The schedule of ICTS courses for Aug  Nov 2019 are given below:

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 oneyear graduate level course in algebra
First meeting: 11:00 am, Tuesday, 6th August 2019
For more details, see the PDF

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/MA3962019.html
Office hours: to be announced later.
Office location: to be announced later.
Class time and location: Tu Th 2.003.30 PM, LH3, IISc Mathematics department.
Prerequisite: This is a graduate level topics course in probability theory. 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 (highdimensional) stochastic systems. The course will begin with 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 its application in statistical physics will be discussed.
Suggested books:
 Amir Dembo and Ofer Zeitouni, Large Deviations Techniques and Applications.
 Firas RassoulAgha and Timo Seppäläinen, A Course on Large Deviations with an Introduction to Gibbs Measures.
 Marc Mézard and Andrea Montanari, Information, Physics, and Computation.
 Sourav Chatterjee, Large Deviations for Random Graphs.
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.

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
 Pointset topology: open sets, closed sets, notions of continuity, connected sets, compact sets etc, homeomorphism, homotopy etc.
 Covering spaces, Fundamental Group and Simplicial Homology basic defintions and examples and methods of computing them.
Topology
 Differential geometry of curves and surfaces: curvature of curves, SerreFrenet formula, tangent planes, Gauss map, prinicipal curvatures, Gaussian and mean curvature.
 Manifolds, vector fields on manifolds, Lie algbera, Lie group, their action on manifolds.
 Differential forms on manifolds; de Rham cohomology
The following is the list of courses offered at IISc. For the current list see:
Core Elective CoursesCourse No.  Course Title 
MA 212  Algebra I 
MA 219  Linear Algebra 
MA 221  Analysis I: Real Anaysis 
MA 231  Topology 
MA 261  Probability Models 
MA 223  Functional Analysis 
MA 232  Introduction to Algebraic Topology 
MA 242  Partial Differential Equations 
MA 213  Algebra II 
MA 222  Analysis II : Measure and Integration 
MA 224  Complex Analysis 
MA 229  Calculus on Manifolds 
MA 241  Ordinary Differential Equations 
Advanced Elective Courses
Course No.  Course Title 
MA 215  Introduction to Modular Forms 
MA 277  Advanced PDE and Finite Element Method 
MA 361  Probability Theory 
MA 368  Topics in Probability and Stochastic Processes 
MA 278  Introduction to Dynamical Systems Theory 
MA 313  Algebraic Number Theory 
MA 314  Introduction to Algebraic Geometry 
MA 315  Lie Algebras and their Representations 
MA 317  Introduction to Analytic Number Theory 
MA 319  Algebraic Combinatorics 
MA 320  Representation Theory of Compact Lie Groups 
MA 332  Algebraic Topology 
MA 364  Linear and Nonlinear Time Series Analysis 
MA 369  Quantum Mechanics 
The schedule of ICTS courses for Jan  Apr 2019 are given below:

Bordism and topological field theory (Reading)
Instructor: Pranav Pandit
Venue: Feynman Lecture Hall, ICTS Campus, Bangalore
Timings: Tuesday and Thursdays, 2:304:00pm
First Class: Wednesday (6:00  7:30 pm), 15 January, 2019, Feynman Lecture Hall, ICTS Campus, Bangalore
Topics:
The core topics for this course will be:
 Cobordism as a generalized cohomology theory, basic homotopy theory, spectra
 The PontrjaginThom construction (reducing cobordism to homotopy theory)
 The AtiyahSegal axiomatization of topological quantum field theories
 The classification of 2d TQFTs in the AtiyahSegal framework.
 The notion of an extended topological field theory, and the statement of the classification theorem for such theories (the cobordism hypothesis). 1 Possible advanced topics, depending on the time available and the interests of the participants, include:
 Extended 2d TFTs appearing in topological string theory; CalabiYau A∞categories.
 Constructing 3d TFTs from modular tensor categories; examples of interest in condensed matter physics.
 Factorization algebras (algebras of observables) and factorization homology.
For more details, see <PDF link>

