Past

I will start with a quick reminder of what we have learned so far about
transplanckian-energy collisions of particles, strings and branes.
I will then address the (so-far unsolved) problem of gravitational
bremsstrahlung from massless particle collisions at leading order in the
gravitational deflection angle.
Two completely different calculations, one classical and one quantum, lead
to the same final, though somewhat puzzling, result.

For liquid films with a thickness in the order of 10¹−10³ molecule layers, classical models of continuum mechanics do not always give a precise description of thin-film evolution: While morphologies of film dewetting are captured by thin-film models, discrepancies arise with respect to time-scales of dewetting.

In this talk, we study stochastic thin-film equations. By multiplicative noise inside an additional convective term, these stochastic partial differential equations differ from their deterministic counterparts, which are fourth-order degenerate parabolic. First, we present some numerical simulations which indicate that the aforementioned discrepancies may be overcome under the influence of noise.

In the main part of the talk, we prove existence of almost surely nonnegative martingale solutions. Combining spatial semi-discretization with appropriate stopping time arguments, arbitrary moments of coupled energy/entropy functionals can be controlled.

Having established Hölder regularity of approximate solutions, the convergence proof is then based on compactness arguments - in particular on Jakubowski’s generalization of Skorokhod’s theorem - weak convergence methods, and recent tools for martingale convergence.

The results have been obtained in collaboration with K. Mecke and M. Rauscher and with J. Fischer, respectively

This talk concerns a twenty-thousand-year old mistake: The natural numbers record only the result of counting and not the process of counting. As algebra is rooted in the natural numbers, the higher algebra of Joyal and Lurie is rooted in a more basic notion of number which also records the process of counting. Long advocated by Waldhausen, the arithmetic of these more basic numbers should eliminate denominators. Notable manifestations of this vision include the Bökstedt-Hsiang-Madsen topological cyclic homology, which receives a denominator-free Chern character, and the related Bhatt-Morrow-Scholze integral p-adic Hodge theory, which makes it possible to exploit torsion cohomology classes in arithmetic geometry. Moreover, for schemes smooth and proper over a finite field, the analogue of de Rham cohomology in this setting naturally gives rise to a cohomological interpretation of the Hasse-Weil zeta function by regularized determinants as envisioned by Deninger.

We consider L^2-approximations of white noise within the framework of regularity structures. Possible applications include support theorems for SPDEs driven by degenerate noises and numerics. Joint work with Ilya Chevyrev, Peter Friz and Tom Klose. 

We give new obstructions to the existence of planar open books on contact structures, in terms of the homology of their fillings. I will talk about applications to links of surface singularities, Seifert fibred spaces, and integer homology spheres. No prior knowledge of contact or symplectic topology will be assumed. This is joint work with Paolo Ghiggini and Olga Plamenevskaya.
 

This talk is based on a joint work with Dmitry Beliaev.

We study the volume distribution of nodal domains of families of naturally arising Gaussian random field on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.

We discuss mathematical studies on the Vafa-Witten theory, one of topological twists of N=4 super Yang-Mills theory in four dimensions, from the viewpoints of both differential and algebraic geometry. After mentioning backgrounds and motivation, we describe some issues to construct mathematical theory of this Vafa-Witten one, and explain possible ways to sort them out by analytic and algebro-geometric methods, the latter is joint work with Richard Thomas.

In this year’s Simonyi Lecture, Geoffrey West discusses the universal laws that govern everything from the growth of plants and animals to cities and corporations. These laws help us to answer big, urgent questions about global sustainability, population explosion, urbanization, ageing, cancer, human lifespans and the increasing pace of life.

Why can we live for 120 years but not for a thousand? Why do mice live for just two or three years and elephants for up to 75? Why do companies behave like mice, and are they all destined to die? Do cities, companies and human beings have natural, pre-determined lifespans?

Geoffrey West is a theoretical physicist whose primary interests have been in fundamental questions in physics and biology. West is a Senior Fellow at Los Alamos National Laboratory and a distinguished professor at the Sante Fe Institute, where he served as the president from 2005-2009. In 2006 he was named to Time’s list of The 100 Most Influential People in the World.

