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9:00am 


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12:00pm 


1:00pm 


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 kautomorphisms of S such that
R is the ring of invariants is already very interesting. Then many nice
results are proved.
These include works of AuslanderBuchsbaum, ChevalleyShephardTodd,
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 Lfunctions and congruences between modular forms.
Abstract: In this talk, we will discuss an important object in number
theory : Lfunctions. A wellknown example is the Riemann zeta function.
We will focus on the arithmetic properties of the special values of
Lfunctions. 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 Lvalues and congruences of Siegel modular
forms.


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