Special Lectures 2019

Table of Contents

Spring 2019

SL1907: Branched covers of the sphere #

Speaker: Prof. Shubhojoy Gupta (IISc, Bengaluru)
Abstract: There is an old unsolved problem of Hurwitz in topology, concerning branched covers of the sphere. I will say what this problem is, and describe some surprising links to complex analysis and number theory. Some knowledge of basic topology will be assumed, but I will try to keep the talk accessible to all.
Date and Time: Sunday, 21st April 2019, 4:00 PM - 5:00 PM
Venue: G-24 Classroom, Academic Building

Speaker: Prof. Arvind Ayyer (IISc, Bengaluru)
Abstract: Starting with a formula for the determinant of a matrix due to Lewis Carroll, we will motivate the definition of alternating sign matrices. Enumerating them was one of the major open problems in combinatorics during the last two decades of the past century. We will go through some of the ideas leading to the proof of their enumeration. Along the way, we will meet some of the main players in the story such as descending plane partitions, totally symmetric self-complementary plane partitions and fully packed loop configurations.
Date and Time: Saturday, 13th April 2019, 3:00 PM - 4:00 PM
Venue: G-24 Classroom, Academic Building

Speaker: Prof. Jaikumar Radhakrishnan (TIFR, Mumbai)
Abstract: There is an undirected graph \(G\) with two special vertices \(s\) and \(t\). Our computer needs to determine if \(t\) is reachable from \(s\). The graph \(G\) is big and stored in external memory, but we have only a small amount of working space in our computer. With this problem as running example, we will discuss the following.
(i) If we walk randomly along the edges in \(G\) starting from \(s\), remembering at any point only the current edge we are using, we will with high probability quickly reach \(t\). (Aleliunas, Karp, Lipton, Lovasz, Rackoff 1979).
(ii) Every efficient randomized algorithm running with small space can be made deterministic with only a small increase in space and a modest loss in efficiency. (Nisan 1992)
(iii) There is a deterministic algorithm that uses a small amount of space and efficiently determines if \(t\) is reachable from \(s\). (Reingold 2005).
Our discussion will involve notions such as cover time of random walks on graphs, random families of hash functions, pseudorandomness, graph eigen values, zig-zag products and expander graphs.
Date and Time:
- Saturday, 9th March 2019,
  - 3:00 PM - 3:45 PM
  - break
  - 4:00 - 4:45 PM
- Sunday, 10th March 2019,
  - 11:15 AM - 12:00 PM
  - break
  - 12:15 PM - 12:45 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Prof. Parthanil Roy (ISI Bangalore)
Abstract: In this talk, we will discuss a two-moment based Stein-Chen method (due to Arratia, Goldstein and Gordon (1989)) of establishing Poisson approximation for dependent Bernoulli random variables. We will use this method to give rate of convergence results for extreme values of a dynamical system arising out of continued fractions.
This is based on a joint work with Maxim Solund Kirsebom and Anish Ghosh. Familiarity with standard (discrete and absolutely continuous) probability distributions will be sufficient for following this talk.
Date: Saturday, 2nd March 2019, 3:15 PM - 4:50 PM, with a 5 minutes break at 4:00 PM
Venue: G-24 Classroom, Academic Building

Speaker: Abhishek Khetan (Dead Mathematicians Society, TIFR Mumbai)
Abstract: In this talk we will state and prove the Minkowski’s convex body theorem and see how it can be applied to prove Dirichlet’s theorem on (simultaneous) diophantine approximation and to prove the fact that if \(p\) is a prime with \(p\equiv 1\pmod{4}\) then \(p\) can be written as a sum of two squares.
Date and Time: Tuesday, 19th February 2019, 4:30 PM
Venue: G-24 Classroom, Academic Building

Speaker: Prof. Maxim A. Vsemirnov (Steklov Institute of Mathematics, St. Petersburg)
Abstract: A pseudoprime is an integer that shares a property common to all prime numbers but is not actually prime. We will talk about some primality tests that employ pseudoprimes. We will also talk about some classical problems, ongoing works and properties of such numbers.
Date and Time: Saturday, 12th January 2019, 3:00 PM - 5:00 PM
Venue: 2nd Floor Auditorium, Academic Building