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Lecture Series 2018

Table of Contents

LS1805: Random Matrix Theory #

Number of Talks: 5

  • Speaker: S. Nanda Kishore Reddy (Ph.D)
  • Pre-requisites:
    • Basic Linear Algebra
    • Probability I and II
    • Multivariate Calculus
  • Venue: G-23 Classroom, Academic Building
Part 1 #
  • Title: Jacobian computations in Random Matrix Theory
  • Abstract: We shall discuss exact eigenvalue densities of certain random matrix ensembles.
  • Date and Time:
    • Saturday, 22nd September 2018, 3:00 PM
    • Sunday, 23rd September 2018, 3:00 PM
Part 2 #
  • Title: Law of Large numbers and Central limit theorem for eigenvalues and singular values for certain random matrix ensembles.
  • Abstract: We extend the results of sums of i.i.d. random variables to products of random matrices.
  • Date and Time:
    • Saturday, 29th September 2018, 3:00 PM
    • Saturday, 6th October 2018, 3:00 PM
    • Sunday, 7th October 2018, 3:00 PM

LS1804: Deep Learning with Natural Language Processing #

Number of Talks: 2

  • Speaker: Soumyabrata Kundu (B. Math, 2020)
  • Abstract: Natural Language Processing is a recent topic which has emerged in the past decade. Natural Language Processing, abbreviated as NLP, is the application of computational techniques to the analysis and synthesis of natural language and hence helps machines “read” text by simulating the human ability to understand language. In these lectures we shall explore the architecture behind the machine learning algorithms used to train a model for processing human language. In the first lecture we will discuss about the older versions used for NLP like Skip-Gram and Bag-of-Words. In the second lecture we will see how the older techniques pave way for advanced tools like GloVe to process language.
  • Pre-requisites: Basic Linear Algebra
  • Date and Time:
    • Saturday, 1st September 2018, 3:00 PM
    • Sunday, 2nd September 2018, 3:00 PM
  • Venue: G-23 Classroom, Academic Building

LS1803: Classification of Root System #

Number of Talks: 2

  • Speaker: Sumit Kumar Singh (B. Math, 2020)
  • Abstract: Root system is an algebraic combinatoric object which has always been in the hindsight of Lie Theory. It is widely recognized as a method to classify semi-simple Lie Algebras and Coxeter and reflection groups, as every semi-simple Lie algebra induces a root system. The main objects besides the root system in Euclidean spaces, are Weyl groups, Weyl chambers, and bases associated with the root system. In the first lecture, I am going to give proof of their relation which induces a construction of Coxeter-Dynkin diagram for irreducible root systems, after that it is a completely combinatoric argument which is going to classify the root systems; this would be discussed in the second lecture.
  • Pre-requisites:
    • Basic Linear Algebra
    • Basic Group Theory (knowledge of group actions will be sufficient)
  • Date and Time:
    • Friday, 25th August 2018, 3:00 PM
    • Saturday, 26th August 2018, 3:00 PM
  • Venue: G-23 Classroom, Academic Building

LS1802: Intuitive Introduction to Lie Groups #

Number of Talks: 2

  • Speaker: Akshay Sateesh Hegde (B. Math, 2019)
  • Abstract: We will explore the basic properties of Lie Groups. The key idea is to study properties of certain groups by “localizing” them (here, the group we are interested in is the Lie Group and we localize them by associating Lie Algebra of the group). Our prototypical examples are (topologically) closed subgroups of . Then we will classify all the connected commutative Lie Groups. One of the important theorems in the beginning of this vast theory is Cartan’s theorem, which says that any closed subgroup of a Lie Group is also a Lie Group. If time permits, I will say a few words about group actions on manifolds.
  • Pre-requisites:
    • Basic Linear ALgebra
    • Basic Multivariate Analysis
    • Some knowledge of manifolds will definitely help.
  • Date and Time:
    • Friday, 18th August 2018, 3:00 PM
    • Saturday, 19th August 2018, 3:00 PM
  • Venue: G-23 Classroom, Academic Building

LS1801: Random walks, Markov Chains and Branching processes #

Number of talks: 2

  • Speaker: Suvadip Sana (B. Math, 2019)
  • Abstract: The concepts of random walks are trending these days. Researchers from diverse fields are trying to incorporate the structure of a random walk in their own area of research. We will try to understand random walks on integer lattices. We will also look at random walks on any connected graph. We will briefly look at Markov chains and try to understand the concepts of transient and recurrent states. We will also look at various examples of Markov Chains such as the Gambler’s Ruin problem and the Ehrenfest Model of diffusion. We will then talk about the Galton-Watson process which is a branching process. Recently one of my friends (Dwaipayan Basu of St. Xaviers Kolkata, department of microbiology) and I tried to model cancer using the Galton-Watson model. If time permits we will look at Branching Random walks (Prof. Parthanil Roy recently published a paper on that topic). If even further time is permitted I will talk about my ongoing work with my friend, about explaining protein folding using Markov Chains.
  • Pre-requisites: Basic Probability theory (mostly basics of conditional probability).
  • Further Note: Main takeaway from this talk would be the idea of Random Walks and Markov Chains. Without any pre-requisites you can still get the ideas involved. As such, this talk is accessible to all.
  • Date and Time:
    • Friday, 11th August 2018, 3:00 PM
    • Saturday, 12th August 2018, 3:00 PM
  • Venue: G-23 Classroom, Academic Building