The schedule of ICTS courses for Jan - Apr 2020 are given below

    1. Topics in Rigorous Statistical Mechanics (Elective)

      Instructor:  Riddhipratim Basu

      Venue: IISc Mathematics department, room TBA

      Class Timings: Tuesday - Thursday 3:30-5:00 pm

      Course Description:This is not a physics course!! We shall cover a selection of topics in probability theory coming from statistical physics models on the Euclidean lattice. A few possible examples of the models include: Ising model, O(N) model, Gaussian free field, contact process, voter model and exclusion processes.

      Prerequisites:This course will be aimed at Int-Ph.D. and Ph.D. students working in probability theory and related areas. A course in graduate probability theory is useful, but not absolutely necessary. A student with a strong undergraduate background in probability (i.e., without measure theory) might also find this course accessible.

      For more details:http://math.iisc.ac.in/all-courses/ma397.html

    2.  

    3. Condensed Matter Physics-1 (Elective)

      Instructor:  Chandan Dasgupta and Subhro Bhattacharjee

      Venue: Chern Lecture Hall, ICTS

      Class Timings: Monday and Wednesday 5-6.30 PM

      First Meeting: 2nd January 2020, 3:15 pm

      Course Description:This course is aimed to introduce the basics of condensed matter physics. These ideas and techniques form the building blocks for studies in quantum many-body physics and a large class of quantum field theories that form the basis of our present understanding of materials around us. A detailed outline is available on the ICTS website. Students interested in aspects of quantum many-body physics are strongly encouraged to credit/audit the course.

      Prerequisites:Quantum Mechanics II, Statistical Mechanics I

      For more details: Click here

    4.  

    5. Learning from Data (Elective)

      Instructor:  Amit Apte and Sreekar Vadlamani

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Mon + Wed 09:30-11:15; Lab: Tue 09:30-11:30 (Chern Lecture Hall)

      First Meeting: Wed 08 Jan 11:00-12:30

      Text Books:

      1. An Introduction to Statistical Learning, with Applications in R, by Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani (ISLR in the rest of the document)
      2. Other references announced in class when they are needed (probably some parts of “Machine Learning: a Probabilistic Perspective,” by Kevin Murphy)

      Prerequisites:Basic probability theory; Linear algebra; Python (or R / Matlab / Julia, but the instructors will use and can help with python only!); Access to laptop with python / R / Matlab / Julia

      Structure of the course:The course will consist of ≈7 units of ≈7.5 hours each, consisting of lectures and labs, with approximately 2 hours of the lab for 3 hours of lectures. For each topic mentioned below, “N hours + M hours” means N hours of lectures and M of a lab.

      What should the students gain out of this course?
      On successful completion of this course, it is intended that the students would be able to perform data analytic routines involving fitting statistical models to the given dataset for different cases (qualitative and quantitative) of response and predictor variables. Specifically, the student will learn algorithms to unravel patterns in data and make predictions and inferences using data.

      How will the course achieve the goals?
      The lectures will cover the basic theory of each of the methods while the students will get hands-on experience of implementing the routines discussed in class on different datasets in lab sessions.

      What is the assessment?
      Regular homework assignments and in-class quizzes; p ≈ 40%
      Either a final exam or a project (to be decided, based on many factors): (100-p)%

    6.  

    7. Statistical mechanics (Core)

      Instructor:  Anupam Kundu

      Venue: Emmy Noether Seminar Hall

      Class Timings: Wednesday 03:30 PM - 05:00 PM Chern lecture hall and Friday 04:00 PM - 05:30 PM Chern lecture hall

      First Meeting: Wednesday 08 Jan 05:00 - 06:30

      For more details: Click here

    8.  

    9. Classical Electromagnetism Course (Core)

      Instructor:  Loganayagam R

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Tuesday and Fridays, 11:00-12:30 AM(Tentative)

      Tutorials on Wednesday: 3:00-4:00 PM(Tentative)

      First Class (Introduction): Friday (02:00 pm - 05:00 pm), 3rd January, 2020
      Emmy Noether Seminar Hall (Note unusual venue/timing for the first class.)

      For more details: Click here

    10.  