This lecture will take place at the Oxford Playhouse, Beaumont Street. Book here

I will describe our research on numerical methods for atmospheric dynamical cores based on compatible finite element methods. These methods extend the properties of the Arakawa C-grid to finite element methods by using compatible finite element spaces that respect the elementary identities of vector-calculus. These identities are crucial in demonstrating basic stability properties that are necessary to prevent the spurious numerical degradation of geophysical balances that would otherwise make numerical discretisations unusable for weather and climate prediction without the introduction of undesirable numerical dissipation. The extension to finite element methods allow these properties to be enjoyed on non-orthogonal grids, unstructured multiresolution grids, and with higher-order discretisations. In addition to these linear properties, for the shallow water equations, the compatible finite element structure can also be used to build numerical discretisations that respect conservation of energy, potential vorticity and enstrophy; I will survey these properties. We are currently developing a discretisation of the 3D compressible Euler equations based on this framework in the UK Dynamical Core project (nicknamed "Gung Ho"). The challenge is to design discretisation of the nonlinear operators that remain stable and accurate within the compatible finite element framework. I will survey our progress on this work to date and present some numerical results.

Feedback control is found extensively in many natural and technological systems. Indeed, many biological processes use feedback
to regulate key processes – examples include bacterial chemotaxis and negative autoregulation in genetic circuits. Despite the prevalence of
feedback in natural systems, its design and implementation in a Synthetic Biological context is much harder.  In this talk I will give
examples of how we implemented feedback systems in three different biological systems. The first one concerns the design of a synthetic
recombinase-based feedback loop, which results into robust expression. The second describes the use of small RNAs to post-transcriptionally
regulate gene expression through interaction with messenger RNA (mRNA). The third involves the introduction of negative feedback in a
two-component signalling system through a controllable phosphatase.  Closing, I will outline the challenges posed by the design of such
systems, both theoretical and on their implementation.

Rita Maria del Rio Chanona:

Global financial contagion on a Multiplex Network

We explore the global financial system, in particular the risk of global financial contagion through network theory. Although there is extensive literature on contagion in networks, we argue that it is important to consider different channels of contagion. Therefore we deem into the multilayer framework, where nodes are countries and each layer represents a different type of financial obligation. The multiplex network is built using data provided by collaborators in the IMF. We study contagion with a percolation model and conclude that financial shocks can be amplified considerably when the multilayer structure is taken into account.


Johannes Wiesel:

Robust Superhedging vs Robust Statistics

In this talk I try to reconcile the different understanding of robustness in mathematical finance and statistics. Motivated by recent advances in the estimation of risk measures, I present estimators for the superhedging price of a claim given a history of observed prices. I discuss weak efficiency and convergence speed of these estimators. Besides I explain how to apply classical notions of sensitivity for the estimation procedure. This talk is based on ongoing work with Jan Obloj.

 

Railway traffic management is the combination of monitoring the progress of trains, forecasting of the likely future progression of trains, and evaluating the impact of intervention options in near real time in order to make traffic adjustments that minimise the combined delay of trains when measured against the planned timetable.

In a time of increasing demand for rail travel, the desire to maximise the usage of the available infrastructure capacity competes with the need for contingency space to allow traffic management when disruption occurs. Optimisation algorithms and decision support tools therefore need to be increasingly sophisticated and traffic management has become a crucial function in meeting the growing expectations of rail travellers for punctuality and quality of service.

Resonate is a technology company specialising in rail and connected transport solutions. We have embarked on a drive to maximise capacity and performance through the use of mathematical, statistical, data-driven and machine learning based methods driving decision support and automated traffic management solutions.

Manifolds, the main objects of study in Differential Geometry, do not have nice categorical properties. For example, the category of manifolds with smooth maps does not contain all fibre products.
The algebraic counterparts to this (varieties and schemes) do have nice categorical properties. 

A method to ‘fix’ these categorical issues is to consider C^infinity schemes, which generalise the category of manifolds using algebraic geometry techniques. I will explain these concepts, and how to translate to manifolds with corners, which is joint work with my supervisor Professor Dominic Joyce.

Phytoplankton moving in the ocean, spermatozoa making their way  through the female reproductive tract and harmful bacteria that form biofilms on implanted medical devices interact with a surrounding fluid. Their length scales are small enough so that viscous effects dominate inertial effects allowing the resulting fluid dynamics to be described by the linear Stokes equations. However,  nonlinear behavior can occur because these structures are flexible and their form evolves with the flow. In addition, the fluid environment may also  be complex because of embedded microstructures that further complicate the dynamics.  We will discuss recent successes and challenges in describing these elastohydrodynamic systems.

