
Advanced Classical Electromagnetism  Core (PHY207.5)
Instructor: Loganayagam R
Venue: Online
Class timings: Thursdays & Saturdays: 11:002:30 pm (Tutorials on Wednesdays: 2:003:30 pm)
First meeting: Thursday (10:00  13:00 Hrs), 11th February, 2021
Course description: Please click here
The grading policy: will be based on the following weightage
– Assignments : 35% for PhD students, 40% for I.PhD students
– Mid term Exam : 30%
– End term Exam : 30%
– Term paper (a thorough review of a topic in electromagnetism not covered in textbooks below, see below for suggestions) : 5% Extra credit (Compulsory for PhD Students) Note that Assignments form a central part of this course, since one of the main aims of this course is to train students to solve problems

Advanced Classical Mechanics  Core (PHY204.5)
Instructor: Abhishek Dhar
Venue: Online
Class timings: 11 am12:30 pm on Wednesdays & Fridays
First meeting: 15th January 2021
TA: Saurav Pandey, saurav.pandey@icts.res.in
Course description:
1. Recap of basic ideas of Newtonian mechanics
2. Central force problem
3. Small oscillations
4. Dynamical systems theory basics
5. Lagrangian and Hamiltonian formulation of classical mechanics
6. Poisson brackets and symplectic structure
7. Hamilton Jacobi theory
8. Rigid body motion
9. Integrability, Chaos, and Nonlineardynamics
Prerequisites:
First course in classical mechanics; Ability to write simple programs in any language (c, python, fortran, etc.)
Books:
(a) Goldstein: Classical Mechanics (b) Reichl: The Transition to Chaos (c) Saletan and Jose: Classical Dynamics
Course evaluation: Assignments – 50 %; Midterm and Final Exam – 50 %

Lab Course  Core (PHY108.5)
Instructor:
(i) Vishal Vasan and Amit Apte: Atmospheric sciences module
(ii) Abhishek Dhar: Active matter module
(iii) Pallavi Bhat and P. Ajith: Astrophysics module
Venue:Online
Course goals:
Due to the current pandemic, the version of the experimental methods course offered will differ from the traditional one. In this course you will be introduced to several different areas of physics where experimental data play a key role. In particular you will be exposed to datasets as gathered by experimentalists working in the lab and from observation studies. You will learn how to do simple analysis & visualisation, investigate the nature and sources of systematic and random errors, and verify theoretical predictions against experimental data.
Course structure and evaluation:
The course is split into three modules: Atmospheric science, Active matter and Astrophysics. Each module will be between 2 weeks to 4 weeks long. In each module you will be introduced to some experimental methods and datasets related to that particular subfield in physics. All modules will focus on the comparisons of theory and experiment introducing the student to subtle issues of validating a model from data. At the end of each module, students will submit a written report based on their findings. Class participation is crucial. Discussions form an essential part of science and class participation will be part of the final grade. Note: the course involves data analysis and thus a significant part of the course will involve programming in a language (most likely Python). Though prior experience with programming is not necessary, it will certainly be beneficial.
Topics:
(i) Atmospheric science: Dispersive waves, Fourier series and the FFT. Waves in atmosphere and ocean as seen in temperature, pressure, clouds and other similar datasets. Precipitation.
(ii) Active matter: Brownian motion and detection of such motion experimentally. Active matter and deviation from Brownian motion.
(iii) Astrophysics: TBA.
Evaluation: Students will be evaluated on the following basis
(i) (60%=3×20%) Written report for each module
(ii) (30%) Homework assignments
(iii) (10%) Class participation
Class timings:
The course will begin with the atmospheric science module and classes will be held twice a week on tue/thur at 2:303:30pm. Note the timings for the remaining modules may change and you will need to check with your instructors!

Research Methodology and Ethics  Core (PHY200.5)
Instructor: Loganayagam R
Venue: Online
Class timings: Mondays 5:306:30 pm & Thursdays 4:005:30 pm
First meeting:Thursday 4:005:30 pm, 11th Feb, 2021.
Course description: Please click here
The grading policy: There will be no drop test for this course.
The grading policy: will be based on the following weightage
– Class participation/presentations : 50%
– Written Assignments : 50%

