Date and Time: Wednesday 7 August, 2:45 pm - 3:45 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Ramification in Commutative Algebra and Algebraic Geometry.
Abstract: We will consider mainly the following situation.
Let R,S be complete normal local domains over an alg. closed field k of
char. 0 such that S is integral over R. Our aim is to describe three
ideals in S; I_N, I_D, I_K (Noether, Dedekind, Kahler differents resp.)
each of which capture the ramified prime ideals in S over R. In general
these three ideals are not equal. An important special case when all are
equal is when S is flat over R.
The case when there is a finite group G of k-automorphisms of S such that
R is the ring of invariants is already very interesting. Then many nice
results are proved.
These include works of Auslander-Buchsbaum, Chevalley-Shephard-Todd,
Balwant Singh, L. Avramov, P. Roberts, P. Griffith, P. Samuel,....
I will try to discuss all these results.
I believe that these results and ideas involved in them will be very
valuable to students and faculty both.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium Talk 2.
Speaker: Ameya Pitale.
Affiliation: University of Oklahoma.
Date and Time: Wednesday 7 August, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Special values of L-functions and congruences between modular forms.
Abstract: In this talk, we will discuss an important object in number
theory : L-functions. A well-known example is the Riemann zeta function.
We will focus on the arithmetic properties of the special values of
L-functions. These have very interesting applications to congruences
between modular forms. We will give a gentle introduction to these
concepts highlighting several examples and important results in the
literature. We will present recent joint research with Abhishek Saha and
Ralf Schmidt regarding special L-values and congruences of Siegel modular
forms.