    11. Basics of Nonequilibrium Statistical Physics (Elective)

      Instructor:  Abhishek Dhar

      Venue: Emmy Noether Seminar Hall, ICTS
      On 3rd Feb ARC seminar Room
      on 29th Jan and 5th Feb S N Bose meeting room

      First Meeting: First Meeting: Friday, Jan 3, 4 PM Chern lecture hall, ICTS Campus, Bangalore

      Class Timings: 11:00 to 12:30 PM Monday and Wednesday

      The topics to be covered are:
      (i) Basics of random walks
      (ii) Basics of Markov processes.
      (iii) Brownian motion, classical and quantum Langevin equations
      (iv) Fokker Planck equations and quantum master equations
      (v) Linear response theory

      The course will be aimed at understanding the formalism through examples.
      Requirements: Students should have a solid basic knowledge of statistical physics and quantum physics

      Books:
      (i) Stochastic processes in physics and chemistry: van Kampen
      (ii) Nonequilibrium Statistical Physics: Noelle Pottier

    12.  

    13. Geometry and Topology in Physics (Elective)

      Instructor:  Joseph Samuel

      Class Timings: Wednesday 02:00 PM - 03:30 PM Chern lecture hall and Thursday 11:00 AM - 12:30 PM Chern lecture hall

      First Meeting: 2nd January 2020, 11:00 am Feynman

      Prerequisites: Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics. (all at the level of Landau and Lifshitz), basic complex analysis and 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 fifteen-minute 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. The remaining 60% is from the final exam

    14.  

    15. An Introduction to GW Physics & Astronomy (Elective)

      Instructor:  P.Ajith and Bala Iyer

      Venue: Chern Lecture Hall, ICTS

      Class Timings: 10:00 - 11:30 am on Wed & Fri (to be confirmed after the first meeting)

      First Meeting: 10:00 am, Jan 17 (Fri)

      Prerequisites: General Relativity, exposure to Python and Mathematica

      Contents:

      • Theory of GWs
      • Detection of GWs
      • GW data analysis
      • GW source modeling
      • Astrophysics of GW sources

      Evaluation: 50% assignments + 50% written test.

      Books:

      • Bernard Schutz, A First Course in General Relativity (Cambridge)
      • Michele Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford)
      • Jolien D. E. Creighton & Warren G. Anderson, Gravitational-Wave Physics and Astronomy: An Introduction to Theory, Experiment and Data Analysis (Wiley-VCH)
      • Nils Andersson, Gravitational-Wave Astronomy: Exploring the Dark Side of the Universe (Oxford)
      • Stuart L. Shapiro Saul A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (Wiley-VCH)

    16.  

    17. String theory II (Reading)

      Instructor:  Loganayagam R

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Tuesday and Friday, 02:30-4:00 PM(Tentative)

      First Meeting: Tuesday (02:30 PM), 7th Jan 2020

      For more details: Click here

    18.  

    19. Topics in Fluid Mechanics (Reading)

      Instructor:  Rama Govindarajan

  • Physical Sciences
  • The schedule of ICTS courses for Aug - Nov 2019 are given below

    1. Introduction to General Relativity (Reading)

      Instructor:  Bala Iyer

      Venue: Amal Raychaudhuri Meeting room, ICTS Campus, Bangalore

      Class Timings: Monday 1:45-3:15 pm, Friday 1:45-3:15 pm

      First Class: Monday, 12 August, 2019

      Text Books:

      1. Introducing Einstein’s Relativity: Ray D’Inverno
      2. A first course in general relativity: B. Schutz

      Structure of the course:
      The reading course has three components:

      1. Weekly Presentation and Participation
      2. Problem solving
      3. Final Oral Exam/Seminar

      Presentations will be Twice a week (1.5 hrs each) where all students take turns in reading the assigned text and presenting them. I will start off the course with an Overview Lecture on GR and Information on Standard Texts they can consult. Problems on various modules will be evaluated by a TA. There will be an end-semester Oral Exam (which may be replaced by a Seminar)

      Final Grades will be based on:

      1. Class presentation/participation: 30%
      2. Problems: 30%
      3. End term Oral Exam (or Seminar): 40%
    2.  

    3. String Theory I (Reading)

      Instructor:  R.Loganayagam

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Wednesday and Friday, 11:00-12:30 AM(Tentative)

      First Class: Wednesday (10:00 am), 7th August, 2019

      Structure of the course: The reading course has three components : Presentation/Class participation, assignments and exams.

