- Time:
- 3:30pm
- Location:
- Ramanujan Hall
- Description:
- SPEAKER: Krishnaswami Alladi

AFFILIATION: University of Florida

TITLE: "On the local distribution of the number of small prime

factors - a variation of the classical theme"

DAY & DATE: Thursday, 3rd January 2018.

TIME: 3.30 PM.

VENUE: Ramanujan Hall.

ABSTRACT: The global distribution of $\nu_y(n)$, the number

of (distinct) prime factors of $n$ which are $

role in the proof of the celebrated Erd\"os -Kac theorem on the

distribution of $\nu(n)$, the number of distinct prime factors

of $n$. Although much is known about the "local distribution"

of $\nu(n)$, namely the asymptotics of the function $N_k(x)=

\sum_{n\le x, \nu(n)=k}1$ (Landau-Sathe-Selberg), little attention

has been paid to the local distribution of $\nu_y(n)$. In discussing

the asymptotic behavior of $N_k(x,y)=\sum_n\le x, \nu_y(n)=k)1$,

we noticed a very interesting variation of the classical theme that

seems to have escaped attention. To explain this phenomenon,

we will obtain uniform asymptotic estimates for $N_k(x,y)$ by a variety of

analytic techniques such as those of Selberg, and of Buchstab-De Bruijn

(involving difference-differential equations). This is joint work with my

recent PhD student Todd Molnar. The talk will be accessible to

non-experts.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr. Ayan Bhattacharya

Researcher in Stochastics

CWI, Amsterdam.

Time: 4 pm, Tuesday, 8th January.

Venue: Ramanujan Hall.

Title: Large deviation for extremes in branching random walk

Abstract:

We shall consider branching random walk with displacements having

regularly varying tails. Extreme positions of particles are very

important to study in the context of statistical physics, computer

science, probability and biology. Point process is the best known tool in

extreme value theory to study joint asymptotic behavior of extremes.

In this talk, we shall focus on large deviation results for point

processes arising in the above mentioned model.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Prof. Ramesh Gangoli, University of Washington.

Time: 4pm, Wednesday, 9th January.

Venue: Ramanujan Hall.

Title: Some unpublished work of Harish-Chandra.

Abstract:

When Harish-Chandra died in 1983, he left behind a voluminous pile of

handwritten manuscripts on harmonic analysis on semisimple Lie groups over

real/complex and p-adic fields. The manuscripts were turned over to the

archives of the Institute for Advanced Study at Princeton, and are

archived there.

Robert Langlands is the Trustee of the Harish- Chandra archive, and has

always been interested in finding a way of salvaging whatever might be

valuable in these manuscripts. Some years ago, at a conference in UCLA, he

asked if V. S. Varadarajan and I might look at some of these.

The results of our efforts have resulted in the publication of the Volume

5 (Posthumous) of the Collected works of Harish-Chandra by Springer

Verlag.

My talk will be devoted to a bare outline of the results in this volume,

without much detail, but I will try to convey some information about the

key method used in the work.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr. Mrinal Kumar, Simons Institute for the Theory of Computing,

Berkeley, USA.

Time: 11 am, Friday, 11th January.

Venue: Ramanujan Hall.

Title : Some closure results for polynomial factorization and applications

Abstract : In a sequence of seminal results in the 80's, Kaltofen showed

that if an n-variate polynomial of degree poly(n) can be computed by an

arithmetic circuit of size poly(n), then each of its factors can also be

computed an arithmetic circuit of size poly(n). In other words,

the complexity class VP (the algebraic analog of P) of polynomials, is

closed under taking factors.

A fundamental question in this line of research, which has largely

remained open is to understand if other natural classes of

multivariate polynomials, for instance, arithmetic formulas, algebraic

branching programs, constant depth arithmetic circuits or the

complexity class VNP (the algebraic analog of NP) of polynomials, are

closed under taking factors. In addition to being fundamental

questions on their own, such 'closure results' for polynomial

factorization play a crucial role in the understanding of hardness

randomness tradeoffs for algebraic computation.

I will talk about the following two results, whose study was motivated

by these questions.

1. The class VNP is closed under taking factors. This proves a

conjecture of B{\"u}rgisser.

2. All factors of degree at most poly(log n) of polynomials with

constant depth circuits of size

poly(n) have constant (a slightly larger constant) depth arithmetic

circuits of size poly(n).

This partially answers a question of Shpilka and Yehudayoff and has

applications to hardness-randomness tradeoffs for constant depth

arithmetic circuits. Based on joint work with Chi-Ning Chou and Noam

Solomon.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Professor Paulo Vasconcelos from University of Porto, Portugal

Day and Date: Wednesday, 16th January 2019

Time: 4:00 - 5:00 pm

Title of the talk: Solving integer-differential problems with Lanczos'

spectral Tau method

Venue: Ramanujan Hall, 2nd floor, Department Mathematics

All interested are invited.