This talk will report on the definition of some motivic cohomology classes and the proof that they satisfy the norm relations expected of Euler systems, emphasizing a connection with the local Gan-Gross-Prasad conjecture.

 In the first part of the talk, we present some recent and new developments in the theory of control and optimal stopping with nonlinear expectations. We first introduce an optimal stopping game with nonlinear expectations (Generalized Dynkin Game) in a non-Markovian framework and study its links with nonlinear doubly reflected BSDEs. We then present some new results (which are part of an ongoing work) on mixed stochastic stochastic control/optimal stopping problems (as well as stochastic control/optimal stopping game problems) in a non-Markovian framework and their relation with constrained reflected BSDEs with lower obstacle (resp. upper obstacle). These results are obtained using some technical tools of stochastic analysis. In the second part of the talk, we discuss applications to the $\cal{E}^g$ pricing of American options and Game options in complete and incomplete markets (based on joint works with M.C.Quenez and Agnès Sulem).
 

Because of atmospheric turbulence, images of objects in outer space acquired via ground-based telescopes are usually blurry.  One way to estimate the blurring kernel or point spread function (PSF) is to make use of the aberration of wavefront received at the telescope, i.e., the phase. However only the low-resolution wavefront gradients can be collected by wavefront sensors. In this talk, I will discuss how to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase and the PSF in high accuracy. I will end by relating the problem to high-resolution image reconstruction and methods for solving it.
Joint work with Rui Zhao and research supported by HKRGC.

In this talk I will discuss acoustic and electromagnetic transmission problems; i.e. problems where the wave speed jumps at an interface. I will focus on what is known mathematically about resonances and trapped waves (e.g. When do these occur? When can they be ruled out? What do we know in each case?). This is joint work with Andrea Moiola (Pavia).

Can mathematics really help us in our fight against infectious disease? Join Julia Gog as we explore some exciting current research areas where mathematics is being used to study pandemics, viruses and everything in between, with a particular focus on influenza.

Julia Gog is Professor of Mathematical Biology, University of Cambridge and David N Moore Fellow at Queens’ College, Cambridge.

Please email: @email to regsiter

Classifying line arrangements on the plane is a problem that has been around for a long time. There has been a lot of work from the perspective of incidence geometry, but after a paper of Hirzebruch in in 80's, it has also attracted the attention of algebraic geometers for the applications that it has on classifying complex algebraic surfaces of general type. In this talk I will present various results around this problem, I will show some specific questions that are still open, and I will explain how it relates to complex surfaces of general type. 
 

It is well known that the theory of differentially closed fields of characteristic 0 has prime models and that they are unique up to isomorphism. One can ask the same question for the theory ACFA of existentially closed difference fields (recall that a difference field is a field with an automorphism).

In this talk, I will first give the trivial reasons of why this question cannot have a positive answer. It could however be the case that over certain difference fields prime models (of the theory ACFA) exist and are unique. Such a prime model would be called a difference closure of the difference field K. I will show by an example that the obvious conditions on K do not suffice.

I will then consider the class of aleph-epsilon saturated models of ACFA, or of kappa-saturated models of ACFA. There are natural notions of aleph-epsilon prime model and kappa-prime model. It turns out that for these stronger notions, if K is an algebraically closed difference field of characteristic 0, with fixed subfield F aleph-epsilon saturated, then there is an aleph-epsilon prime model over K, and it is unique up to K-isomorphism. A similar result holds for kappa-prime when kappa is a regular cardinal.

None of this extends to positive characteristic.
 

We consider a generalization of degeneracy loci of morphisms between vector bundles based on orbit closures of algebraic groups in their linear representations. Using a certain crepancy condition on the orbit closure we gain some control over the canonical sheaf in a preferred class of examples. This is notably the case for Richardson nilpotent orbits and partially decomposable skew-symmetric three-forms in six variables. We show how these techniques can be applied to construct Calabi-Yau manifolds and Fano varieties of dimension three and four.

This is a joint work with Vladimiro Benedetti, Laurent Manivel and Fabio Tanturri.

We provide the rate of convergence of general monotone numerical schemes for parabolic Hamilton-Jacobi-Bellman equations in bounded domains with Dirichlet boundary conditions. The so-called "shaking coefficients" technique introduced by Krylov is used. This technique is based on a perturbation of the dynamics followed by a regularization step by convolution. When restricting the equation to a domain, the perturbed problem may not satisfy such a restriction, so that a special treatment near the boundary is necessary.