Wed, August 7, 2019
Public Access

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2:00pm [2:45pm] R.V. Gurjar: Mathematics Colloquium
Description:
Mathematics Colloquium Talk 1. Speaker: R.V. Gurjar. Affiliation: IIT Bombay. 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.
3:00pm
4:00pm [4:00pm] Ameya Pitale : University of Oklahoma: Mathematics Colloquium
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.

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