Geometry and Topology in Physics  Topical (PHY403.5)
Instructor: Joseph Samuel
Venue: Online
Class timings: 11 am12:30 pm on Mondays and Tuesdays
First meeting: 12 January 2021
Course description:
Prerequisites:
Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics, (all at the level of Landau and Lifshitz), complex analysis, group theory.
Textbooks:
There are no fixed textbooks for the course. We will be drawing on many sources from the published literature and the internet.
Structure of the course:
The course will cover a number of applications of geometry and topology in the context of physical examples. The emphasis will be on the examples rather than on rigour. This course will be complementary to mathematics courses on geometry and topology.
Exposure to such courses will be helpful, but not a prerequisite to follow the course.
What students will gain from the course:
An appreciation of the commonality between different areas of physics; the unifying nature of geometric and topological ideas in physics.
How the course will achieve its goals:
We will take specific examples of systems from different areas of physics and analyse them from a geometric perspective. Make connections wherever possible between the different examples. The course will start with simple examples and graduate to more advanced ones. The choice of examples will depend on the feedback I get from the students.
Assessment:
Some classes will include a twentyminute quiz, in which students are asked to answer simple questions related to the class discussion. For example, filling in missing steps in the derivation; consideration of special cases etc. This will be 40% of the assessment. There will also be regular assignments, which the students will have to turn in on time. These will count as 30%. The remaining 30% is for the final exam. It is not presently clear if the pandemic will permit inperson classes. We hope that the situation will improve by Jan 2021. If this does not happen, classes will be conducted online. In this case, students taking the course will be required to have a good internet connection. If you need help in this regard, please contact the ICTS and consult your appointment letter for more details.

Introductory Fluid Mechanics  Topical (PHY402.5)
Instructor: Rama Govindarajan
Venue: Online
Class timings: 9 am10:30 am on Tuesdays and Wednesdays
First meeting: 12th January 2021
Course description: Following is a course summary but is subject to change depending on students' interests:
1. Continuum formulation of fluid mechanics, limitations
2. Lagrangian and Eulerian perspectives
3. Conservation of mass (the continuity equation)
4. Similarity transforms
5. Stream functions, Angular momentum, Velocity gradient tensor – Symmetric and Antisymmetric parts etc.
6. Conservation of Momentum – Euler and NavierStokes Equations
7. Dynamic similarity – Buckingham Pi theorem
8. Kelvin’s Circulation theorem
9. Couette and Poiseuille Flow
10. Introduction to Turbulence – Scaling laws, and energy budget equation
11. Fully developed turbulence – K41 hypothesis
12. Singular Perturbation Theory
13. Bernoulli’s function and principle
14. Boundary layer theory
15. Flow past a plate, Blasius equation
16. Vortex Dynamics
17. Use of complex techniques for inviscid, incompressible vortex and mass source induced velocity fields.
18. Method of images
19. Potential flow past a cylinder
20. Blasius theorem – Force and torque on a solid body in a fluid (inviscid, incompressible)
21. Conformal Mapping
22. Flow instabilities – Study of Linearized equations for stability
23. Rayleigh Plateau instability
24. OrrSommerfeld equation
25. Benard Problem
26. Taylor problem on centrifugal instability
27. Reynoldsaveraged NavierStokes Equations
Evaluation: Homeworks, one midterm and one final exam.

Open Quantum Systems  Topical (PHY405.5)
Instructor: Manas Kulkarni
Venue: Online
Class timings: 4:00 pm5:30 pm on Tuesdays and Fridays
First meeting: 15th January 2021
Course description:
1. Dissipation in Quantum Mechanics: General setup and various approaches
2. Damped Quantum Harmonic Oscillator, two time averages and quantum regression
3. Spin Boson Model (Dephasing) and some generalizations
4. Dissipative twolevel and multilevel systems
5. CavityQuantum Electrodynamics (cavityQED): Exact solutions of the JaynesCummings Model (JCM)
6. Dispersive limit of the JCM and its generalizations (reduction to BoseHubbard systems)
7. Dissipative process in cavityQED systems
8. DrivenDissipative Quantum Systems and applications (driven JCM)
9. Dicke Model and phase transitions
Prerequisites:
Quantum Mechanics, Statistical Physics
Textbooks: Below are some suggested books. I will also be making additional notes.
1. Howard Carmichael, Statistical Methods in Quantum Optics 1. Master Equations and FokkerPlanck Equations (Springer)
2. Girish S. Agarwal, Quantum Optics (Cambridge University Press)
3. HeinzPeter Breuer and Francesco Petruccione, The theory of open quantum systems (Oxford University Press)
Term paper topics: Below are suggested topics for the term paper (report + presentation). The suggested references for each of them will be updated. Students will need to pick a topic (latest by February 15, 2021) and make a report and then give a presentation (at the end of the semester).
1. NonHermitian Random Matrices
2. Quantum Dot circuitQED systems
3. Optomechanical Systems
4. Selftrapping, localization in NonHermitian Systems
5. ParityTime Symmetric Systems
Grading Policy:
Homework – 40 %
Term paper (report and presentation) – 30 %
Final Exam – 30 %