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Prof. Dominique Guillot, University of Delaware, USA.

Date and time: 18th January, Friday, 3:30 PM.

Venue: Ramanujan Hall.

Title: Totally nonnegative GCD matrices and kernels

Abstract: Let X=(x_1, ... ,x_n) be a vector of distinct positive integers. The n x n

matrix with ij-th entry equal to gcd(x_i,x_j), the greatest common divisor of x_i

and x_j, is called the GCD matrix on X. By a surprising result of Beslin and Ligh

(1989), all GCD matrices are positive definite. In this talk, we will discuss new

characterizations of the GCD matrices satisfying the stronger property of being

totally nonnegative (i.e., all their minors are nonnegative). Joint work with Lucas

Wu (U. Delaware).

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Maria Esteban

Affiliation: Universite Paris-Dauphine.

Time: 4pm, Wednesday, January 23.

Venue: Ramanujan Hall.

TITLE: Symmetry and symmetry breaking: rigidity and flows for PDEs and for

inequalities

ABSTRACT: In this talk, I will review recent results about how the use of

linear and nonlinear flows has been key to prove functional inequalities

and qualitative properties for their extremal functions. I will also

explain how from these inequalities and their best constants, optimal

spectral estimates can be obtained for Schrodinger operators. This is a

topic which is at the crossroads of nonlinear analysis and probability,

with implications in differential geometry and potential applications in

modelling in physics and biology.

- Time:
- 11:30am - 1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 9:30am - 11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 11:30am - 1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Title : Introduction to Algebraic K Theory.

Speaker: Prof. Tony Puthenpurakal.

Time : 3:30 pm - 5 pm

Date : Friday 25 Jan 2019.

Venue : 215.

- Time:
- 9:30am - 11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 11:30am - 1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra Seminar

Title: Some Questions on Hilbert-Samuel functions.

Time & Venue: 3:30 - 5 p.m., Room 215

Dates: Monday, 28th January, 2018.

- Time:
- 9:30am - 11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 3:30pm - 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry Seminar

Speaker: Radhika Gupta (Technion, Israel).

Title: `Cannon-Thurston maps for CAT(0) groups with isolated flats'.

Time: 15:30 - 16:30, Tuesday, January 29, 2019.

Venue: Ramanujan Hall.

Abstract:

Consider a hyperbolic 3-manifold, called a mapping torus, that fibers over

a circle with fiber a closed orientable surface of genus at least 2.

Cannon and Thurston showed that the inclusion map from the surface into

the 3-manifold extends to a continuous, surjective map between the visual

boundaries of the respective universal covers. This gives a surjective map

from a circle to a 2-sphere. Mj showed that a Cannon-Thurston map also

exists for a hyperbolic group and its normal hyperbolic subgroups. In this

talk, we will explore what happens when we consider the mapping torus of a

surface with boundary, which is not hyperbolic but CAT(0) with isolated

flats under some conditions.

- Time:
- 9:30am - 11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 11:00am - 12:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra Seminar

Speaker: Dilip Patil.

Time & Date: 11:00 a.m. - 12:30 p.m., Wednesday, 30th Jan 2019.

Venue: Room 215.

Title: Some Questions on Hilbert-Samuel functions.

- Time:
- 11:30am - 1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Lecture Series

Speaker: Dipendra Prasad.

Time: 2pm (-3:30pm), Wednesday, 30 January 2019.

Venue: Room 216.

Title: An introduction to Lie groups, Symmetric spaces, and Shimura

varieties based on examples".

Abstract: I will give an introductory course of 3-4 lectures on the topics

mentioned in the title to an audience without any prior knowledge of the

subject which is a meeting ground for Differential geometry, Algebraic

geometry, and Number theory.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium

Speaker: Aditya Karnataki, Beijing International Center for Mathematical

Research

Date: Wednesday, 30 January 2019.

Time: 4:00-5:00pm.

Venue: Ramanujan Hall.

Title - Finiteness of cohomology of arithmetic families of $(\varphi,

\Gamma)$-modules.

Abstract - We will explain constructions of Robba rings and $(\varphi,

\Gamma)-modules of p-adic Hodge theory. We will describe new proofs of

some results on finiteness of cohomology of these modules, and indicate

their applications to the theory of $p$-adic families of automorphic

forms. This is part of ongoing work with Eugen Hellmann and Ruochuan Liu.

- Time:
- 9:30am - 11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 11:30am - 1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra Seminar

Title: Some Questions on Hilbert-Samuel functions.

Time & Venue: 3:30 - 5 p.m., Room 215

Dates: Thursday, 31th January, 2018.

- Time:
- 3:45pm - 5:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- K-Theory Seminar

Speaker : Sudarshan Gurjar.

Title : Topolgical vector bundles.

Time : 3:45 pm - 5:15 pm.

Date : Thursday 31st Jan 2019.

Venue : Ramanujan Hall.