Mon, 13 Mar 2017

09:30 - 10:30
L5

Surgery on manifolds: the early days

Terry Wall
(Liverpool)
Abstract

In 1956 Milnor published a paper proving that there are manifolds homeomorphic to the 7-sphere but not diffeomorphic to it. Seeking to generalise this example, he was led in around 1960 to introduce a construction for  killing homotopy groups of manifolds. When this was generalised to killing relative homotopy groups it became a general and powerful method of construction. An obstruction arises to killing the last group, and the analysis of this obstruction in general leads to a new theory.

Mon, 27 Feb 2017
15:45
L6

From moduli spaces of manifolds to K-theory

Ulrike Tillmann
(Oxford)
Abstract

For mapping class groups of surfaces it is well-understood that their homology stability is closely related to the fact that they give rise to an infinite loop space. Indeed, they define an operad whose algebras group complete to infinite loop spaces.

In recent work with Basterra, Bobkova, Ponto and Yaekel we define operads with homology stability (OHS) more generally and prove that they are infinite loop space operads in the above sense. The strong homology stability results of Galatius and Randal-Williams for moduli spaces of manifolds can be used to construct examples of OHSs. As a consequence the map to K-theory defined by the action of the diffeomorphisms on the middle dimensional homology can be shown to be a map of infinite loop spaces.

Mon, 06 Mar 2017

12:45 - 13:45
L3

Holographic renormalization and supersymmetry

Pietro Benetti-Genolini
(Oxford)
Abstract

Localization and holography are powerful approaches to the computation of supersymmetric observables. The computations may, however, include divergences. Therefore, one needs renormalization schemes preserving supersymmetry. I will consider minimal gauged supergravity in five dimensions to demonstrate that the standard holographic renormalization scheme breaks supersymmetry, and propose a set of non-standard boundary counterterms that restore supersymmetry. I will then show that for a certain class of solutions the improved on-shell action correctly reproduces an intrinsic observable of four-dimensional SCFTs, the supersymmetric Casimir energy.

 
Mon, 20 Feb 2017

12:45 - 13:45
L3

Dualities of Deformed N=2 SCFTs from torus knots and links

Fabian Ruehle
(Oxford)
Abstract

We study D3 brane theories that are described as deformations of N=2 SCFTs. They arise at the self-intersection of a 7-brane in F-Theory. As we shall explain, the associated string junctions and their monodromies can be studied via torus knots or links. The monodromy reduces (potentially different) flavor algebras of dual deformations of N=2 theories and projects out charged states, leading to N=1 SCFTs. We propose an explanation for these effects in terms of an electron-monopole-dyon condensate.

 
 
Wed, 15 Feb 2017
16:00
C2

Topological properties of some subsets of ßN

Dona Strauss
(Leeds)
Abstract

 Anyone who has worked in $\beta $N will not be surprised to learn that some of the algebraically defined subsets of $\beta N$ are not topologically simple, even though their algebraic definition may be very simple.  I shall show that the following subsets of $\beta N$ are not Borel: $N^*+N^*$; the smallest ideal of $\beta N$; the set of idempotents in $\beta N$; any semiprincipal right ideal in $\beta N$; the set of idempotents in any left ideal in $\beta N$.

Thu, 16 Feb 2017
11:00
C5

Model Theory of Shimura Varieties

Sebastian Eterovic
Abstract


Given a Shimura variety, I will show how to define a corresponding two-sorted structure. Based on work of Chris Daw and Adam Harris, we will study what is needed for the class of this structures to be categorical. Of course, an introduction to Shimura varieties will be given.
 

Thu, 16 Feb 2017
11:00
C5

Model Theory of Shimura Varieties

Sebastian Eterovic
Abstract


Given a Shimura variety, I will show how to define a corresponding two-sorted structure. Based on work of Chris Daw and Adam Harris, we will study what is needed for the class of this structures to be categorical. Of course, an introduction to Shimura varieties will be given.

In an interview with Rolling Stone Magazine in 1965, Bob Dylan was pushed to define himself: Do you think of yourself primarily as a singer or a poet? To which, Dylan famously replied: Oh, I think of myself more as a song and dance man, y’know. Dylan’s attitude to pigeonholing resonates with many applied mathematicians. I lack the coolness factor of Dylan, but if pushed about defining what kind of mathematician I am, I would say: Oh, I think myself more as an equation and matrix guy, y’know. 

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