Date: Monday 5 Nov
Venue: Room 215
Time: 3.30-5.00
Speaker: Clare D'Cruz
Chennai Mathematical Institute
Title: Symbolic powers of certain monomial curves
Abstract: The generators of symbolic powers of an ideal, in general, are
hard to determine. A natural question is the relation between symbolic
powers and ordinary powers. In this context, Bocci and Harbourne gave an
asymptotic quantity called resurgence. Though this is hard to determine, in
some cases it is known. In this talk, we focus on certain monomial curves.
We discuss the regularity for symbolic powers and the resurgence.
Time:
2:00pm-3:30pm
Location:
Room 215, Department of Mathematics
Description:
Date: Thursday 8 November
Venue: Room 215
Time: 2.00-3.30
Speaker: Dale Cutcosky, University of Missouri at Columbia, MO
Title: Multiplicities and volumes-I
Abstract: We show how multiplicities of (not necessarily Noetherian)
filtrations on a Noetherian ring can be computed from volumes of
appropriate Newton Okounkov bodies. We discuss applications and examples.
Time:
4:00pm
Location:
Room 215, Department of Mathematics
Description:
PDE seminar on Control and homogenization:
Title: Control of wave equation.
Speaker: Debanjana Mitra,
Time: Thursday, 08-11-18, 4p.m.-5p.m.
Venue: Room 215, Department of Mathematics, IIT Bombay.
Abstract: In this talk, we will continue the discussion on the control of
wave equation from where we stopped at the previous lecture.
The observability inequality for wave equation will be proved by
multiplier method.
Time:
11:30am-1:00pm
Location:
Room 215, Department of Mathematics
Description:
Date: Friday, 9 November
Venue: Room 215
Time: 11.30-1.00
Speaker: Dale Cutcosky, University of Missouri at Columbia, MO
Title: Multiplicities and volumes-II
Abstract: We show how multiplicities of (not necessarily Noetherian)
filtrations on a Noetherian ring can be computed from volumes of
appropriate Newton Okounkov bodies. We discuss applications and examples.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Date and time : 9th November 2018, 4.00 - 5.00 pm,
Venue: Ramanujan Hall
Title: Concentration Bounds for Stochastic Approximation with Applications
to Reinforcement Learning
Speaker: Gugan Thoppe
Affiliation: Duke University, Durham, USA
Abstract: Stochastic Approximation (SA) refers to iterative algorithms that
can be used to find optimal points or zeros of a function, given only its
noisy estimates. In this talk, I will review our recent advances in
techniques for analysing SA methods. This talk has four major parts. In the
first part, we will see a motivating application of SA to network
tomography and, alongside, discuss the convergence of a novel stochastic
Kaczmarz method. In the second part, we shall see a novel analysis approach
for non-linear SA methods in the neighbourhood of an isolated solution. The
main tools here include the Alekseev formula, which helps exactly compare
the solutions of a non-linear ODE to that of its perturbation, and a novel
concentration inequality for a sum of martingale differences. In the third
part, we will extend the previous tool to the two timescale but linear SA
setting. Here, I will also present our ongoing work to obtain tight
convergence rates in this setup. In parallel, we will also see how these
results can be applied to gradient Temporal Difference (TD) methods such as
GTD(0), GTD2, and TDC that are used in reinforcement learning. For the
analyses in the second and third parts to hold, the initial step size must
be chosen sufficiently small, depending on unknown problem-dependent
parameters; or, alternatively, one must use projections. In the fourth
part, we shall discuss a trick to obviate this in context of the one
timescale, linear TD(0) method. We strongly believe that this trick is
generalizable. We also provide here a novel expectation bound. We shall end
with some future directions.
Time:
4:00pm
Location:
Room 215, Department of Mathematics
Description:
Geometry and Topology seminar
9th November, 4:00 PM
Room 215
Title. Shafarevich question on the universal covering of a smooth
projective variety, and it's applications.
Speaker. R.V. Gurjar
Abstract. I. Shafarevich has raised the following very general question.
'Is the universal covering space of every smooth connected projective
variety holomorphically convex ?'
This is a generalization of the famous Uniformization Theorem for Riemann
Surfaces. We will discuss some applications of a positive solution of the
Sharafevich question, viz. A conjecture of Madhav Nori is true, and the
second homotopy group of a connected smooth projective surface is a free
abelian group.
We will also mention positive solutions for the Shafarevich question in
several interesting cases.