PhD and Integrated PhD coursework
 

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