Ninety Seventh Meeting of the
University of Sheffield
Friday 27 November 2015
The talks will take place in Lecture Theatre 6 on floor E of the Hicks
Building. Tea/coffee will be in the Common Room (I15) on I floor of the
There are various places for lunch - follow a group of locals if in doubt.
A group is likely to be going for drinks and an early dinner after the last talk - all are welcome to join.
|12:00-13:00||Fionntan Roukema (Sheffield)|
A DIY exceptional pair construction kit
|14:00 - 15:00||André Henriques (Oxford and Utrecht)|
Representation theory for fusion categories
|15:00 - 16:00||Tea/coffee|
|16:00 - 17:00||David Pauksztello (Manchester)|
Silting pairs and stability conditions
Abstracts of talks
Fionntan Roukema (Sheffield): A DIY exceptional pair construction kit
exterior of the minimally twisted four chain link contains two properly
embedded annuli, a properly embedded torus, and the open three chain
link is a trivial surgery on each component. Thus, it is fertile ground
for growing 3-manifolds with properly embedded topological surfaces
with non-negative Euler characteristic and small Seifert spaces.
will visually see how the four chain link can be obtained by surgery on
a hyperbolic chain link in multiple ways. Via some lovely pictures, and
some boring GCSE algebra, we will develop a DIY kit for building
hyperbolic manifolds with pairs/triples/quadruples/quintuples/sextuples of non-hyperbolic fillings with specified topological obstructions to hyperbolicity.
The simple construction we present will produce all (known) examples of certain exceptional pairs.
André Henriques (Oxford and Utrecht): Representation theory for fusion categories
Given a finite group G then, by definition, EG denotes a contractible G-space with free action.
me start by describing a question. The question is not well-defined but
its answer is nevertheless interesting. If one restricts attention
to linear representations of G, what is that best possible
approximation to the notion "EG"? We would like the answer to be: each
irrep of G arises in the representation with infinite multiplicity.
This is called a "universal representation" of G, also known as a
"complete G-universe". If V is a universal representation
in particular, the subset of vectors v in V whose orbit is free is
contractible. So a universal representation does indeed look a little
bit like EG. If one restricts attention to unitary representations on
Hilbert spaces, then universal representations are unique up to
contractible space of choice in the following strong sense: there is
only one such representation up to isomorphism, and the automorphism
group of the representation is contractible.
goal of this talk is to explore analogous notions to the ones presented
above when the group G is replaced by a fusion category (a semisimple
tensor category with finitely many simple objects). A representation of
a fusion category C consists of a ring R and a tensor functor C -->
Bim(R) to the category of R-R-bimodules. We will see that every fusion
category admits a left regular representation (coming from the left
action of C on itself). We will then describe what we believe to be a
universal representation of C. We conjecture is that this
representation is unique up to isomorphism, and also unique up to
contractible space of choices. However, unlike in the case of finite
group, that representation is not a direct sum of smaller
David Pauksztello (Manchester): Silting pairs and stability conditions
This will be a report on joint work with Nathan Broomhead and David
Ploog. The notion of a silting object is a generalisation of tilting
object, which turns up in the context of derived equivalences. Silting
objects come equipped with a rich combinatorial structure, which is
related to mutation in cluster theory. In this talk, we shall discuss a
CW complex arising from silting objects and their connection to the
space of Bridgeland stability conditions for certain algebraic examples.
Everyone who wishes to participate is welcome, particularly
postgraduate students. The usual criteria for
assistance with travel expenses apply. Beneficiaries will need to
complete the standard forms, which are available at the