Speaker: Sai Krishna P M S
[This is a continuation of the previous talk.]
Time: 5:00–6:00 PM
Venue: Ramanujan Hall
Speaker: Sai Krishna P M S
Abstract: The Jacobian conjecture states that given n polynomials in k[x1,…,xn] where k is a field of characteristic zero such that the determinant of the Jacobian of these n polynomials is a non-zero constant then these n polynomials generate the polynomial ring as a k-algebra. This is only known for n = 1. In this talk, we we will discuss the Jacobian conjecture. We will reformulate the Jacobian conjecture as a version of Rolle's theorem and look at some partial results/reductions related to it.
Time: 5:00–6:00 PM
Venue: Ramanujan Hall
Speaker: Omkar Javadekar
[This is a continuation of the previous talk.]
Time: 5:00–6:00 PM
Venue: Ramanujan Hall
Speaker: Omkar Javadekar
Abstract: The Fundamental Theorem of Algebra (FTA) states that every non-constant polynomial with complex coefficients has a complex root. The first "widely accepted" proof of the FTA was given by Gauss in 1799, and today many proofs of the theorem are known. In this talk, we will see two elementary proofs of the theorem: one based on techniques from linear algebra which was given by H. Derksen in 2003, and another using basic real analysis. If time permits, we will also see a generalization of the FTA.
Time: 5:00–6:00 PM
Venue: Ramanujan Hall
Speaker: Madhur Agrawal
Abstract: We shall take a look at MDPs, which are Markov chains where at each node you have a choice of transition functions and rewards, and shall examine what optimal policies look like in such a context. We shall look at the Bellman Optimality Operator and how to show its convergence to an optimal policy. This talk is an excerpt from material covered in the course CS 747, by Prof. Shivaram Kalyanakrishnan.
Time: 3:00–4:00 PM
Venue: Ramanujan Hall