      Presentations will be twice a week (1.5-2hrs each) where all students take turns in reading the assigned text and presenting them. I will start off the course with a set of 6 to 8 lectures (i.e, 3 − 4 weeks) giving a brief survey at the level of basic textbooks mentioned below.

      Assignments will be a set of problems on various modules which need to be handed over by those who are crediting the course. Since I do not really have a TA for this course, I want the students who credit this course to grade each others’ assignments.

      There will be a mid-semester and an end-semester exam (the latter can be replaced by a term-paper, see below for details).

      The grading policy will be based on the following weightage :

      – Class presentation/participation : 20% – Assignments : 40%
      – Mid term Exam : 20%
      – End term Exam (or) Term paper : 20%

      For more details, see the PDF

    4.  

    5. Classical Mechanics (Core)

      Instructor:  Manas Kulkarni  

      Class Timings: Wednesdays - 3:30 to 5:00 pm and Fridays – 4 pm to 5:30 pm

      Venue: Chern lecture hall, ICTS Campus, Bangalore

      First Class: Wednesday (4:00pm), 7th August, 2019

      Topics:

      1. Recap:
        -Recap of Newton's laws and their consequences
        -System of point masses, Rigid Bodies
        -Classical driven-dissipative systems
         
      2. Lagrangian Formulation:
        -Principle of least action
        -Noether's Theorem, Symmetries
        -Small Oscillations, Applications
         
      3. Rigid body motion:
        -Euler Angles
        -Tops
         
      4. Hamiltonian formulation:
        -Liouville's Theorem
        -Action-Angle variables
        -Hamilton-Jacobi Equations
         
      5. Classical Integrable Models and Field Theory:
        -Lax Pairs
        -Toda Model
        -Calogero Family of Models
        -Integrable Field Theories
        -Integrable Partial Differential Equations and applications in physics.
    6.  

      Books:

      1. Landau Lifshitz course on theoretical physics: Vol 1: Classical Mechanics
      2. Classical Mechanics by Herbert Goldstein, Charles P. Poole, John L. Safko
      3. Analytical Mechanics by Louis N. Hand, Janet D. Finch
      4. classical integrable finite-dimensional systems related to Lie algebras, M.A. Olshanetsky, A.M.Perelomov, Physics Reports, Volume 71, Issue 5, May 1981, Pages 313-400

       

    7. Physics of Living Matter (Elective)

      Instructor:  VijayKumar Krishnamurthy  

      Prerequisites: A first course on statistical physics

      Outline: Basic phenomenology of living systems. Bionumbers. Statistical physics in biology (active particles, chemical kinetics, feeding by diffusion, membrane potentials). Molecular machines (molecular motors, polymerases, synthases, enzymes, ion-pumps, mitochondria). Macromolecular assemblies (polymers, membranes). Sensing and signalling (receptor-ligand interactions, MWC model, biochemical pathways, physical limits to sensing). Hydrodynamics (Navier-Stokes, low Reynolds number flows, swimming, generalized hydrodynamics, active matter, physics of the actomyosin cytoskeleton). Pattern formation (morphogen gradients, Turing patterns, mechanochemical patterns)

      Time: Tuesdays and Thursdays 10:00 am - 11:30 am

      First Meeting: Thursday, 8th August 2019

      Venue: Feynman Lecture Hall, ICTS, Bangalore

      Webpage: https://biophysics.icts.res.in/teaching/physics-of-living-matter/

      Sign up: https://forms.gle/n5KDAzauZZBtXDbk8

    8.  

    9. Statistical Physics of Turbulent Flows (Elective)

      Instructor:  Samriddhi Sankar Ray  

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Meeting Time: Wednesdays and Thursdays: 2.00 pm - 3:30 pm

      First Meeting: Wednesday, 7th August 2019

      Course Outline:

      1. Basics of Fluid Dynamics
      2. Fourier Analysis
      3. Isotropic Turbulence: Phenomenology of Three-Dimensional Turbulence
      4. Analytical Theories (closures, etc) and Stochastic Models
      5. Two-Dimensional Turbulence

    10.  

