The basic ingredients of Darwinian evolution, selection and
mutation, are very well described by simple mathematical models. In
1973, John Maynard Smith linked game theory with evolutionary
processes through the concept of evolutionarily stable...
I will explain the main notions of the microlocal theory of
sheaves: the microsupport and its behaviour with respect to the
operations, with emphasis on the Morse lemma for sheaves. Then,
inspired by the recent work of Tamarkin but with really...
In this talk we will discuss recent progresses meant as a
contribution to the GLS-project, the second generation proof of the
Classification of Finite Simple Groups (jointly with R. Lyons, R.
Solomon, Ch. Parker).
Topological spaces given by either (1) complements of coordinate
planes in Euclidean space or (2) spaces of non-overlapping
hard-disks in a fixed disk have several features in common. The
main results, in joint work with many people, give...
I will introduce two basic problems in random geometry. A
self-avoiding walk is a sequence of steps in a d-dimensional
lattice with no self-intersections. If branching is allowed, it is
called a branched polymer. Using supersymmetry, one can map...
I will survey the development of modern infinite cardinal
arithmetic, focusing mainly on S. Shelah's algebraic pcf theory,
which was developed in the 1990s to provide upper bounds in
infinite cardinal arithmetic and turned out to have
applications...
This will be an introduction to special value formulas for
L-functions and especially the uses of modular forms in
establishing some of them -- beginning with the values of the
Riemann zeta function at negative integers and hopefully arriving
at...
