Bas Lemmens (Warwick), "Transitive actions of finite abelian groups of isometries"

Jozef Skokan (LSE), Numbers in Ramsey Theory

Ben Green (Trinity College, Cambridge)

"Linear equations in primes"

Abstract:

Many classical questions in the additive theory of prime numbers concern linear equations in primes. For example Vinogradov's famous 1937 result states that the equation p_1 + p_2 + p_3 = N is always soluble provided that N is large and odd. An arithmetic progression of k primes may be viewed as a simultaneous solution to the system

p_1 + p_3 = 2p_2,

...,

p_{k-2} + p_k = 2p_{k-1},

and together with T. Tao I proved that this system has many solutions. More recently Tao and I have looked at systems of linear equations of primes in general, with the more ambitious goal of counting (asymptotically) the number of solutions to a given system inside a given box. I will report on this programme of research and its current status.

The talk will be suitable for a general mathematical audience.

Norman Biggs (LSE)

"The critical group from a cryptographic perspective"

Harald Helfgott (Bristol), " Growth and generation in SL_2(Z/pZ)"

James McKee (RHUL): Integer symmetric matrices with all their eigenvalues in the interval [-2,2].

Abstract:

This is joint work with Chris Smyth (Edinburgh). In 1969, John Smith described all graphs that have all their eigenvalues in the interval [-2,2]. We extend this to signed graphs, and to general integer symmetric matrices, giving a complete classification up to a natural notion of equivalence.

Samir Siksek (Warwick):

'Fermat's Last Theorem and some Classical Diophantine Problems of J.H.E. Cohn'

Abstract:

Wiles' proof of Fermat's Last Theorem is one of the happiest memories of the 20th century. Unfortunately, Wiles' proof does not readily extend in a way that allows us to solve many other classical Diophantine problems. In this talk, based on joint work with Bugeaud and Mignotte, we explain how the proof of Fermat's Last Theorem can be combined with older analytic techniques due to Baker, in a way that solves several classical Diophantine problems, originally suggested and pioneered by J.H.E. Cohn.

no seminar

Christian List (LSE), "Judgement aggregation: paradoxes and impossibility results"

Eugene Shargorodsky (King's College London)

"Stokes waves, Bernoulli free boundaries, and the Riemann-Hilbert problem"

Abstract:

A Bernoulli free-boundary problem is one of finding domains in the plane on which a harmonic function simultaneously satisfies homogeneous Dirichlet and inhomogeneous Neumann boundary conditions. The boundary of such a domain (called the free boundary because it is not prescribed a priori) is the essential ingredient of a solution. The classical Stokes waves provide an important example of a Bernoulli free-boundary problem.

The talk is intended as a nontechnical review of some aspects of this field, in particular of the relatively recent variational approach which allows one to use methods of the Riemann-Hilbert theory.

Charles Leedham-Green (Queen Mary Univ. of London), "Classifying p-groups up to isomorphism !"

David Conlon (Cambridge), "New bounds on Ramsey numbers"