Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
23 November 2017

l-adic cohomology was built to provide an etale cohomology with coefficients in a field of characteristic 0. This, via the Grothendieck trace formula, gives  a cohomological interpretation of L-functions - a fundamental tool in Deligne's theory of weights developed in Weil II. Instead of l-adic coefficients one can consider coefficients in ultra products of finite fields. I will state the fundamental theorem of Weil II for curves in this setting and explain briefly what are the difficulties to overcome to adjust Deligne's proof. I will then discuss how this ultra product variant of Weil II allows to extend to arbitrary coefficients  previous results of Gabber and Hui, Tamagawa and myself for constant $\mathbb{Z}_\ell$-coefficients.  For instance,  it implies that, in an $E$-rational compatible system of smooth $\overline{\mathbb{Q}}_\ell$-sheaves all what is true for $\overline{\mathbb{Q}}_\ell$-coefficients (semi simplicity, irreducibility, invariant dimensions etc) is true for $\overline{\mathbb{F}}_\ell$-coefficients provided $\ell$ is large enough or that the $\overline{\mathbb{Z}}_\ell$-models are unique with torsion-free cohomology provided $\ell$ is large enough.

  • Number Theory Seminar
23 November 2017
Alexander Bradley

It is thought that the hairy legs of water walking arthropods are able to remain clean and dry because the flexibility of the hairs spontaneously moves drops off the hairs. We present a mathematical model of this bending-induced motion, or bendotaxis, and study how it performs for wetting and non-wetting drops. Crucially, we show that both wetting and non-wetting droplets move in the same direction (using physical arguments and numerical solutions). This suggests that a surface covered in elastic filaments (such as the hairy leg of insects) may be able to universally self-clean. To quantify the efficiency of this effect, we explore the conditions under which drops leave the structure by ‘spreading’ rather than translating and also how long it takes to do so.

  • Industrial and Applied Mathematics Seminar
24 November 2017
Professor Julia Gog

This will be a whistle-stop tour of a few topics on infectious disease modelling, mainly influenza. Topics to include:

  • challenges in capturing dynamics of pathogens with multiple co-circulating strains
  • untangling the 2009 influenza pandemic from medical insurance claims data from the US
  • bioinformatic methods to detect viral packaging signals
  • and a big science project (top secret until the talk!)

Julia will be visiting the Mathematical Institute on sabbatical this term, and hopes this talk will help us find areas of overlapping interests.

  • Mathematical Biology and Ecology Seminar
24 November 2017
Richard Wade and Andrey Kormilitzin

Richard Wade:   Classifying spaces, automorphisms, and right-angled Artin groups 

Right-angled Artin groups (otherwise known as partially commutative groups, or graph groups), interpolate between free abelian groups and free groups. These groups have seen a lot of attention recently, much of this due to some surprising links to the world of hyperbolic 3-manifolds.We will look at classifying spaces for such groups and their associated automorphism groups. These spaces are useful as they give a topological way to understand algebraic invariants of groups. This leads us to study some beautiful mathematical objects: deformation spaces of tori and trees. We will look at some recent results that aim to bridge the gap between these two families of spaces.
Andrey Kormilitzin:   Learning from electronic health records using the theory of rough paths

In this talk, we bring the theory of rough paths to the study of non-parametric statistics on streamed data and particularly to the problem of regression and classification, where the input variable is a stream of information, and the dependent response is also (potentially) a path or a stream.  We informally explain how a certain graded feature set of a stream, known in the rough path literature as the signature of the path, has a universality that allows one to characterise the functional relationship summarising the conditional distribution of the dependent response. At the same time this feature set allows explicit computational approaches through machine learning algorithms.

Finally, the signature-based modelling can be applied to some real-world problems in medicine, in particular in mental health and gastro-enterology.

27 November 2017

In this talk, we will discuss about some recent results of optimal investment problems and related backward stochastic differential equations (BSDE).

In the first part, we will solve utility maximization with (unbounded) random endowments by using the tools from quadratic BSDE with unbounded terminal data. This will in turn solve a long-term outstanding problem about utility indifference valuation of unbounded payoffs (e.g. call options). Joint work with Ying Hu and Shanjian Tang.  

In the second part, we will present a new class of dynamic utilities, called forward performance criteria, firstly introduced by Musiela and Zariphopoulou. We will show how they can be constructed by using ergodic BSDE and infinite horizon BSDE. As an application, we will study the large maturity behavior of (forward) entropic risk measures. Joint work with Alfred Chong, Ying Hu and Thaleia Zariphopoulou.

  • Stochastic Analysis Seminar


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