    11. Advanced Quantum Mechanics (Core)

      Instructor:  Suvrat Raju  

      Venue and Timings: 2:30 to 4:00 pm Feynman Lecture hall, Thursdays: 2:30 to 4:00 pm Chern Lecture hall

      Course Outline

      • Mathematical preliminaries of quantum mechanics: Linear Algebra; Hilbert spaces (states and operators)
      • Heisenberg and Schrodinger pictures
      • Symmetries: Role of symmetries and types (space-time and internal, discrete and continuous); Symmetries and quantum numbers; Simple examples of symmetry (Translation, parity, time reversal); Rotations and representation theory of Angular momentum; Creation and annihilation operator formalism for a simple harmonic oscillator.
      • Perturbation Theory
      • Scattering

      We will also study some additional topics, including some elements of quantum information theory.

      Textbook:
      Modern Quantum Mechanics by Sakurai.

    12.  

    13. Lab Course (Core)

      Instructors:   Abhishek Dhar, Vishal Vasan

      Timings for first meet: 2 pm Monday, 19th August 2019

      Venue: J C Bose Lab

      Course structure:
      Students will rotate amongst 4 experiments, devoting two weeks to each experimental setup. Students are expected to devote 8 − 10 hours per week to each experiment. At the end of the allotted two week period for each experiment, students will give a short presentation to the instructors and rest of the class. Students will submit a report detailing the theory for their experiment, the experimental procedure, their data and analysis as well as their conclusions regarding the challenges, what remains to be investigated and their advice to the next team.

      List of experiments:

      1. Exploring drag force on an object moving in a fluid
      2. Observing Brownian motion and estimating Avogadro’s number
      3. Surface gravity waves and dispersion relations
      4. Resonance of acoustic waves in cavities

      Evaluation:

      1. (60%) Written report and presentation for each experiment
      2. (20%) Participation in discussions
      3. (10%) Ability to achieve open-ended goals of the experiment
      4. (10%) Final quiz: at the end of the final experiment each student will be individually quizzed on all experiments, for their understanding of the various concepts/ideas discussed throughout the term.

    The schedule of ICTS courses for Jan - Apr 2019 are given below

    1. Classical field theory (Reading)

      Instructor:  VijayKumar Krishnamurthy  

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Timings: Monday 11:00-12:30Pm, Thursday 4:00-5:30 Pm

      Topics:

      Elasticity theory and fluid dynamics with rudiments of the dynamics of anisotropic fluids and pattern formation in biology.  The course will also discuss developing finite element numerical codes in Python using FEniCS. The emphasis in the course will be on applications relevant to understanding the physics of living systems. 

      Prerequisites: Classical Mechanics and prior knowledge of the Python language. Exposure to numerical methods will be an advantage.

      Evaluation: There will be two exams and around 4 assignments which will also include coding assignments. Both the assignments and exams will carry equal weight.

      Interested people should send an email to <vijaykumar@icts.res.in> by 1700, 24th January 2019. Further details will be communicated by email.

      References:

      1. Modern Classical Physics <https://press.princeton.edu/titles/10157.html>
      2. Elasticity and Geometry <https://global.oup.com/academic/product/elasticity-and-geometry-9780198506256 >
      3. Pattern Formation and Dynamics in Nonequilibrium Systems <https://doi.org/10.1017/CBO9780511627200>
      4. Soft Matter Physics <https://link.springer.com/book/10.1007/b97416>

      FEniCS <https://fenicsproject.org/>

    2.  

    3. Bordism and topological field theory (Reading)

      Instructor Pranav Pandit

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Timings: Tuesday and Thursdays, 2:30-4:00pm

      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: 

      1. Cobordism as a generalized cohomology theory, basic homotopy theory, spectra 
      2. The Pontrjagin-Thom construction (reducing cobordism to homotopy theory)
      3. The Atiyah-Segal axiomatization of topological quantum field theories 
      4. The classification of 2d TQFTs in the Atiyah-Segal framework.
      5. 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: 
      6. Extended 2d TFTs appearing in topological string theory; Calabi-Yau A∞-categories.
      7. Constructing 3d TFTs from modular tensor categories; examples of interest in condensed matter physics.
      8. Factorization algebras (algebras of observables) and factorization homology.

      For more details, see <PDF link>

    4.  

