Previous Special Year Seminar

This is an exposition of work on Artin's Conjecture on the zeros of p-adic forms.A variety of lines of attack are described ,going back to 1945.However there is particular emphasis on recent developments concerning quartic forms on the one hand ,and...

In this talk I will construct a class of probabilistic random Euler products to model the behavior of L-functions in the strip 1/2 Re(s) 1. We then deduce results on the distribution of extreme values of several families of L-functions, including...

We describe how various fundamental algebraic structures (involving, for example, number fields, class groups, and algebraic curves) can be parameterized via the orbits of appropriate group representations. By developing techniques to count such...

Let E be an elliptic curve over Q and let Q(E[n]) be its n-th division field. In 1972, Serre showed that if E is without complex multiplication, then the Galois group of Q(E[n])/Q is as large as possible, that is, GL_2(Z/n Z), for all integers n...

We describe how various fundamental algebraic structures (involving, for example, number fields, class groups, and algebraic curves) can be parameterized via the orbits of appropriate group representations. By developing techniques to count such...

I first present an algorithm to compute the truncated theta function in poly-log time. The algorithm is elementary and suited for computer implementation. The algorithm is a consequence of the periodicity of the complex exponential, and the self...

This talk will give a more detailled account of the ``basic" results in A^1-homotopy theory which are used in our approach: Hurewicz theorem, Lower central series spectral sequence, A^1-derived functors of nonadditive functors, Eilenberg-Moore...

This talk will give a more detailled account of the ``basic" results in A^1-homotopy theory which are used in our approach: Hurewicz theorem, Lower central series spectral sequence, A^1-derived functors of nonadditive functors, Eilenberg-Moore...