Mon, 08 Feb 2016

12:00 - 13:00
L5

Causality constraints on the graviton 3-point vertex

Jose Edelstein
(Santiago de Compostela)
Abstract

I will consider higher derivative corrections to the graviton 3-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond that of Einstein’s theory. I will argue that these structures are constrained by causality, and show that the problem cannot be fixed by adding conventional particles with spins J ≤ 2, but adding an infinite tower of massive particles with higher spins. Implications of this result in the context of AdS/CFT, quantum gravity in asymptotically flat space-times, and non-Gaussianity features of primordial gravitational waves are discussed.

 
 
 
Mon, 22 Feb 2016
16:30
C1

Congruence and non-congruence level structures on elliptic curves: a hands-on tour of the modular tower

Alexander Betts
((Oxford University))
Abstract
Classically, one puts an algebraic structure on certain "congruence" quotients of the upper half plane by interpreting them as spaces parametrising elliptic curves with certain level structures on their torsion subgroups. However, the non-congruence quotients don't admit such a straightforward description.
 
We will sketch the classical theory of congruence modular curves and level structures, and then discuss a preprint by W. Chen which extends the above notions to non-congruence modular curves by considering so-called Teichmueller level structures on the fundamental groups of punctured elliptic curves.
Mon, 08 Feb 2016

16:00 - 17:00
L4

Pseudo-differential operators on Lie groups

Veronique Fischer
(University of Bath)
Abstract
In this talk, I will present some recent developments in the theory of pseudo-differential operators on Lie groups. First I will discuss why `reasonable' Lie groups are the interesting manifolds where one can develop global symbolic pseudo-differential calculi. I will also give a brief overview of the analysis in the context of Lie groups. I will conclude with some recent works developing pseudo-differential calculi on certain classes of Lie groups.
Thu, 04 Feb 2016
15:00
L4

Basic aspects of n-homological algebra

Peter Jorgensen
(Newcastle)
Abstract

Abstract: n-homological algebra was initiated by Iyama
via his notion of n-cluster tilting subcategories.
It was turned into an abstract theory by the definition
of n-abelian categories (Jasso) and (n+2)-angulated categories
(Geiss-Keller-Oppermann).
The talk explains some elementary aspects of these notions.
We also consider the special case of an n-representation finite algebra.
Such an algebra gives rise to an n-abelian
category which can be "derived" to an (n+2)-angulated category.
This case is particularly nice because it is
analogous to the classic relationship between
the module category and the derived category of a
hereditary algebra of finite representation type.
 

Mon, 15 Feb 2016
15:45
L6

The Curved Cartan Complex

Constantin Teleman
(Oxford)
Abstract

  
The Cartan model computes the equivariant cohomology of a smooth manifold X with 
differentiable action of a compact Lie group G, from the invariant functions on 
the Lie algebra with values in differential forms and a deformation of the de Rham 
differential. Before extracting invariants, the Cartan differential does not square 
to zero. Unrecognised was the fact that the full complex is a curved algebra, 
computing the quotient by G of the algebra of differential forms on X. This 
generates, for example, a gauged version of string topology. Another instance of 
the construction, applied to deformation quantisation of symplectic manifolds, 
gives the BRST construction of the symplectic quotient. Finally, the theory for a 
X point with an additional quadratic curving computes the representation category 
of the compact group G.

Tue, 26 Jan 2016

12:00 - 13:15
L4

Elliptic polylogarithms and string amplitudes

Dr Erik Panzer
(Oxford)
Abstract
Recent results showed that the low energy expansion of closed superstring amplitudes can be expressed in terms of

single-valued multiple elliptic polylogarithms. I will explain how these functions may be defined as iterated integrals on the torus and

sketch how they arise from Feynman integrals.
Wed, 20 Jan 2016

11:00 - 12:30
S2.37

Bieberbach's Theorems

Robert Kropholler
(Oxford)
Abstract
I will go through a proof of Bieberbach's theorems proving that a group acting cocompactly on Euclidean n-space has a subgroup consisting of n independent translations. Time permitting I will also prove that there is a bound on the number of such groups for each dimension n. I will assume very little requiring only a small amount of group theory and linear algebra for the proofs. 
Tue, 01 Mar 2016
14:30
L6

Ramsey Classes and Beyond

Jaroslav Nešetřil
(Charles University, Prague)
Abstract

Ramsey classes may be viewed as the top of the line of Ramsey properties. Classical and not so classical examples of Ramsey classes of finite structures were recently extended by many new examples which make the characterisation of Ramsey classes  realistic (and in many cases known). Particularly I will cover recent  joint work with J. Hubicka.
 

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