Physics of Compact Objects  Topical (PHY404.5)
Instructor: Parameswaran Ajith & Bala Iyer
Tutor: Shasvath Kapadia
Venue: Online
Class timings: Wednesdays from 3:30 pm5:00 pm & Fridays from 2:15pm3:45pm
First meeting: 13th January 2021
Plan: 15 lectures + 15 tutorials (each 90 mins; 45 contact hrs)
Course description:
This course aims to provide a general introduction to the physics and astrophysics of compact objects, and compactobject binaries. We will start with introductory topics and will end by surveying some of the current research. We will draw content from several textbooks and review articles.
Stellar structure, evolution and collapse  3 lectures
 Hydrostatic equilibrium, Equations of stellar structure, Solutions to equations of stellar structure, Stellar evolution, Gravitational collapse and supernovae.
White dwarfs  3 lectures
 Electron degeneracy pressure, Structure of white dwarfs, Chandrasekhar limit, Massradius relation of white dwarfs.
Neutron stars  3 lectures
 Equation of state at higher densities, Structure of neutron stars, Mass limit of neutron stars, Massradius relation of neutron stars, Pulsars.
Black holes  3 lectures
 Schwarzschild solution, Particle and photon orbits in Schwarzschild geometry, Kerr solution, Astrophysical black holes, xray binaries, galactic nuclei.
Exotic compact objects  1 lecture
 Exotic objects and their possible observational signatures.
Compact object binaries  2 lectures
 Compact binary evolution, Binary pulsars, Compact binary coalescence, their gravitationalwave signatures.
References (not exclusive):
1. Saul Teukolsky and Stuart L. Shapiro. Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (WileyVCH; 1983).
2. T. Padmanabhan, Theoretical Astrophysics: Volume 2, Stars and Stellar Systems (Cambridge 2001).
3. Bernard F. Schutz, A First Course in General Relativity (Cambridge, 2009).
Evaluation: 70% based on assignments and homework. 30% based on final term paper.

The Black Hole Information Paradox  Topical (PHY412.5)
Instructor: Suvrat Raju
Venue: Online
Class timings: 6:30 pm 8 pm on Wednesdays and Thursdays
First meeting: 13th January 2021
Course description:
This is an advanced elective course covering recent developments in our understanding of the blackhole information paradox. We will emphasize the broader lessons that puzzles about blackhole evaporation and the blackhole interior hold for theories of quantum gravity. The topics that we plan to cover include the following:
1. Hawking's original formulation of the information paradox.
2. Paradoxes involving the blackhole interior and the monogamy of entanglement.
3. The principle of holography of information.
4. Quantum extremal Islands.
5. Paradoxes involving large AdS black holes
6. Construction of the blackhole interior in AdS/CFT
7. State dependence
8. Fuzzballs, firewalls and other proposals for horizon structure
We will use the recent review "Lessons from the Information Paradox" as a guide for the lectures.
Prerequisites:
Quantum field theory, general relativity, familiarity with blackhole thermodynamics and quantum fields in curved spacetime.
Lecture details:
The course will be entirely virtual.
We will have 2 virtual lectures per week starting the week of 11 January and continuing till midApril. Each lecture will be 1.5 hours. In addition, we will have officehours/tutorials each week for questions and discussion.
Lecture timings will be fixed later based on the convenience of the students attending.