    5. Magnetism (Elective)

      InstructorSubhro Bhattacharjee  

      VenueEmmy Noether Seminar Room, ICTS Campus, Bangalore

      Timings: Wednesday and Friday, 6:00 - 7:30 Pm

      First Class: Wednesday (4:00 - 5:30 pm), 16 January, 2019, Chern Lecture Hall, ICTS Campus, Bangalore 

      Topics:

      1. Introduction to magnetism
      2. Magnetic materials
      3. Mean eld theory for magnetic ordering and fluctuations
      4. Spin path integral
      5. Magnetism in one dimensional spin systems
      6. Quantum spin liquid and topological order
      7. Quantum Phase transitions in Magnetic systems

      For more details, see <PDF link>

      References:

      1.  Reference material will be mentioned in class topic-wise. General references include
      2. Quantum phase transition, Subir Sachdev
      3. Interacting electrons and quantum magnetism, Assa Auerbach
      4. Lectures on Many-body physics, P. Fazekas

      Grading:

      Assignments (50 %) : Typically one assignment every 2 weeks.

      End semester Exam (50%)

    6.  

    7. Classical Electromagnetism (Core)

      InstructorR.Loganayagam

      TutorsAkhil Sivakumar and Srikanth Pai

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Timings : Wednesday - 10:00 - 11:30 Am

      Tutorials : Friday - 2:30 - 3:30 Pm

      First Class: Wednesday (2:30 pm), 2nd January, 2019,(Preliminary Test I);Emmy Noether Seminar Room, ICTS Campus; Bangalore

      For more details, see <PDF link>

      The grading policy will be based on the following weightage :

      1. Quiz/Tests during Tutorials : 15% for Int.PhDs, 10% for PhD. students
      2. Assignments : 25% 
      3. Mid term Exam : 30%
      4. End term Exam : 30%
      5. 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)
    8.  

    9. Mathematical Methods for physics (Core)

      InstructorParameswaran Ajith 

      Teaching AssistantRahul Kashyap (ICTS)  

      Venue: Chern Lecture Hall, ICTS Campus, Bangalore

      Timings : Tuesday 10:00 - 11:30 Hrs and Thursday 16:00 - 17:30 Hrs

      First Class: Tuesday, 8th January, 2019

      Topics:

      Vector analysis in general coordinates, tensor analysis. Matrices, operators, diagonalization, eigenvalues and eigenvectors. Infinite series, convergence, Taylor expansion. Complex analysis, Cauchy’s integral theorem, Laurent expansion, singularities, calculus of residues, evaluating integrals. Partial differential equations, separation of variables, series solutions, Green’s function. Sturm-Liouville theory. Fourier and Laplace transforms.  

      References:

      G. Arfken & H. Weber : Mathematical Methods for Physicists (Academic) 

      B. F. Schutz, A First Course in General Relativity (Cambridge) 

      Evaluation:

      Assignments: 40%

      Mid term test: 30%

      Final test: 30%

      Course web page

    10.  

    11. Advanced Statistical Physics (Core)

      Instructor: Anupam Kundu

      Venue: Emmy Noether Seminar Room, ICTS Campus, Bangalore

      Timings: Tuesday 4:00 - 5:30pm and Friday 3:00 - 4:30 pm (Tentative)

      First Class: Wednesday (4:00 - 5:30Pm), 2nd January, 2019

      Topics:

      1. Brief overview of the statistical mechanics
      2. Interacting systems: Thermodynamic limits, fields, Collective phenomena
      3. Phenomenological description of phase transition and critical phenomena
      4. Statistical fields: Mean-field theory, Variational problem, Landau-Ginzburg theory, Saddle point approximations, Continuous and discrete symmetry breaking, domain walls.
      5. Correlations and fluctuations, Distribution functions
      6. Lattice systems, exact and approximate methods (Series expansions, Bethe-Pierls approximation, Duality in two dimension)
      7. Monte Carlo Simulations
      8. Scaling hypothesis (Homogeneity assumptions, divergence of correlation length, self similarity)
      9. Renormalisation Group theory (Conceptual, Gaussian model, Perturbative RG)
      10. Dissipative dynamics

       

      Books:

      1. Statistical Physics of fields, Mehran Karder
      2. Lectures on phase transitions and Renormalisation group, N. Goldenfeld
      3. Statistical field theory, G. Mussardo
    12.  

