonomous oscillator that regulates its target genes in a novel way.

Fri, 01 Nov 2013

10:00 - 11:00
L5

TBA

Svenn Anton Halvorsen, Teknova
(Teknova)
Thu, 31 Oct 2013

17:15 - 18:15
L6

Positive characteristic version of Ax's theorem

Piotr Kowalski
(Wroclaw)
Abstract

Ax's theorem on the dimension of the intersection of an algebraic subvariety and a formal subgroup (Theorem 1F in "Some topics in differential algebraic geometry I...") implies Schanuel type transcendence results for a vast class of formal maps (including exp on a semi-abelian variety). Ax stated and proved this theorem in the characteristic 0 case, but the statement is meaningful for arbitrary characteristic and still implies positive characteristic transcendence results. I will discuss my work on positive characteristic version of Ax's theorem.

Thu, 31 Oct 2013

16:00 - 17:30
C6

D-modules: PDEs, flat connections, and crystals

Emily Cliff
Abstract

Motivated by the study of PDEs, we introduce the notion of a D-module on a variety X and give the basics of three perspectives on the theory: modules over the sheaf of differential operators on X; quasi-coherent modules with flat connection; and crystals on X. This talk will assume basic knowledge of algebraic geometry (such as rudimentary sheaf theory).

Thu, 31 Oct 2013

16:00 - 17:00
L3

Coherent Lagrangian vortices: The black holes of turbulence

George Haller
((ETH) Zurich)
Abstract

We discuss a simple variational principle for coherent material vortices

in two-dimensional turbulence. Vortex boundaries are sought as closed

stationary curves of the averaged Lagrangian strain. We find that

solutions to this problem are mathematically equivalent to photon spheres

around black holes in cosmology. The fluidic photon spheres satisfy

explicit differential equations whose outermost limit cycles are optimal

Lagrangian vortex boundaries. As an application, we uncover super-coherent

material eddies in the South Atlantic, which yield specific Lagrangian

transport estimates for Agulhas rings. We also describe briefly coherent

Lagrangian vortex detection to three-dimensional flows.

Thu, 31 Oct 2013

14:00 - 15:00
L4

Cluster combinatorics and geometrical models (part I)

Lisa Lamberti
(Oxford)
Abstract

In this talk I will give a definition of cluster algebra and state some main results.

Moreover, I will explain how the combinatorics of certain cluster algebras can be modeled in geometric terms.

Thu, 31 Oct 2013

14:00 - 15:00
L5

Don't be afraid of the 1001st (numerical) derivative

Professor Folkmar Bornemann
(Technical University Munich)
Abstract

The accurate and stable numerical calculation of higher-order

derivatives of holomorphic functions (as required, e.g., in random matrix

theory to extract probabilities from a generating function) turns out to

be a surprisingly rich topic: there are connections to asymptotic analysis,

the theory of entire functions, and to algorithmic graph theory.

Thu, 31 Oct 2013

13:00 - 14:00
L6

see below

James Newbury and Zhaoxu Hou
Abstract

\textbf{James Newbury} \newline

Title: Heavy traffic diffusion approximation of the limit order book in a one-sided reduced-form model. \newline

Abstract: Motivated by a zero-intelligence approach, we try to capture the

dynamics of the best bid (or best ask) queue in a heavy traffic setting,

i.e when orders and cancellations are submitted at very high frequency.

We first prove the weak convergence of the discrete-space best bid/ask

queue to a jump-diffusion process. We then identify the limiting process

as a regenerative elastic Brownian motion with drift and random jumps to

the origin.

\newline

\textbf{Zhaoxu Hou} \newline

Title: Robust Framework In Finance: Martingale Optimal Transport and

Robust Hedging For Multiple Marginals In Continuous Time

\newline

Abstract: It is proved by Dolinsky and Soner that there is no duality

gap between the robust hedging of path-dependent European Options and a

martingale optimal problem for one marginal case. Motivated by their

work and Mykland's idea of adding a prediction set of paths (i.e.

super-replication of a contingent claim only required for paths falling

in the prediction set), we try to achieve the same type of duality

result in the setting of multiple marginals and a path constraint.

Wed, 30 Oct 2013
16:00
C6

Learning spaces

Sophie Raynor
(University of Aberdeen)
Abstract

Working together with the Blue Brain Project at the EPFL, I'm trying to develop new topological methods for neural modelling. As a mathematician, however, I'm really motivated by how these questions in neuroscience can inspire new mathematics. I will introduce new work that I am doing, together with Kathryn Hess and Ran Levi, on brain plasticity and learning processes, and discuss some of the topological and geometric features that are appearing in our investigations.

Wed, 30 Oct 2013
11:30
Queen's College

Straight edge and compass to Origami

Robert Kropholler
Abstract

I will look at the classical constructions that can be made using a straight edge and compass, I will then look at the limits of these constructions. I will then show how much further we can get with Origami, explaining how it is possible to trisect an angle or double a cube. Compasses not supplied.

