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Organized by The (Indian) Mathematics Consortium
Co-hosted by IIT Bombay and ICTS, Bangalore |
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The Distinguished Lecture Series (DLS) is an initiative of the (Indian) Mathematics Consortium (TMC) and it aims to host virtual colloquiums by some of the best researchers and expositors around the world. The speakers are carefully chosen by the Scientific Committee among mathematicians who are not only distinguished researchers, but also known for the quality of their exposition. The principal aim is to make the talks as widely accessible as possible, especially to Ph.D. students. With this in view, the format of most of the talks will be as follows:
First, a pre-recorded talk by the speaker will be posted online. Interested audience can view this at their leisure and communicate questions, if there are any, to the organizers.
A live interactive session between the speaker and interested participants will be held in about 2 weeks after posting the online talk. This will be chaired by a member of the Scientific Committee.
The approximate duration of the talk will be about 45 minutes and that of the interactive session will be about 30 minutes. However, this is not rigid. The interactive sessions will not be recorded.
To receive announcements about upcoming colloquia and the Zoom links for interactive sessions, please register at the homepage of the TMC DLS.
After giving a general introduction to the representation theory of GL(n,C) and other classical groups, I will focus attention on Dibyendu Biswas's thesis work around the question of tensor product of representations of GL(n,C) and other classical groups.
...more We shall initially discuss what symmetries mean in the context of dynamical systems of different flavors: complex analytic, Hamiltonian, or smooth. We shall then discuss progress towards a resolution of a conjecture of Smale: a generic smooth dynamical system has only trivial s...more
For any finite group G, it is easy to see there exists a compact, oriented 3 dimensional manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and H finite ...more
A locally testable code (LTC) is an error-correcting code that admits a very efficient membership test. The tester reads a constant number of (randomly - but not necessarily uniformly - chosen) bits from a given word and rejects words with probability proportional to ...more
In this talk, I will present a connection between dynamical systems and arithmetic geometry. Building on a simple relation -- between periodic points for a particular class of systems in dimension 1 and the torsion points for the group structure on a 2-dimensional com...more
Asymptotic dimension is an analog of topological dimension in the large-scale context of geometric group theory. This talk will introduce asymptotic dimension, and describe some of its basic properties. One of the important aspects of the theory is to establish that several fin...more
Class field theory describes abelian extensions of a number field in terms of data intrinsic to the field. Hilbert’s 12th problem, or explicit class field theory, goes further and asks for explicit generators of abelian extensions of a number field as values of analytic funct...more
It is known that one can cut any open necklace with beads of t types in at most (k-1)t points and partition the resulting intervals into k collections, each containing the same number of beads of each type (up to 1). This number of cuts is optimal. I will discuss some...more
In this talk, we will review some recent results on computing PDEs with deep neural networks. The focus will be on the design of neural networks as fast and efficient surrogates for PDEs. We will start with parametric PDEs and talk about novel modifications that enable standard...more
Humans tend to be better at physics than at mathematics. When an apple falls from a tree, there are more people who can catch it—we know physically how the apple moves—than people who can compute its trajectory from a differential equation. Applying physical ideas to ...more
The MLC Conjecture, on local connectivity of the Mandelbrot set, is one of the central open problems in Holomorphic Dynamics. It turned out to be intimately related to many other geometric themes of the area: Fatou's Conjecture on the density of hyperbolicity, self-similarity f...more
Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and...more
What is the most singular possible singularity? What can we say about its geometric and algebraic properties? This seemingly naive question has a sensible answer in characteristic p. The "F-pure threshold," which is an analog of the log canonical threshold, can be used to "meas...more
In one of the simplest epidemic models, one lets p_n denote the number of new infections during week n and assumes that (during the early stages of the epidemic) p_{n+1} = R_0 p_n c_n where c_n measures the “fraction of usual contact” that takes place between people during the nth w...more
Several well-known open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) ( in the hyperlinear case )?
In the ...more
We shall discuss mathematical forms of the uncertainty principle and its relationship with quantum unique ergodicity.
...more This seminar spans a bridge between 19th century geometry to 21st century computing. We start with a classical theme that was featured in the January 2020 issue of the Notices of the American Mathematical Society, namely the 3264 conics that are tangent to five given conics in the plane. We discu...more
In the seventies Harish-Chandra introduced the tempered representations of a semisimple real Lie group G as those that occur in the analog on G of the Fourier-Plancherel formula. Nowadays, those representations are ubiquitous.
In this talk we will recall their defini...more