    13. Condensed Matter Physics -1 (Elective)  

      InstructorChandan Dasgupta and Subhro Bhattacharjee  

      Venue: Chern Lecture Hall, ICTS Campus, Bangalore

      Timings: Tuesday and Thursdays, 2:30-4:00 pm

      First Class: Thursday (2:30 pm), 3rd January, 2019

      Description: This course is aimed to introduce the basics of condensed matter physics. These ideas and techniques form the building blocks for studies in quantum many-body physics and a large class of quantum field theories that form the basis of our present understanding of materials around us. A detailed outline is attached and students interested in aspects of quantum many-body physics are strongly encouraged to credit/audit the course.

      Helpful Prerequisites

      Quantum Mechanics II, Statistical Mechanics I.

      Tentative Topics

      1. Topic 0 : Introduction to quantum condensed matter (3-4 lectures) 
      2. Topic 1: Electron Gas (7 lectures)
      3. Topic 2 : Lattice (8 lectures)
      4. Topic 3 : Electrons in crystalline solids (6 lectures)
      5. Topic 4 : Magnetism (2 lectures)
      6. Topic 5 : Superconductivity (4 lectures)

       

      For more details, see <PDF link>

       

      Grading

      1. Assignments (50%): Typically one assignment every 2 weeks.
      2. End semester Exam (50%)

     

    The schedule of ICTS courses for Aug - Nov 2018 are given below:

     

    1. Course on Fluid Mechanics (Elective: Aug- Nov 2018)

      Instructor: Rama Govindarajan

      Venue: Chern lecture hall, ICTS Campus, Bangalore

      Time: Tuesdays and Thursdays, 11:00 AM

      First Meeting: Tuesday, 21st August, 2018

    2.  

    3. Advanced Quantum Mechanics (Core)

      Instructor: Suvrat Raju

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Timings: Tuesdays and Thursdays, 2:30 - 4:00 pm

      First Class: Tuesday (2:30 pm), 7th August, 2018

      Description: This is a core course covering some fundamental concepts in quantum mechanics. We will discuss some simple linear algebra, Hilbert spaces, the Heisenberg and Schrodinger pictures, discrete symmetries, continuous symmetries with a focus on the theory of angular momentum, perturbation theory, identical particles and some elements of scattering theory. If time permits, we will also discuss some selected topics from quantum information theory.

      Textbook: The course will closely follow the textbook "Modern Quantum Mechanics" by Sakurai. Additional references, if required, will be provided in class.

    4.  

    5. Classical Mechanics (Core)

      Instructor: Manas Kulkarni

      Venue: Chern lecture hall, ICTS Campus, Bangalore

      Timings: Wednesdays and Fridays, 4:00 - 5:30 pm

      First Class: Wednesday (4:00pm), 1st August, 2018

      Topics:

      1) Recap:

      - Recap of Newton's laws and their consequences
      - System of point masses, Rigid Bodies
      - Classical driven-dissipative systems

      2) Lagrangian Formulation:

      - Principle of least action
      - Noether's Theorem, Symmetries
      - Small Oscillations, Applications

      3) Rigid body motion:

      - Euler Angles
      - Tops

      4) Hamiltonian formulation:

      - Liouville's Theorem
      - Action-Angle variables
      - Hamilton-Jacobi Equations

      5) Classical Integrable Models and Field Theory:

      - Lax Pairs
      - Toda Model
      - Calogero Family of Models
      - Integrable Field Theories
      - Integrable Partial Differential Equations and applications in physics.

    6.  

    7. Statistical Physics-I (Core)

      Instructor: Abhishek Dhar

      Venue: Chern Lecture Hall, ICTS Campus, Bangalore

      Timings: Monday 4:00 - 5:30pm, Wednesday: 2:30 - 4:00pm

      First Class:Friday, 3rd August, 2018. at 2:15pm

      Details: The course on statistical physics-I will be based on the book Statistical Physics of Particles: Mehran Kardar 

      Topics to be covered:

      1. Thermodynamics, 
      2. Probability,  
      3. Kinetic theory of gases
      4. Classical statistical mechanics
      5. Interacting particles
      6. Quantum statistical mechanics
      7. Ideal quantum gases
    8.  

