The schedule of ICTS courses for **Aug - Nov 2017 **are** **given below:

**Introduction to Minimal Surfaces (Elective)**

** Instructor**: Rukmini Dey

__ Prerequisites__: Some very basic knowledge of complex analysis will be assumed.

** Venue: **S N Bose Meeting Room, ICTS Campus, Bangalore

__ Meeting Time__: Monday, Wednesday and Friday: 2:30 - 3:30 pm

**First Class:**** **Wednesday (2:30 pm), August 16, 2017

__ Course contents__:

- Serre-Frenet formula for curves, Parametric surfaces, Isothermal parameters, Gauss Map, Gaussian Curvature, Mean curvature, Area functional etc.
- Surfaces that locally minimise area in Euclidean space (minimal surfaces). Harmonic coordinates in isothermal parameters. A lot of examples of minimal surfaces.
- Minimal surfaces with boundary : Plateau’s problem
- The Gauss map for minimal surfaces with some examples.
- Weierstrass-Enneper representation of minimal surfaces. Many more examples of minimal surfaces.
- Conjugate minimal surfaces. One parameter family of isometric minimal surfaces.
- The Björling problem and Schwartz’s solution to it.

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**If time permits**: - Surfaces that locally maximise area in Lorenztian space (maximal surfaces). A lot of examples and analogous results, as in minimal surface theory, for maximal surfaces.
- Connection between minimal and maximal surfaces and Born-Infeld solitons.
- Constant mean curvature surfaces of non-zero mean curvature – the optimization problem they solve.

**Reference Books:**

- Differential Geometry of curves and surfaces: Manfredo Do Carmo
- A survey of minimal surfaces : Robert Osserman
- Minimal Surfaces I : Dierkes, Hildebrandt, Küster, Wohlrab
- Lectures on MInimal surfaces: J. Nitsche
- Lectures on Minimal Surfaces in R 3 : Yi Fang
- Surfaces of constant mean curvature: K. Kenmotsu.
- Some papers on Minimal and Maximal surfaces and Born-Infeld solitons by various authors including Rukmini Dey, Pradip Kumar and Rahul Kumar Singh.

**Quantum Mechanics II (Core)**

** Instructor**: Suvrat Raju

** Venue: **Emmy Noether Seminar Room, ICTS Campus, Bangalore

__ Meeting Time__: Tuesday & Thursday - 3:30 pm - 5:00 pm

(Meeting Times are subject to change. If this clashes with some other class or commitment, please try and come to the first lecture so that we can decide on a time that is convenient for everyone then.)

**First Class:**** **Friday (2:30 pm), August 4, 2017

__ 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.

**Statistical Physics II (Core)**

** Instructor**: Anupam Kundu

** Venue: **Emmy Noether Seminar Room, ICTS Campus, Bangalore

__ Meeting Time__: Wednesday: 11:00 am - 12:30 pm &

Friday 2:30 pm - 4:00 pm

__ First Class__: Tuesday (3:30 pm), 8th August, 2017

**Course outline**:

__ Revision__:

Thermodynamics & Probability

Formulation of Statistical Mechanics,

Gibbs distribution, Connection with thermodynamics,

Rules of Calculation

__ Examples__:

Ideal gases, Magnet (classical)

Quantum statistical mechanics, ideal gases (quantum)

Other examples: Harmonic crystals, Black body radiation, Diatomic molecules

Interacting gas

**Exact models**

Phase transitions: Criticality, Universality

Mean field theory

Landau Ginzburg Theory

Correlations and fluctuations

Renormalization Group theory

Kinetic theory of gases: BBGKY hierarchy,

The Boltzmann equation, H-Theorem and Irreversibility

Transport theory

***If time permits**:

Random Processes: Markov Processes,

Random walk, Brownian motion

Master equation, Fokker-Planck equation

Linear response theory

__ References__:

We will mainly follow :

- Statistical Physics of particles, M. Kardar
- Statistical Mechanics, R. K. Pathria and P. D. Baule

__ Additional references__:

- Statistical Physics, L.D. Landau and E. M. Lifshitz
- Statistical Mechanics, F. Schwabl
- Applications of Classical Physics, R. G. Blandford and Kip S. Thorne

**Classical Mechanics (Core)**

** Instructor**: Samriddhi Sankar Ray

** Venue: **Emmy Noether Seminar Room, ICTS Campus, Bangalore

__ Meeting Time__:

**Tuesday & Thursday: 1:45 pm - 3:15 pm**

** First Class**: Tuesday (1:45 pm), 8th August, 2017

__ Topics__:

- Recapitulation of Newton's laws and their implications
- Lagrangian Formulation:

2a. Principle of least action

2b. Noether's Theorem. Symmetries

2c. Small Oscillations - Rigid body motion

3a. Euler Angles

3b. Tops - Hamiltonian formulation

4a. Liouville's Theorem

4b. Action-Angle variables

4c. Hamilton-Jacobi - Chaos theory and dynamical systems

5a. KAM theorem.

__ Grading__:

Assignments: 7 or 8 in all. 40% weightage on final grade

Numerical Assignement: 1. 10% weightage on final grade

Mid-Semester Exam: early October. 20% weightage on final grade

End-Semester Exam: early December. 30% weightage on final grade

**Basics of non-equilibrium physics (Elective)**

**Instructor:*** *Abhishek Dhar

__ Venue__: ICTS Campus, Bangalore

__Course contents__

- Random walks
- Master equation approaches for l Markov processes
- Brownian motion, Langevin equations
- Microscopic derivation of Langevin equations
- Fokker Planck equations
- Linear response theory

**Classical theory of Gauge fields (Reading)**

**Instructor:*** *Loganayagam R

__ Venue__: ICTS Campus, Bangalore

** Course contents: **Please Click here