Introduction to Mechanics
Instructor: Vishal Vasan
Venue: CAM Lecture Hall 111, Bangalore
Timings: Tuesday & Thursday 9:00  10:30am
First Class: Tuesday, 8th January, 2019
Required background: This course is meant to introduce a typical student of mathematics to certain PDE/ODE models as they arise in physics. As such, this course is targeted towards students with no prior physics background. Familiarity with ideas from ODE/PDE theory and functional analysis will be very useful.
Tentative Topics
I. Classical Mechanics
(a) Elements of Newtonian mechanics and formulations: Lagrangian, Hamiltonian
(b) Principle of stationary action
(c) Legendre transform
(d) Noether’s theorem
(e) HamiltonJacobi theory
II. Continuum Mechanics
(a) Conservation equations, strain and constraint tensors
(b) Constitutive laws (solid and fluid), frame indifference, isotropy
(c) Stokes, NavierStokes and Euler systems
(d) Maxwell system
III. Waterwaves
(a) Potential flow in a freely moving boundary
(b) Hamiltonian formulation of water waves
(c) Multiple scales and asymptotic models
(d) Shallowwater waves
(e) Quasigeostrophic equations
IV. Quantum mechanics
(a) Quantum states
(b) Observers and Observables
(c) Amplitude evolution
(d) Simple examples
(e) Evolution of expectations and conservation laws
Evaluation and homeworks
 Homeworks will be assigned typically every other week and due in two weeks time. Homeworks count for 50% of the final grade and there will likely be 4 − 5 homeworks.
 Students will be expected to submit a report. Topics will be chosen after discussion with the instructor, but typically will be a specific PDE model. The report will discuss the relevance, derivation and open problems associated with the PDE model and any other related issues.
 Each student will submit one draft (as a midterm) and a final draft (as a final exam). Writing is an essential part of the course and all reports must be prepared using LATEXor similar software.
 Students may also expect to be assigned required reading materials (articles, book chapters, etc.)
Reference books
The main reference will be An Brief Introduction to Classical, Statistical and Quantum Mechanics by O. B¨uhler.
In addition, the students may find the following list of texts useful throughout the course to supplement their understanding.
(1) V.I Arnold, Mathematical Methods in Classical Mechanics
(2) G. Duvaut, Mechanics of continuous media
(3) H. Goldstein, C.P. Poole & J. Safko, Classical Mechanics
(4) R. Dautray & J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology
(5) A. Chorin & Marsden, A Mathematical Introduction to Fluid Mechanics.
(6) P. Kundu, Fluid Mechanics
(7) E. Zeidler, Nonlinear Functional Analysis and its Applications IV.
(8) T. Frankel, Geometry of Physiscs
(9) M. Peyrard & T. Dauxois, Physics of Solitons
(10) J. Pedlosky, Waves in the ocean and atmosphere
(11) C. CohenTannoudji, Quantum Mechanics Vol. I
Dynamics Systems
Instructor: Amit Apte
Venue: Feynman Lecture Hall, ICTS Campus, Bangalore
Timings: Monday and Wednesdays, 4:15  5:45 pm
First Class: Wednesday (11:00am), 2nd January, 2019
Topics:
1) Linear dynamical systems:
 autonomous systems,
 Floquet theory for periodic systems,
 Lyapunov exponents and their stability,
 numerical techniques for computing Lyapunov exponents2) Nonlinear systems:
 flows, stable and unstable manifolds
 limit sets and attractors3) Bifurcations and chaos
 normal forms, Lyapunov exponents (again!)
4) Ergodic theory and hyperbolic dynamical systems.
Reference Texts1. Introduction to Linear Systems of Differential Equations by L. Ya. Adrianova; https://bookstore.ams.org/mmono146
2. Differential Equations and Dynamical Systems by Lawrence Perko
3. Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris W. Hirsch, Stephen Smale, and Robert L. Devaney
4. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer and Philip Holmes
5. Introduction to Smooth Ergodic Theory by Luis Barreira and Yakov Pesin
N+1. Review articles and other papers as and when required
The following is the list of courses offered at IISc. For the current list see:
Core Elective CoursesCourse No.  Course Title 
MA 212  Algebra I 
MA 219  Linear Algebra 
MA 221  Analysis I: Real Anaysis 
MA 231  Topology 
MA 261  Probability Models 
MA 223  Functional Analysis 
MA 232  Introduction to Algebraic Topology 
MA 242  Partial Differential Equations 
MA 213  Algebra II 
MA 222  Analysis II : Measure and Integration 
MA 224  Complex Analysis 
MA 229  Calculus on Manifolds 
MA 241  Ordinary Differential Equations 
Advanced Elective Courses
Course No.  Course Title 
