Past

Question: Is it a realistic proposition for a mathematician to use his/her skills to make a living from sports betting? The introduction of betting exchanges have fundamentally changed the potential profitability of gambling, and a professional mathematician's arsenal of numerical and theoretical weapons ought to give them a huge natural advantage over most "punters", so what might be realistically possible and what potential risks are involved? This talk will give some idea of the sort of plan that might be required to realise this ambition, and what might be further required to attain the aim of sustainable gambling profitability.

We show that for every $n\ge 2$ there exists a torsion-free one-ended word-hyperbolic group $G$ of rank $n$ admitting generating $n$-tuples $(a_1,\ldots ,a_n)$ and $(b_1,\ldots ,b_n)$ such that the $(2n-1)$-tuples $$(a_1,\ldots ,a_n, \underbrace{1,\ldots ,1}_{n-1 \text{ times}})\hbox{ and }(b_1,\ldots, b_n, \underbrace{1,\ldots ,1}_{n-1 \text{ times}} )$$ are not Nielsen-equivalent in $G$. The group $G$ is produced via a probabilistic construction (joint work with Ilya Kapovich).

TQFTs have received widespread attention in recent years. In mathematics

for example due to Lurie's proof of the cobordism hypothesis. In physics

they are used as toy models to understand structure, especially

boundaries and defects.

I will present a lattice construction of 2d Spin TFT. This mostly

motivated as both a toy model and stepping stone for a mathematical

construction of rational conformal field theories with fermions.

I will first describe a combinatorial model for spin surfaces that

consists of a triangulation and a finte set of extra data. This model is

then used to construct TFT correlators as morphisms in a symmetric

monoidal category, given a Frobenius algebra as input. The result is

shown to be independent of the triangulation used, and one obtains thus

a 2dTFT.

All results and constructions can be generalised to framed surfaces in a

relatively straightforward way.

 This lecture will cover two recent works on the mock modular
forms of Ramanujan.

I. Solution of Ramanujan's original conjectures about these functions.
(Joint work with Folsom and Rhoades)

II. A new theorem that mock modular forms are "generating functions" for
central L-values and derivatives of quadratic twist L-functions.
(Joint work with Alfes, Griffin, Rolen).

Worst-case portfolio optimization has been introduced in Korn and Wilmott

(2002) and is based on distinguishing between random stock price

fluctuations and market crashes which are subject to Knightian

uncertainty. Due to the absence of full probabilistic information, a

worst-case portfolio problem is considered that will be solved completely.

The corresponding optimal strategy is of a multi-part type and makes an

investor indifferent between the occurrence of the worst possible crash

and no crash at all.

We will consider various generalizations of this setting and - as a very

recent result - will in particular answer the question "Is it good to save

for bad times or should one consume more as long as one is still rich?"

Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream. Distinct from stick-slip on northern hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be be controlled by fast processes at the bed and by tidally-induced stress. Modelling approaches to studying this phenomenon typically consider ice to be an elastically-deforming solid (e.g. Winberry et al, 2008; Sergienko et al, 2009). However, there remains a question of whether irreversible, i.e. viscous, deformation is important to the stick-slip process; and furthermore whether the details of stick-slip oscillations are important to ice stream evolution on longer time scales (years to decades).

To address this question I use two viscoelastic models of varying complexity. The first is a modification to the simple block-and-slider models traditionally used to examine earthquake processes on a very simplistic fashion. Results show that the role of viscosity in stick-slip depends on the dominant stress balance. These results are then considered in the context of a continuum description of a viscoelastic ice stream with a rate-weakening base capable of exhibiting stick-slip behavior. With the continuum model we examine the spatial and temporal aspects of stick-slip, their dependence on viscous effects, and how this behavior impacts the mean flow. Different models for the evolution of basal shear stress are examined in the experiments, with qualitatively similar results. A surprising outcome is that tidal effects, while greatly affecting the spectrum of the stick-slip cycle, may have relatively little effect on the mean flow.

In this talk, we will review the classical Bass-Serre theory of groups acting on trees and introduce its real version, Rips' theory. If time permits, I will briefly discuss some higher dimensional spaces that are currently being investigated, namely cubings and real cubings.

