Past Special Lecture

Abstract: In this talk, we will introduce new affine algebraic varieties 
for algebras given by quiver and relations. Each variety contains a 
distinguished element in the form of a monomial algebra. The properties 
and characteristics of this monomial algebra govern those of all other 
algebras in the variety. We will show how amongst other things this gives 
rise to a new way to determine whether an algebra is quasi-hereditary. 
This is a report on joint work both with Ed Green and with Ed Green and 
Lutz Hille.

Abstract: This is joint work with Ragnar-Olaf Buchweitz and Colin Ingalls. 
The classical McKay correspondence relates the geometry of so-called 
Kleinian surface singularities with the representation theory of finite 
subgroups of SL(2,C). M. Auslander observed an algebraic version of this 
correspondence: let G be a finite subgroup of SL(2,K) for a field K whose
characteristic does not divide the order of G. The group acts linearly on 
the polynomial ring S=K[x,y] and then the so-called skew group algebra
A=G*S can be seen as an incarnation of the correspondence. In particular
A is isomorphic to the endomorphism ring of S over the corresponding 
Kleinian surface singularity.
Our goal is to establish an analogous result when G in GL(n,K) is a finite 
subgroup generated by reflections, assuming that the characteristic
of K does not divide the order of the group. Therefore we will consider a 
quotient of the skew group ring A=S*G, where S is the polynomial ring in n 
variables. We show that our construction yelds a generalization of 
Auslander's result, and moreover, a noncommutative resolution of the 
discriminant of the reflection group G.

Abstract: Joint work with Carlson, Grodal, Nakano. In this talk we will
present some recent results on an 'important' class of modular 
representations for an 'important' class of finite groups. For the 
convenience of the audience, we'll briefly review the notion of an 
endotrivial module and present the main results pertaining endotrivial 
modules and finite reductive groups which we use in our ongoing work.

I shall describe recent work with Srikanth Iyengar, Henning 
Krause and Julia Pevtsova on the representation theory and cohomology
of finite group schemes and finite supergroup schemes. Particular emphasis 
will be placed on the role of generic points, detection of projectivity
for modules, and detection modulo nilpotents for cohomology.

 

In Your Third Year & want to find out about opportunities for

summer placements and future graduate study?

Why not visit Oxford and hear from graduate students about their research

TALKS ON

Dynamics of jumping elastic toys

Vertex models in developmental biology

Modelling of glass sheets

Glimpse into the mathematics of information

Network analysis of consumer data

Complex singularities in jet and splash flows

Complementary Lunch & Drinks Reception - TRAVEL BURSARIES AVAILABLE (up to £50)

Please RSVP to @email

In Your Third Year & want to find out about opportunities for summer placements and future graduate study?

Why not visit Oxford and hear from graduate students about their research

Saturday 21 January 2017: 1-6pm

Mathematical Institute, University of Oxford

TALKS ON

• Dynamics of jumping elastic toys
• Vertex models in developmental biology
• Modelling of glass sheets
• Glimpse into the mathematics of information
• Network analysis of consumer data
• Complex singularities in jet and splash flows

Complementary Lunch & Drinks Reception - TRAVEL BURSARIES AVAILABLE (up to £50)

Please RSVP to @email

Bayesian optimization (BO) is a powerful tool for sequentially optimizing black-box functions that are expensive to evaluate, and has extensive applications including automatic hyperparameter tuning, environmental monitoring, and robotics. The problem of level-set estimation (LSE) with Gaussian processes is closely related; instead of performing optimization, one seeks to classify the whole domain according to whether the function lies above or below a given threshold, which is also of direct interest in applications.

In this talk, we present a new algorithm, truncated variance reduction (TruVaR) that addresses Bayesian optimization and level-set estimation in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs, non-uniform noise, and multi-task settings. We provide a general theoretical guarantee for TruVaR covering these phenomena, and use it to obtain regret bounds for several specific settings. We demonstrate the effectiveness of the algorithm on both synthetic and real-world data sets.

In his talk, Kerry will explore the pressing practical problem of how hurricane activity will respond to global warming, and how hurricanes could in turn be influencing the atmosphere and ocean.

In his talk, Kerry will explore the pressing practical problem of how hurricane activity will respond to global warming, and how hurricanes could in turn be influencing the atmosphere and ocean

For full details please visit:

http://blogs.bodleian.ox.ac.uk/adalovelace/files/2015/10/Ada-Lovelace-S…

In 1943 Fisher, together with Corbet and Williams, published a study on the relation between the number of species and the number of individuals, which has since been recognized as one of the most influential papers in 20th century ecology. It was a combination of empirical work backed up by a simple theoretical argument, which describes a sort of universal law governing random partitions, such as the celebrated Ewens partition whose original derivation flows from the Fisher-Wright model. This talk will discuss several empirical studies of a similar sort, including Taylor's law and recent work related to Fairfield-Smith's work on the variance of spatial averages.

