1. Krishna Jalan 

​​

​Introduction to Black Hole Thermodynamics 

​​

Black hole thermodynamics is an ongoing development in understanding the enigmatic black holes as

the central players at the intersection of general relativity, quantum physics, and thermodynamics. This

lecture series aims to introduce this fascinating interplay of the three subjects through the lens of black

hole physics. I will begin with the classical properties of black holes, and then explain the proposal

of Bekenstein that black holes should have entropy. We will see Hawking’s calculation of black hole

radiance, due to quantum effects, and his explanation for why black holes should have a temperature,

thereby fundamentally linking them to thermodynamic systems. The lectures will also introduce some

ideas of quantum field theory in curved spacetimes and discuss the most basic example of the Unruh

effect, an analogous phenomenon to Hawking’s black hole radiance. The latter half of the lecture series

could cover some of the more advanced topics like (i) some details of the proofs of the four laws of black

hole thermodynamics, (ii) introduction to covariant phase space and Wald’s entropy formula, (iii) the

generalized second law and its proof by Aron Wall for semi-classical Einstein gravity, (iv) “derivation”

of Einstein’s field equations from the first law due to Ted Jacobson, and/or (v) introduction to Ryu-

Takayanagi formula.​

​

2. Amit Suthar 

 

Positive geometry of scattering amplitudes: Associahedron and Amplituhedron

​

These lectures aim to give the audience a glimpse of the geometric structures in scat-

tering amplitudes. The lectures are divided into two parts: the first three lectures cover the

spinning particles, and the later two lectures cover the scalar particles. In the first part,

I introduce the appropriate kinematic variables: spinor helicity variables and the momen-

tum twistors, and present a short introduction to the ’on-shell methods’ for computation

of amplitudes. I describe how certain amplitudes of Yang-Mills theory are proportional to

volumes of polytopes in the projective space. Explaining how this extends to the maximally

supersymmetric Yang-Mills, I define the tree-amplituhedron. Towards the end of the first

part, I define the positive geometry and discuss the central idea behind it.

In the second part, we discuss the positive geometry description for scalars. I define the

abstract combinatorial associahedron and motivate its connection with the scalar scatter-

ings. I describe the ABHY associahedron and its loop variants. I also discuss the tropical

limit of the open string amplitude, and how it leads to the integral over global Schwinger

parameters: the curve integral formula.

 

Pre-requisites: The lectures are pedagogical and assume only basic QFT as a pre-

requisite. Only the last lecture uses some string amplitudes, but the knowledge of the string

theory is not crucial to follow the lecture.

​

3. Ritwick Kumar Ghosh 

​

Matrix Models

​​

In these lectures we will try to cover the basics of matrix models or random matrix theory.

​

Pre-requisites: Quantum Field theory

4. K.S. Dhruva 

(Super) Conformal Field Theory

​

The study of conformal field theories (CFTs) using tools from the modern ampli-

tudes program such as Spinor Helicity variables and Twistors presents a rich and

interesting avenue to explore. This approach is complementary to the traditional

position space analysis and has applications to a wide variety of topics such as cos-

mology, the S-matrix bootstrap, double copy relations, and much more. The main

aim of this course is to introduce some of these developments and their applications to

three-dimensional CFTs and, through holography, four-dimensional quantum gravity

in (Anti-)de Sitter space.

​

Prerequisites: Basic QFT and group theory.

​

Useful tools: Wolfram Mathematica (although not compulsory).

 

Potential future directions: Higher-point spinning bootstrap, CFT/AdS analog of

BCFW recursion relations, the potential of representing CFT correlators as geometric

structures (like the amplituhedron) etc..

​

5. Gopal Yadav

​

 Introduction to AdS/CFT correspondence

​

This lecture will provide an overview of AdS/CFT correspondence. We will start

with why AdS/CFT is needed and then go through CFT and AdS spacetime. Using

these results, we will provide the details of AdS/CFT correspondence followed by

explicit examples and generalization of this duality to other spacetimes.

​

Prerequisites: Quantum field theory and General theory of relativity.