The plan: start with an introduction to several random matrix ensembles and discuss asymptotic properties of the eigenvalues of the matrices, the last one being the so-called "Normal Matrix Model", and the connection described in the title will be explained. If all goes well I will end with an explanation of asymptotic computations for a new normal matrix model example, which demonstrates a form of universality.

(NOTE CHANGE OF VENUE TO L2)

In this talk, two concepts are brought together: Algebras with triangular decomposition (as studied by Bazlov & Berenstein) and pointed Hopf algebra. The latter are Hopf algebras for which all simple comodules are one-dimensional (there has been recent progress on classifying all finite-dimensional examples of these by Andruskiewitsch & Schneider and others). Quantum groups share both of these features, and we can obtain possibly new classes of deformations as well as a characterization of them.

We propose a strategy which allows computing eigenvalue enclosures for the Maxwell operator by means of the finite element method. The origins of this strategy can be traced back to over 20 years ago. One of its main features lies in the fact that it can be implemented on any type of regular mesh (structured or otherwise) and any type of elements (nodal or otherwise). In the first part of the talk we formulate a general framework which is free from spectral pollution and allows estimation of eigenfunctions.

We then prove the convergence of the method, which implies precise convergence rates for nodal finite elements. Various numerical experiments on benchmark geometries, with and without symmetries, are reported.

We study the behavior of atomistic models under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to- continuum limit the minimal energy satisfies a particular cleavage law with quadratic response to small boundary displacements followed by a sharp constant cut-off beyond some critical value. Moreover, we show that the minimal energy is attained by homogeneous elastic configurations in the subcritical case and that beyond critical loading cleavage along specific crystallographic hyperplanes is energetically favorable. We present examples of mass spring models with full nearest and next-to-nearest pair interactions and provide the limiting minimal energy and minimal configurations.

Hrushovski-Martin-Rideau have proved rationality of Poincare series counting 
numbers of equivalence classes of a definable equivalence relation on the p-adic field (in connection to a problem on counting representations of groups). For this they have proved 
uniform p-adic elimination of imaginaries. Their work implies that these Poincare series are 
motivic. I will talk about their work.

I will introduce and motivate the concept of largeness of a group. I will then show how tools from different areas of mathematics can be applied to show that all free-by-cyclic groups are large (and try to convince you that this is a good thing).

Kazhdan introduced property (T) for locally compact topological groups to show that certain lattices in semisimple Lie groups are finitely generated. This talk will give an introduction to property (T) along with some first consequences and examples. We will finish with a classic application of property (T) due to Margulis: the first known construction of expanders.

We consider the parameter $a(H)$, which is the smallest a such that if $|E(G)|$ is at least/exceeds $a|V(H)|/2$ then $G$ has an $H$-minor. We are especially interested in sparse $H$ and in bounding $a(H)$ as a function of $|E(H)|$ and $|V(H)|$. This is joint work with David Wood.

It is often difficult to include sufficient biological detail when modelling cell population growth to make models with real predictive power. Continuum models often fail to capture physical and chemical processes happening at the level of individual cells and discrete cell-based models are often very computationally expensive to solve. In the first part of this talk, I will describe a phenomenological continuum model of cell aggregate growth in a specific perfusion bioreactor cell culture system, and the results of numerical simulations of the model to determine the effects of the bioreactor operating conditions and cell seeding on the growth. In the second part of the talk, I will introduce a modelling approach used to derive continuum models for cell population growth from discrete cell-based models, and consider possible extensions to this framework.

This will be an informal discussion developing the details of the Amplituhedron for the loop integrand.

The 'pyjama stripe' is the subset of the plane consisting of a vertical

strip of width epsilon about every integer x-coordinate. The 'pyjama

problem' asks whether finitely many rotations of the pyjama stripe about

the origin can cover the plane.

I'll attempt to outline a solution to this problem. Although not a lot

of this is particularly representative of techniques frequently used in

additive combinatorics, I'll try to flag up whenever this happens -- in

particular ideas about 'limit objects'.