Tue, 29 Oct 2013

15:45 - 16:45
L4

Quasimaps, wall-crossings, and Mirror Symmetry II

Ionut Ciocan-Fontanine
(Minnesota)
Abstract

Quasimaps provide compactifications, depending on a stability parameter epsilon, for moduli spaces of maps from nonsingular algebraic curves to a large class of GIT quotients. These compactifications enjoy good properties and in particular they carry virtual fundamental classes. As the parameter epsilon varies, the resulting invariants are related by wall-crossing formulas. I will present some of these formulas in genus zero, and will explain why they can be viewed as generalizations (in several directions) of Givental's toric mirror theorems. I will also describe extensions of wall-crossing to higher genus, and (time permitting) to orbifold GIT targets as well.
The talk is based on joint works with Bumsig Kim, and partly also with Daewoong Cheong and with Davesh Maulik.

Tue, 29 Oct 2013

14:30 - 15:00
L5

Structure exploitation in Hessian computations

Patrick Farrell
(University of Oxford)
Abstract

Hessians of functionals of PDE solutions have important applications in PDE-constrained optimisation (Newton methods) and uncertainty quantification (for accelerating high-dimensional Bayesian inference).  With current techniques, a typical cost for one Hessian-vector product is 4-11 times the cost of the forward PDE solve: such high costs generally make their use in large-scale computations infeasible, as a Hessian solve or eigendecomposition would have costs of hundreds of PDE solves.

In this talk, we demonstrate that it is possible to exploit the common structure of the adjoint, tangent linear and second-order adjoint equations to greatly accelerate the computation of Hessian-vector products, by trading a large amount of computation for a large amount of storage. In some cases of practical interest, the cost of a Hessian-
vector product is reduced to a small fraction of the forward solve, making it feasible to employ sophisticated algorithms which depend on them.

Tue, 29 Oct 2013

14:30 - 15:30
C2

Hypergraph matchings

Peter Keevash
(University of Oxford)
Abstract

Perfect matchings are fundamental objects of study in graph theory. There is a substantial classical theory, which cannot be directly generalised to hypergraphs unless P=NP, as it is NP-complete to determine whether a hypergraph has a perfect matching. On the other hand, the generalisation to hypergraphs is well-motivated, as many important problems can be recast in this framework, such as Ryser's conjecture on transversals in latin squares and the Erdos-Hanani conjecture on the existence of designs. We will discuss a characterisation of the perfect matching problem for uniform hypergraphs that satisfy certain density conditions (joint work with Richard Mycroft), and a polynomial time algorithm for determining whether such hypergraphs have a perfect matching (joint work with Fiachra Knox and Richard Mycroft).

Tue, 29 Oct 2013

14:00 - 14:30
L5

Quantitative sparse signal recovery guarantees of nonconvex nonsmooth first-order methods

Coralia Cartis
(University of Oxford)
Abstract

Finding a sparse signal solution of an underdetermined linear system of measurements is commonly solved in compressed sensing by convexly relaxing the sparsity requirement with the help of the l1 norm. Here, we tackle instead the original nonsmooth nonconvex l0-problem formulation using projected gradient methods. Our interest is motivated by a recent surprising numerical find that despite the perceived global optimization challenge of the l0-formulation, these simple local methods when applied to it can be as effective as first-order methods for the convex l1-problem in terms of the degree of sparsity they can recover from similar levels of undersampled measurements. We attempt here to give an analytical justification in the language of asymptotic phase transitions for this observed behaviour when Gaussian measurement matrices are employed. Our approach involves novel convergence techniques that analyse the fixed points of the algorithm and an asymptotic probabilistic analysis of the convergence conditions that derives asymptotic bounds on the extreme singular values of combinatorially many submatrices of the Gaussian measurement matrix under matrix-signal independence assumptions.

This work is joint with Andrew Thompson (Duke University, USA).

Tue, 29 Oct 2013

14:00 - 15:00
L4

Quasimaps, wall-crossings, and Mirror Symmetry I

Ionut Ciocan-Fontanine
(Minnesota)
Abstract

Quasimaps provide compactifications, depending on a stability parameter epsilon, for moduli spaces of maps from nonsingular algebraic curves to a large class of GIT quotients. These compactifications enjoy good properties and in particular they carry virtual fundamental classes. As the parameter epsilon varies, the resulting invariants are related by wall-crossing formulas. I will present some of these formulas in genus zero, and will explain why they can be viewed as generalizations (in several directions) of Givental's toric mirror theorems. I will also describe extensions of wall-crossing to higher genus, and (time permitting) to orbifold GIT targets as well.
The talk is based on joint works with Bumsig Kim, and partly also with Daewoong Cheong and with Davesh Maulik.

Tue, 29 Oct 2013
00:00
Oxford-Man Institute

CANCELLED

CANCELLED
Mon, 28 Oct 2013

17:00 - 18:00
C5

Mixed Motives in Number Theory

Netan Dogra
Abstract

Mixed motives turn up in number theory in various guises. Rather than discuss the rather deep foundational questions involved, this talk will aim

to give several illustrations of the ubiquity of mixed motives and their realizations. Along the way I hope to mention some of: the Mordell-Weil

theorem, the theory of height pairings, special values of L-functions, the Mahler measure of a polynomial, Galois deformations and the motivic

fundamental group.