Introduction to Dynamical Systems Theory (IISc course: MA 278; ICTS course: MTH 216.5)
Instructor: Amit Apte
Venue: googlemeet, see link below for the googleclassroom
Class timings: TBA
First meeting: 23rd February 2021 (1011 am)
To join: https://bit D.O.T ly SLASH 3bg0P2l (hope you know what I mean!)
Course description:
Linear stability analysis, attractors, limit cycles, PoincareBendixson theorem, relaxation oscillations, elements of bifurcation theory: saddlenode, transcritical, pitchfork, Hopf bifurcations, integrability, Hamiltonian systems, LotkaVolterra equations, Lyapunov function & direct method for stability, dissipative systems, Lorenz system, chaos & its measures, Lyapunov exponents, strange attractors, simple maps, perioddoubling bifurcations, Feigenbaum constants, fractals. Both flows (continuoustime systems) & discretetime systems (simple maps) will be discussed. Assignments will include numerical simulations.
Prerequisites, if any:
familiarity with linear algebra  matrices, and ordinary differential equations
Desirable:
Ability to write codes for solving simple problems.
Suggested books and references:
1. S. Strogatz, Nonlinear Dynamics and Chaos: with Applications to physics, Biology, Chemistry, and Engineering, Westview, 1994.
2. S. Wiggins, Introduction to applied nonlinear dynamics & chaos, SpringerVerlag, 2003.
3. K. Alligood, T. Sauer, & James A.Yorke, Chaos: An Introduction to Dynamical Systems, SpringerVerlag, 1996.
4. M.Tabor, Chaos and Integrability in Nonlinear Dynamics, 1989.
5. L. Ya. Adrianova, Introduction to Linear Systems of Differential Equations, AMS 1995.
6. Morris W. Hirsch, Robert L. Devaney, Stephen Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 2012.
Academic Events for this course:
Sr. No.
Event
From
To
1
First meeting
23.02.2021 (10:0011:00)
2
Course Registration
22.02.2021
05.03.2021
3
Course Dropping without mention in the Transcripts
06.03.2021
26.04.2021
3
Course Dropping without mention in the Transcripts
27.04.2021
26.05.2021
4
Last date for Instruction
28.05.2021
5
Terminal Examination  sometime between the dates of 02 to 11 June (exact date TBD)
02.06.2021
11.06.2021
The course time will be adjusted in the first meeting based on any clashes that may arise, so those interested in registering should attend the first meeting without fail.
The mode of instruction will be completely online at least until 31st March. Further decisions will be announced in class.
Note:IISc semester schedule will be followed. Interested ICTS students, please contact the instructor for registration; Interested IISc students, please contact the IISc maths department for registration process (note: IISc students need to register for IISc course number MA 278).
google classroom link is https://classroom.google.com/u/0/c/Mjc1OTY1MTk3OTIw?cjc=jt67mhlp>
It is also mentioned on http://math.iisc.ac.in/courseschedule.html

Probability in High Dimensions (IISc course: MA 363; ICTS course: MTH 217.5)
Instructor: Anirban Basak
Venue: TBA
Class timings: TBA
First meeting: tentatively first week of March (so the course will be from March to around midJune), exact dates TBA
Course description:
Prerequisites:
This is a graduate level topics course in probability theory. Graduate level measure theoretic probability will be useful, but not a requirement. Students are expected to be familiar with basic probability theory and linear algebra. The course will be accessible to advanced undergraduates who have had sufficient exposure to probability and linear algebra.
Course outline:
This course will be aimed at understanding the behavior of random geometric objects in high dimensional spaces such as random vectors, random graphs, random matrices, and random subspaces, as well. Topics will include the concentration of measure phenomenon, nonasymptotic random matrix theory, empirical processes, and some related topics from geometric functional analysis and convex geometry. Towards the latter half of the course, depending on students' interests, a few applications of the topics covered in the first half will be considered such as community detection, covariance estimation, randomized dimension reduction, and sparse recovery problems.
Suggested books and references:
1. Roman Vershynin, Highdimensional probability: An introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Series Number 47), 2018.
2. Roman Vershynin, Introduction to the nonasymptotic analysis of random matrices, Compressed sensing, 210268, Cambridge University Press, 2012.
3. Stéphane Boucheron, Gábor Lugosi, and Pascal Massart, Concentration Inequalities: A nonasymptotic theory of independence, Oxford University Press, 2013.
4. Michel Ledoux and Michel Talagrand, Probability in Banach spaces, Springer Science & Business Media, 2013.
5. Avrim Blum, John Hopcroft, and Ravindran Kannan, Foundations of Data Science, Cambridge University Press, 2020.
6. Joel Tropp, An Introduction to Matrix Concentration Inequalities, Foundations and Trends in Machine Learning, Vol. 8, No. 12, pp 1230, 2015.
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.
Email: anirban.basak@icts.res.in
Course webpage: Link
Office hours: By email appointment.
Note: IISc semester schedule will be followed (the start date and duration to be decided). Interested ICTS students, please contact the instructor for registration; Interested IISc students, please contact the IISc maths department for registration process (note: IISc students need to register for IISc course number MA 363).
The schedule of courses for JanApr 2021 semester is given below
The schedule of courses for September  December 2020 are given below The schedule of ICTS courses for Jan  Apr 2020 are given below:
The schedule of ICTS courses for Aug  Nov 2019 are given below
Books:
