December 2019
Public Access Category: All |

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

Speaker: Danylo Radchenko.

Affiliation: ETH Zurich.

Date and Time: Monday 02 December, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Universal optimality of the E8 and Leech lattices.

Abstract: We look at the problem of arranging points in Euclidean space in

order to minimize the potential energy of pairwise interactions. We show

that the E8 lattice and the Leech lattice are universally optimal in the

sense that they have the lowest energy for all potentials that are given

by completely monotone potentials of squared distance.

The proof uses a new kind of interpolation formula for Fourier

eigenfunctions, which is intimately related to the theory of modular

forms.

The talk is based on a joint work with Henry Cohn, Abhinav Kumar, Stephen

D. Miller, and Maryna Viazovska.

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

Speaker: Jean-Pierre Raymond.

Affiliation: Universite Paul Sabatier Toulouse, France.

Date and Time: Wednesday 04 December, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Analysis of 1D models describing blood flows in the brain.

Abstract: In this talk, we shall review models used to describe blood

flows in the human brain. We shall give new existence, uniqueness and

stability results for some of those models (work in collaboration with D.

Maity TIFR-CAM, Bangalore, and A. Roy, Inria-Lorraine).

We shall address the issue of estimating the pressure from blood flow

measurements, and of the auto regulation phenomenon, which is a natural

stabilisation process.

- Time:
- 4:00pm - 5:00pm
- Location:
- A1A2, CDEEP
- Description:
- Speaker: Ken Ono.

Affiliation: University of Virginia.

Date and Time: Friday, 06 December 2019, 4.00pm - 5.00pm.

Venue: A1A2, CDEEP.

Note: This is a web-cast through NKN of a lecture at TIFR at the same time.

Title: Why Does Ramanujan, “The Man Who Knew Infinity,” Matter?

Abstract: Srinivasa Ramanujan, one of the most inspirational figures in

the history of mathematics, was an amateur gifted mathematician from lush

south India who left behind three notebooks that engineers,

mathematicians, and physicists continue to mine today. Born in 1887,

Ramanujan was a two-time college dropout. He could have easily been lost

to the world, a thought that scientists cannot begin to absorb. He died

in 1920. Prof. Ono will explain why Ramanujan matters today and will

share several clips from the film, “The Man Who Knew Infinity,”

starring Dev Patel and Jeremy Irons. Professor Ono served as an associate

producer and mathematical consultant for the film.

About the Speaker:

Prof. Ken Ono is the Thomas Jefferson Professor of Mathematics at the

University of Virginia, the Asa Griggs Candler Professor of Mathematics

at Emory University and Vice President of the American Mathematical

Society. He is considered an expert in number theory. His contributions

include several monographs and more than 180 research and popular

articles in number theory, combinatorics and

algebra. He earned his Ph.D. from UCLA and has received many awards for

his research in number theory, including a Guggenheim Fellowship, a

Packard Fellowship and a Sloan Research Fellowship. He was awarded a

Presidential Career Award for Science and Engineering (PECASE) by Bill

Clinton in 2000 and was named a Distinguished Teaching Scholar by the

National Science Foundation in 2005. He is also a member of the US

National Committee for Mathematics and

the National Academy of Sciences. He was an associate producer of the film

“The Man Who Knew Infinity” based on the life of Indian mathematician

Srinivasa Ramanujan.

- Time:
- 11:50am - 5:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Distinguished Lectures on Mathematics.

The speakers are

1. Prof. Alex Lubotzky, Einstein Institute of Mathematics, Israel.

2. Prof. C.S. Rajan, TIFR Mumbai.

3. Prof. Dinakar Ramakrishnan, California Institute of Mathematics, USA.

Date and Time: Thursday 12 December, 11:30 am - 5:15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Please see the poster using the following link for more details:

https://hutridurga.files.wordpress.com/2019/12/disti-lectures.pdf

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

Speaker: Phoolan Prasad.

Affiliation: IISc, Bengaluru.

Date and Time: Friday 13 December, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Glimpses of KdV Equation and Soliton Theory - Contributions from

Observation, Physical & Numerical Experiments, and Pure & Applied

Mathematics.

