August 26, 2019 - August 30, 2019
Public Access Category: All |
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- Time:
- 3:30pm-5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra seminar.
Speaker: R V Gurjar.
Affiliation: IIT Bombay.
Date and Time: Monday 26 August, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Lecture series on 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. We will prove many of these statements.
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.
Prerequisites. Basic knowledge of Commutative Algebra and language of
Algebraic Geometry (no sheaf theory!). I will "throw in" topological
proofs from time to time to make the results intuitively more clear.
- Time:
- 12:05pm-1:05pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Probability and Statistics seminar.
Speaker: Vivek Kumar.
Affiliation: IIT Roorkee.
Date and Time: Tuesday 27 August, 12:05 pm - 1:05 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Existence and uniqueness of solutions of generalised stochastic
Burger equation perturbed by Volterra noise.
Abstract:
In this article, we investigate the existence and uniqueness of local mild solutions for the one-dimensional generalized stochastic Burgers equation (GSBE) containing a non-linearity of polynomial type and perturbed by α-regular cylindrical Volterra
process and having Dirichlet boundary conditions. The Banach fixed point theorem (or
contraction mapping principle) is used to obtain the local solvability results. The L∞-
estimate on both time and space for the stochastic convolution involving the α-regular
cylindrical Volterra process is obtained. Further, the existence and uniqueness of global
mild solution of GSBE up to third order nonlinearity is shown.
2010 Mathematics Subject Classification. Primary: 60H15, 60G22; Secondary: 35Q35,
35R60.
Key-words: Stochastic Burgers equation, Volterra process, γ-Radonifying operator,
Stopping time.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.
Speaker: Sandeep Kunnath.
Affiliation: TIFR CAM, Bangalore.
Date and Time: Wednesday 28 August, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Sharp Inequalities, their extremals and related problems.
Abstract: Inequalities play an important role in the analysis of partial
differential equations. The best constants involved in these equations and
the case equality in these inequalities are of particular interest as they
are connected with many interesting phenomenon in various problems. In
this talk we will discuss some of these inequalities and related problems.
- Time:
- 2:30pm-3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Number theory seminar.
Speaker: Guhan Venkat.
Affiliation: Universite Laval, Quebec, Canada.
Date and Time: Friday 30 August, 2:30 pm - 3:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Stark-Heegner cycles for Bianchi modular forms.
Abstract: In his seminal paper in 2001, Henri Darmon proposed a systematic
construction of p-adic points on elliptic curves over the rational
numbers, viz. Stark–Heegner points. In this talk, I will report on the
construction of p-adic cohomology classes/cycles in the
Harris–Soudry–Taylor representation associated to a Bianchi cusp form,
building on the ideas of Henri Darmon and Rotger–Seveso. These local
cohomology classes are conjectured to be the restriction of global
cohomology classes in an appropriate Bloch–Kato Selmer group and have
consequences towards the Bloch–Kato–Beilinson conjecture as well as
Gross–Zagier type results. This is based on a joint work with Chris
Williams (Imperial College London).
- Time:
- 4:30pm-5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.
Speaker: Madhusudan Manjunath.
Affiliation: IIT Bombay.
Date and Time: Friday 30 August, 4:30 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: An Introduction to the Geometry of Numbers.
Abstract: We give a gentle introduction to the geometry of numbers. We
start with the classical theory and then treat some of the modern aspects
of this subject. This talk will be accessible to the general audience.