Prof. Ursula Martin and Dr Ian Griffiths have each been awarded an MPLS Impact Award for 2017-18. The MPLS (Mathematical, Physical, Engineering and Life Sciences Division at the University of Oxford) Impact Awards scheme aims to foster and raise awareness of impact by rewarding it at a local level.
Canonical reduction of stabilizers for stacks with good moduli spaces
Abstract
Some natural moduli problems give rise to stacks with infinite stabilizers. I will report on recent work with Dan Edidin where we give a canonical sequence of saturated blow-ups that makes the stabilizers finite. This generalizes earlier work in GIT by Kirwan and Reichstein, and on toric stacks by Edidin-More. Time permitting, I will also mention a recent application to generalized Donaldson-Thomas invariants by Kiem-Li-Savvas.
Algebraic integers arising as stretch factors of surface homemorphisms
Abstract
I will talk about the properties of algebraic integers that can arise as stretch factors of pseudo-Anosoc maps. I will mention a conjecture of Fried on which numbers supposedly arise and Thurston’s theorem that proves a similar result in the context of automorphisms of free groups. Then I will talk about recent developments on the Fried conjecture namely, every Salem number has a power arising as a stretch factor.
Short Laws for Finite Groups and Residual Finiteness Growth
Abstract
A law for a group G is a non-trivial equation satisfied by all tuples of elements in G. We study the length of the shortest law holding in a finite group. We produce new short laws holding (a) in finite simple groups of Lie type and (b) simultaneously in all finite groups of small order. As an application of the latter we obtain a new lower bound on the residual finiteness growth of free groups. This talk is based on joint work with Andreas Thom.
14:00
Falcon: Compact lattice-based signatures based on the hash & sign paradigm
Abstract
Post-quantum cryptography has been one of the most active subfields of
cryptography in the last few years. This is especially true today as
standardization efforts are currently underway, with no less than 69
candidate cryptographic schemes proposed.
In this talk, I will present one of these schemes: Falcon, a signature
scheme based on the NTRU class of structured lattices. I will focus on
mathematical aspects of Falcon: for example how we take advantage of the
algebraic structure to speed up some operations, or how relying on the
most adequate probability divergence can go a long way in getting more
efficient parameters "for free". The talk will be concluded with a few
open problems.
There have been reports in the press this week of how the examination length for students taking examinations in the Mathematical Institute at the University of Oxford was extended in summer 2017.
We would like to emphasise that the extension was applied to all students taking those examinations and was for academic reasons. This is part of an ongoing review of our examination processes.
What's new in moonshine? CANCELLED
Abstract
The so-called moonshine phenomenon relates modular forms and finite group representations. After the celebrated monstrous moonshine, various new examples of moonshine connection have been discovered in recent years. The study of these new moonshine examples has revealed interesting connections to K3 surfaces, arithmetic geometry, and string theory. In this colloquium I will give an overview of these recent developments.
16:00
Permuting F_q using a density method
Abstract
The construction of permutation functions of a finite field is a task of great interest in cryptography and coding theory. In this talk we describe a method which combines Chebotarev density theorem with elementary group theory to produce permutation rational functions over a finite field F_q. Our method is entirely constructive and as a corollary we get the classification of permutation polynomials up to degree 4 over any finite field of odd characteristic.
This is a joint work with Andrea Ferraguti.