Abstract:

Solitons are solutions of a special class of nonlinear partial differential equations (soliton equations, the best example is the KdV equation). They are waves but behave like particles. The term

“soliton” combining the beginning of the word “solitary” with ending “on” means a concept of a

fundamental particle like “proton” or “electron”.

The events: (1) sighting, by chance, of a great wave of translation, “solitary wave”, in 1834 by ScottRussell, (2) derivation of KdV E by Korteweg de Vries in 1895, (3) observation of a very special type

of wave interactions in numerical experiments by Krushkal and Zabusky in 1965, (4) development

of the inverse scattering method for solving initial value problems by Gardener, Greene, Kruskal

and Miura in 1967, (5) formulation of a general theory in 1968 by P. D. Lax and (5) contributions

to deep theories starting from the work by R. Hirota (1971-74) and David Mumford (1978-79),

which also gave simple methods of solutions of soliton equations, led to the development of one of

most important areas of mathematics in 20th century.

This also led to a valuable application of solitons to physics, engineering and technology.

There are two aspects soliton theory arising out of KdV Equation

• Applied mathematics - analysis of nonlinear PDE leading to dynamics of waves.

• Pure mathematics - algebraic geometry.

It is surprising that each one of these can inform us of the other in the intersection that is soliton

theory, an outcome of KdV equation.

The subject too big but I shall try to give some glimpses (1) of the history, (2) of the inverse scattering method and (2) show that algorithm based on algebraic-geometric approach is much easier

to derive soliton solutions.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Analysis seminar.

Speaker: Sudeshna Basu.

Affiliation: Ramakrishna Mission Vivekananda Educational and Research

Institute, Belur.

Date and Time: Monday 16 December, 4:00 pm - 5:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Linear Hahn Banach Extension of module homomorphisms in Hilbert

and Banach modules.

Abstract: The notion of linear Hahn-Banach extension operator was first

studied in detail by Heinrich and Mankiewicz (1982). Previously, J.

Lindenstrauss (1966) studied similar versions of this notion in the

context of non separable reflexive Banach spaces. Subsequently, Sims and

Yost (1989) proved the existence of linear Hahn-Banach extension operators

via interspersing subspaces in a purely Banach space theoretic set up. In

this paper, we study similar questions in the context of Banach modules

and module homomorphisms, in particular, Banach algebras of operators on

Banach spaces. Based on Dales, Kania, Kochanek, Kozmider and

Laustsen(2013), and also Kania and Laustsen (2017), we give complete

answers for reflexive Banach spaces and the non-reflexive space

constructed by Kania and Laustsen from the celebrated Argyros-Haydon's

space with few operators.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Hossein Movasati.

Affiliation: IMPA, Rio de Janeiro.

Date and Time: Wednesday 18 December, 4:00 pm - 5:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Ramanujan's relations between Eisenstein series.

Abstract: In 1916 S. Ramanujan discovered three identities involving the

Eisenstein series $E_2,E_4,E_6$ and their derivatives. This can be seen as

a vector field in the moduli space of an elliptic curve $E$ enhanced with

a certain frame of the de Rham cohomology of $E$. For this one needs

algebraic de Rham cohomology, cup product and Hodge filtration developed

by Grothendieck and Deligne among many others. Viewed in this way,

Ramanujan's differential equation can be generalized to an arbitrary

projective variety. If time permits I will explain two generalizations of

this picture in the case of Abelian varieties and Calabi-Yau threefolds.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics.
- Description:
- Popular Talk.

Speaker: M. Ram Murty.

Affiliation: Queen's University.

Date and Time: Monday 30 December, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: The Art of Research.

Abstract: We will present several methods of doing research in mathematics

and science and illustrate them through concrete examples. The talk is

aimed at a general scientific audience

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

Speaker: M. Ram Murty.

Affiliation: Queen's University.

Date and Time: Tuesday 31 December, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: The central limit theorem.

Abstract: The central limit theorem is considered perhaps the most

influential theorem of mathematics in the 20th century. It has had

significant applications both within mathematics and beyond, energizing

literally every other field outside such as medicine, economics and even

political theory. After a short history of the evolution of the central

limit theorem, we will describe its impact in algebra and number theory

and discuss some new applications. The talk will be accessible to a

general mathematical audience.