MA 215  Introduction to Modular Forms 
MA 277  Advanced PDE and Finite Element Method 
MA 361  Probability Theory 
MA 368  Topics in Probability and Stochastic Processes 
MA 278  Introduction to Dynamical Systems Theory 
MA 313  Algebraic Number Theory 
MA 314  Introduction to Algebraic Geometry 
MA 315  Lie Algebras and their Representations 
MA 317  Introduction to Analytic Number Theory 
MA 319  Algebraic Combinatorics 
MA 320  Representation Theory of Compact Lie Groups 
MA 332  Algebraic Topology 
MA 364  Linear and Nonlinear Time Series Analysis 
MA 369  Quantum Mechanics 
The schedule of ICTS courses for Aug  Nov 2018 are given below:
 Techniques in discrete probability (Elective)
Instructor: Riddhipratim Basu
Venue: Math department LH5, IISc, Bangalore
Meeting Time: Tuesdays and Thursdays, 2:003:30 pm
First Class: Thursday, 2nd August, 2018
MA 394: Techniques in discrete probability
Credits: 3:0
Prerequisites:
 This course is aimed at Ph.D. students from different fields who expect to use discrete probability in their research. Graduate level measure theoretic probability will be useful, but not a requirement. I expect the course will be accessible to advanced undergraduates who have had sufficient exposure to probability.
We shall illustrate some important techniques in studying discrete random structures through a number of examples. The techniques we shall focus on will include (if time permits)
 the probabilistic method;
 first and second moment methods, martingale techniques for concentration inequalities;
 coupling techniques, monotone coupling and censoring techniques;
 correlation inequalities, FKG and BK inequalities;
 isoperimetric inequalities, spectral gap, Poincare inequality;
 Fourier analysis on hypercube, Hypercontractivity, noise sensitivity and sharp threshold phenomenon;
 Stein’s method;
 entropy and information theoretic techniques.
We shall discuss applications of these techniques in various fields such as Markov chains, percolation, interacting particle systems and random graphs.
Suggested books:
 Noga Alon and Joel Spencer, The Probabilistic Method ,Wiley, 2008.
 Geoffrey Grimmett, Probability on Graphs ,Cambridge University Press, 2010.
 Ryan O'Donnell, Analysis of Boolean Functions ,Cambridge University Press, 2014.
The following is the list of courses offered at IISc. For the current list see:
Core Elective CoursesCourse No.  Course Title 
MA 212  Algebra I 
MA 219  Linear Algebra 
MA 221  Analysis I: Real Anaysis 
MA 231  Topology 
MA 261  Probability Models 
MA 223  Functional Analysis 
MA 232  Introduction to Algebraic Topology 
MA 242  Partial Differential Equations 
MA 213  Algebra II 
MA 222  Analysis II : Measure and Integration 
MA 224  Complex Analysis 
MA 229  Calculus on Manifolds 
MA 241  Ordinary Differential Equations 
Advanced Elective Courses
Course No.  Course Title 
MA 215  Introduction to Modular Forms 
MA 277  Advanced PDE and Finite Element Method 
MA 361  Probability Theory 
MA 368  Topics in Probability and Stochastic Processes 
MA 278  Introduction to Dynamical Systems Theory 
MA 313  Algebraic Number Theory 
MA 314  Introduction to Algebraic Geometry 
MA 315  Lie Algebras and their Representations 
MA 317  Introduction to Analytic Number Theory 
MA 319  Algebraic Combinatorics 
MA 320  Representation Theory of Compact Lie Groups 
MA 332  Algebraic Topology 
MA 364  Linear and Nonlinear Time Series Analysis 
MA 369  Quantum Mechanics 
The schedule of ICTS courses for Jan  Apr 2018 are given below
 Introduction to PDEs (Reading)
Instructor: Rukmini Dey
Venue: S N Bose Meeting Room, ICTS Campus, Bangalore
Meeting Time: Monday and Friday: 11:30 am  1:00 pm
First Class: Monday, 15th January, 2018
Course contents: First 5 chapters of Ian Sneddon's book: Elements of PDEs.
Syllabus: Ordinary Differential Equations in more than 2 variables; Partial Differential Equations of the first order; Partial Differential Equations of the Second Order; Laplace Equation; Wave Equation. If time permits we will go through some chapters of "Fourier Series" by Georgi P. Tolstov.
 Introduction to Dynamical Systems (Reading)
Instructor: Vishal Vasan
Venue: ICTS Campus, Bangalore
Meeting Time: Friday: 4:30 pm  6:00 pm
First Class: Friday, 19th January, 2018
Course contents: Nonlinear Dynamics and Chaos by S Strogatz. Selected reading from Differential Equations and Dynamical Systems by L Perko and other suitable texts.
Syllabus: The course will cover the entire content of Strogatz' book supplemented with more detailed mathematical treatments of selected theorems from other sources.