ICTS

1. Algebra: A Categorical Perspective

   Instructor: Pranav Pandit

   Venue: Chern Lecture Hall, ICTS Campus, Bangalore

   Course description: This will be an advanced course in algebra, emphasizing the categorical viewpoint and the methods of homological algebra. Topics that we will aim to discuss include categories and functors, (co)limits and Kan extensions, adjunctions and monads, derived categories, derived functors, algebras and their representation theory, and Galois theory.

   Prerequisites: The equivalent of a one-year graduate-level course in algebra

   First meeting: 11:00 am, Tuesday, 6th August 2019

   For more details, see the PDF

2. MA 396: Theory of large deviations and related topics

   Instructor: Anirban Basak

   Email: anirban.basak@icts.res.in

   Course webpage: https://home.icts.res.in/~anirban/MA396-2019.html

   Office hours: to be announced later.

   Office location: to be announced later.

   Class time and location: Tu Th 2.00-3.30 PM, LH-3, IISc Mathematics department.

   Prerequisite: This is a graduate level topics course in probability theory. The graduate-level measure-theoretic probability will be useful, but not a requirement. The course will be accessible to advanced undergraduates who have had sufficient exposure to probability.

   Course outline: Large deviations provide quantitative estimates of the probabilities of rare events in (high-dimensional) stochastic systems. The course will begin with the general foundations of the theory of large deviations and will cover classical large deviations techniques. In the latter part of the course some recent developments, such as large deviations in the context of random graphs and matrices, and their application in statistical physics will be discussed.

   Suggested books:

   1. Amir Dembo and Ofer Zeitouni, Large Deviations Techniques and Applications.
   2. Firas Rassoul-Agha and Timo Seppäläinen, A Course on Large Deviations with an Introduction to Gibbs Measures.
   3. Marc Mézard and Andrea Montanari, Information, Physics, and Computation.
   4. Sourav Chatterjee, Large Deviations for Random Graphs.
    

   A weekly schedule will be posted later.

   Grading: Students taking this course for credit are required to do a (reading) project, submit a report, and give a presentation on the same at the end of the semester. Depending on the number of registered students the grading scheme may change.

3. Introduction to Topology and Geometry

   Instructor: Rukmini Dey

   Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

   Meeting Time: Monday: 2:00 pm - 3:00 pm and Friday: 2:00 pm - 4:00 pm

   First Meeting: 7th August 2019

   Syllabus:

   Topology

   1. Pointset topology: open sets, closed sets, notions of continuity, connected sets, compact sets etc, homeomorphism, homotopy etc.
   2. Covering spaces, Fundamental Group and Simplicial Homology --basic definitions and examples and methods of computing them.

   Geometry

   1. Differential geometry of curves and surfaces: the curvature of curves, Serre-Frenet formula, tangent planes, Gauss map, principal curvatures, Gaussian and mean curvature.
   2. Manifolds, vector fields on manifolds, Lie algebra, Lie group, their action on manifolds.
   3. Differential forms on manifolds; de Rham cohomology

The following is the list of courses offered at IISc. For the current list see:

Core Elective Courses

Advanced Elective Courses