I will describe recent joint work with Janos Pintz and Cem
Yildirim on small gaps between primes and primes in tuples. Perhaps
the most surprising result is that if the primes have level of
distributed in arithmetic progressions greater than 1/2...
Paley graphs are well-known combinatorial objects which have
many interesting properties. Many of these properties come from
their symmetry under the automorphisms x-->ax+b of the affine
line over a finite field F with q elements (q=4m+1). We...
Given a higher rank arithmetic group (E.g. SL(3,Z)) it has r(n)
complex irreducible representations of degree n. We will study the
the rate of growth of r(n), the associated zeta function
SUM(r(n)n^(-s)), its Euler factorisation etc. Some...
The classification of finite simple groups is widely
acknowledged to be one of the major results in modern mathematics.
The successful completion of its proof was announced in the early
1980's by Daniel Gorenstein. The original proof occupied...
Closed subgroups of the automorphism group of a tree which acts
locally primitively have a rich structure theory. Combined with
superrigidity for irreducible lattices in products of trees such
that the projection in each factor is locally primitive...
I will discuss a proof of the fact that given a finite
dimensional division algebra D over an arbitrary field, any finite
quotient of the multiplicative group D^* is solvable (joint work
with Y.Segev and G.Seitz). Time permitting, I will also talk...