    9. Biological Physics (Elective)

      Course TitleBiological Physics (Elective)

      Instructor:  Vijay Kumar Krishnamurthy, Sriram Ramaswamy, Shashi Thutupalli

      Venue: Physics department, IISc, Bangalore

      Time: Tuesdays and Fridays, 2:00 pm- 3:30 pm

      First Meeting:Tuesday, 7th August, 2018

      Outline

      • the living state as a physicist sees it
      • what a cell contains
      • noise and biological information
      • random walks, Brownian motion, diffusion
      • fluid flow in cell and microbe biology
      • entropic forces, electrostatics, chemical reactions, self-assembly
      • macromolecules: statistics, forces, folding, melting
      • molecular machines
      • electrical transport across membranes: neurons, nerve impulses
      • cell membrane mechanics: elasticity, order, shape, dynamics
      • the cytoskeleton and cell mechanics
      • collective motility

      Prerequisites

      Mechanics and Statistical physics at 1st-year graduate student level

      Evaluation

      Homework assignments, mid-semester & end-semester exams

      Reference Texts

    References in biophysics

     

    1. Quantum and Statistical field theory (Core)  


      Instructor: Subhro Bhattacharjee

      Tutor : Pushkal Shrivastava

      VenueEmmy Noether Seminar Room, ICTS Campus, Bangalore

      Meeting Time: Tuesdays & Thursdays: 3:15 pm - 4:45 pm

      First Class:  Thursday (3:00 pm), January 4, 2018

      Course Outline :

      • Statistical Mechanics - From the discrete to the continuum
      • Quantum Mechanics of particles to continuum Quantum Fields
      • Functional integral formulation of QM and QFT
      • Parallels and Differences between continuum description of Stat. Mech. and Quantum systems.
      • Spontaneous Symmetry breaking 
      • Wilsonian RG​
      • Additional reading topics selected by the instructor

         
    2. Electromagnetic Theory​ (Core)  


      InstructorR Loganayagam

      Tutor : Chandan Kumar Jana

      VenueEmmy Noether Seminar Room, ICTS Campus, Bangalore

      Meeting Time: Tuesdays & Thursdays: 10:30 am - 12:00 pm

      First Class:  Wednesday (4:30 pm), January 3, 2018

      Course Outline Please click here for more details
       

    3. Condensed Matter Physics - Interacting Systems (Elective)  


      InstructorChandan Dasgupta

      VenueEmmy Noether Seminar Room, ICTS Campus, Bangalore

      Meeting Time: Mondays: 11:30 am - 1:00 pm & Wednesdays: 1:45 pm - 3:15 pm

      First Class:  Wednesday (11:30 am), January 10, 2018

      Prerequisites:  Courses on elementary solid state physics and statistical physics.

      Course Outline

      • Classical systems of particles: Cluster expansion, van der Waals equation, liquid-state theory,classical density functional theory.
      • Interacting electrons: Hartree-Fock approximation, exchange and correlation effects, quasiparticles, Fermi liquid theory, density functional theory. Dielectric function of electron gas - random phase approximation, plasmons, screening. The Hubbard model - metal-insulator transition, spin and charge density wave states.
      • Interacting bosons: Weakly interacting bosonic systems, Bose-Einstein condensation, superfluidity. Anharmonic effects in phonons. 
      • Electron-phonon interaction: Phonons in metals, electron mass renormalization, effective interaction between electrons, polarons.
      • Superconductivity: Cooper instability, BCS theory, Ginzburg-Landau theory, vortex lattice, Josephson effect.
      • Magnetism: Microscopic mechanisms, models, magnetic phase transitions, spin waves.

         
    4. Numerical methods for Physics and Astrophysics (Elective)  


      Instructor: P. Ajith

      Tutor : Ajit Kumar Mehta

      VenueEmmy Noether Seminar Room, ICTS Campus, Bangalore

      Meeting Time: Wednesdays & Fridays: 3:30 pm - 5:30 pm

      First Class:  Wednesday (3:30 pm), January 17, 2018

      More info: click here
       

    5. Classical fields - elasticity theory and fluid dynamics (Reading)

      Instructor: Abhishek Dhar

      Summary:  The course will be based almost entirely on the book "Applications of classical physics" by Roger D. Blandford and Kip S. Thorne. The focus will be on explaining the basics of elasticity theory and fluid dynamics, and  their applications to understanding  various physical phenomena, both from everyday life and from the laboratory.

