Past Special Lecture

24 August 2017
15:00
Jeremy Rickard
Abstract

Abstract: If A is a finite dimensional algebra, and D(A) the unbounded
derived category of the full module category Mod-A, then it is
straightforward to see that D(A) is generated (as a "localizing
subcategory") by the indecomposable projectives, and by the simple 
modules. It is not so obvious whether it is generated by the 
indecomposable injectives. In 2001, Keller gave a talk in which he 
remarked that"injectives generate" would imply several of the well-known
homological conjectures, such as the Nunke condition and hence the 
generalized Nakayama
conjecture, and asked if there was any relation to the finitistic 
dimension conjecture. I'll show that an algebra that satisfies "injectives 
generate" also satisfies the finitistic dimension conjecture and discuss 
some examples. I'll present things in a fairly concrete way, so most of 
the talk won't assume much knowledge of derived categories.

 

24 August 2017
14:00
Lleonard Rubio y Degrassi
Abstract

Abstract: In this talk I will discuss the interplay between the local and
the global invariants in modular representation theory with a focus on the
first Hochschild cohomology $\mathrm{HH}^1(B)$ of a block algebra $B$. In
particular, I will show the compatibility between $r$-integrable 
derivations
and stable equivalences of Morita type. I will also show that if
$\mathrm{HH}^1(B)$ is a simple Lie algebra such that $B$ has a unique
isomorphism class of simple modules, then $B$ is nilpotent with an
elementary abelian defect group $P$ of order at least 3. The second part 
is joint work with M. Linckelmann.

24 August 2017
10:00
Sibylle Schroll (Leicester)
Abstract

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.

23 August 2017
16:45
Eleonore Faber (Michigan/Leeds)
Abstract

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.

23 August 2017
15:00
Nadia Mazza (Lancaster)
Abstract

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.

23 August 2017
14:00
Dave Benson (Aberdeen)
Abstract

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.

 

21 January 2017
13:00
to
18:00
Graduate Students CANCELLED
Abstract

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 InFoMM@maths.ox.ac.uk

21 January 2017
13:00
to
18:00
Abstract

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 InFoMM@maths.ox.ac.uk

6 September 2016
11:30
Volkan Cevher
Abstract

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.

Pages