There is a pleasing correspondence between splittings of a free group over finitely generated subgroups and systems of surfaces in a doubled handlebody. One can use this to describe a family of hyperbolic complexes on which Out(F_n) acts. This is joint work with Camille Horbez.

Two subsets A and B of R^n are equidecomposable if it is possible to partition A into pieces and rearrange them via isometries to form a partition of B. Motivated by what is nowadays known as Banach-Tarski paradox, Tarski asked if the unit square and the disc of unit area in R^2 are equidecomposable. 65 years later Laczkovich showed that they are, at least when the pieces are allowed to be non-measurable sets. I will talk about a joint work with A. Mathe and O. Pikhurko which implies in particular the existence of a measurable equidecomposition of circle and square in R^2.

Divergence, thickness, and relative hyperbolicity are three geometric properties which determine aspects of the quasi-isometric geometry of a finitely generated group. We will discuss the basic properties of these notions and some of the relations between them. We will then then survey how these properties manifest in right-angled Coxeter groups and detail various ways to classify Coxeter groups using them.

This is joint work with Hagen and Sisto.

“Narrative and Proof”, is an interdisciplinary discussion where one of the UK's leading scientists, Marcus du Sautoy, will argue that mathematical proofs are not just number-based, but also rely on narrative. He will be joined by author Ben Okri, mathematician Roger Penrose, and literature expert Laura Marcus, to consider how narrative shapes the sciences as well as the arts.

The discussion will be chaired by Elleke Boehmer, Professor of World Literature in English, University of Oxford, and will be followed by audience questions and a drinks reception.

The event will take place from 5 to 6:30 pm on Tuesday 20 January 2015 at the Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford. The event is free and open to all, but registration is recommended. 

Please click here to register.

This event is co-hosted by the Mathematical Institute and The Oxford Research Centre in the Humanities (TORCH), and celebrates the launch of TORCH’s Annual Headline Series 2014-15, Humanities and Science.
 

In highly concentrated surfactant solutions the surfactant molecules self-assemble into long flexible "wormy" structures. Properties of these wormlike micellar solutions make them ideal for use in oil recovery and in body care products (shampoo). These properties depend strongly on temperature and concentration conditions.   In solution the "worms" entangle, forming a network, but also continuously break and reform, thus earning the name ‘living polymers’. In flow these fluids exhibit spatial inhomogeneities,  shear-banding, and dynamic elastic recoil. In this talk a rheological equation of state that is capable of describing these fluids is described   The resultant governing  macroscale equations consist of a coupled nonlinear partial differential equation system.  Model predictions are presented, contrasted with experimental results, and contrasted with predictions of other existing models.  Generalizations of the model to allow the capturing of  behaviors under changing concentration or temperature conditions, namely power law and stretched exponential relaxation as opposed to exponential relaxation, will be discussed and  particularly a mesoscale stochastic simulation network model will be presented.  

This talk is based on a joint work with B. Rémy (Lyon) in which we study some subgroups of topological Kac–Moody groups and the implications of this study on the subgroup structure of the ambient Kac–Moody group.

In this talk we will discuss when one right-angled Artin group is a subgroup of another one and explain how this basic algebraic problem may provide answers to questions in geometric group theory and model theory such as classification of right-angled Artin groups up to quasi-isometries and universal equivalence.

We know since almost a century that a ball can be decomposed into five pieces and these pieces rearranged so as to produce two balls of the same size as the original. This apparent paradox has led von Neumann to the notion of amenability which is now much studied in many areas of mathematics. However, the initial paradox has remained tied down to an elementary property of free groups of rotations for most of the 20th century. I will describe recent progress leading to new paradoxical groups.

 “Understanding the generation and control of pattern and form is still a challenging and major problem in the biomedical sciences. I shall describe three very different problems. First I shall briefly describe the development and application of the mechanical theory of morphogenesis and the discovery of morphogenetic laws in limb development and how it was used to move evolution backwards. I shall then describe a surprisingly informative model, now used clinically, for quantifying the growth of brain tumours, enhancing imaging techniques and quantifying individual patient treatment protocols prior to their use.  Among other things, it is used to estimate patient life expectancy and explain why some patients live longer than others with the same treatment protocols. Finally I shall describe an example from the social sciences which quantifies marital interaction that is used to predict marital stability and divorce.  From a large study of newly married couples it had a 94% accuracy. I shall show how it has helped design a new scientific marital therapy which is currently used in clinical practice.”