      Course contents:  Chapters 11-15 of "Applications of classical physics" available here  Chapter 11: Elastostatics , Chapter 12: Elastodynamics, Chapter 13: Foundations of Fluid Dynamics,  Chapter 14: Vorticity, Chapter 15: Turbulence

    Courses for Aug - Nov 2017

    Courses for Jan - Apr 2017

    Courses for Aug - Nov 2016

    Courses for Aug - Nov 2015

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

    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.  

    3. 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. 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 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:

      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.

      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.

    4.  

    5. 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 defintions and examples and methods of computing them.

      Topology

      1. Differential geometry of curves and surfaces: curvature of curves, Serre-Frenet formula, tangent planes, Gauss map, prinicipal curvatures, Gaussian and mean curvature.
      2. Manifolds, vector fields on manifolds, Lie algbera, 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
    Course 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:

    1. Bordism and topological field theory (Reading)

      Instructor Pranav Pandit

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Timings: Tuesday and Thursdays, 2:30-4:00pm

      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: 

      1. Cobordism as a generalized cohomology theory, basic homotopy theory, spectra 
      2. The Pontrjagin-Thom construction (reducing cobordism to homotopy theory)
      3. The Atiyah-Segal axiomatization of topological quantum field theories 
      4. The classification of 2d TQFTs in the Atiyah-Segal framework.
      5. 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: 
      6. Extended 2d TFTs appearing in topological string theory; Calabi-Yau A∞-categories.
      7. Constructing 3d TFTs from modular tensor categories; examples of interest in condensed matter physics.
      8. Factorization algebras (algebras of observables) and factorization homology.

      For more details, see <PDF link>

    2.  

    3. Introduction to Mechanics

      InstructorVishal Vasan

      Venue: CAM Lecture Hall 111, Bangalore

      TimingsTuesday & 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) Hamilton-Jacobi theory

             II. Continuum Mechanics

                    (a) Conservation equations, strain and constraint tensors

                    (b) Constitutive laws (solid and fluid), frame indifference, isotropy

                    (c) Stokes, Navier-Stokes and Euler systems

                    (d) Maxwell system

             III. Water-waves

                    (a) Potential flow in a freely moving boundary

                    (b) Hamiltonian formulation of water waves

                    (c) Multiple scales and asymptotic models

                    (d) Shallow-water waves

                    (e) Quasi-geostrophic 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. Home-works 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. Cohen-Tannoudji, Quantum Mechanics Vol. I  

    4.  

    5. 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 exponents

      2) Nonlinear systems:

            - flows, stable and unstable manifolds
            -  limit sets and attractors 

      3)  Bifurcations and chaos  

             - normal forms, Lyapunov exponents (again!)

      4) Ergodic theory and hyperbolic dynamical systems.


      Reference Texts

          1. Introduction to Linear Systems of Differential Equations by L. Ya. Adrianova; https://bookstore.ams.org/mmono-146
          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


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

      Core Elective Courses
      Course 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:


    1. Techniques in discrete probability (Elective)

    Instructor: Riddhipratim Basu

    Venue: Math department LH-5, IISc, Bangalore

    Meeting Time: Tuesdays and Thursdays, 2:00-3:30 pm 

    First Class: Thursday, 2nd August, 2018


    MA 394: Techniques in discrete probability

    Credits: 3:0

    Pre-requisites:

    1. 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)

    1. the probabilistic method;
    2. first and second moment methods, martingale techniques for concentration inequalities;
    3. coupling techniques, monotone coupling and censoring techniques;
    4. correlation inequalities, FKG and BK inequalities;
    5. isoperimetric inequalities, spectral gap, Poincare inequality;
    6. Fourier analysis on hypercube, Hypercontractivity, noise sensitivity and sharp threshold phenomenon;
    7. Stein’s method;
    8. 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:

    1. Noga Alon and Joel Spencer, The Probabilistic Method ,Wiley, 2008.
    2. Geoffrey Grimmett, Probability on Graphs ,Cambridge University Press, 2010.
    3. 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 Courses
    Course 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

    1. 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.​
       

    2. 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.

    Courses for Aug - Nov 2017

    Courses for Jan - Apr 2017