Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Sanjay P. K. 

(NIT Calicut)

6

Distribution Theory 

1. Test function spaces and distributions, Calculus on distributions, Supports of distributions, Distribution as derivatives and tempered distribution, Fourier transform, Paley-Wiener theorem, Sobolev’s lemma, Sobolev Spaces.

2. Applications to differential equations (Fundamental solutions).

Sundaram Thangavelu 

(IISc Bangalore)

6

Fourier Analysis on the Euclidean spaces: 

1. Fourier series on the circle. 

2. Fourier transform on the Euclidean spaces.

3. Interpolation theorems: The Marcinkiewicz interpolation theorem (real method), the Riesz-Thorin interpolation theorem (complex method), and interpolation of the analytic family of operators. 

4. Singular integrals of convolution type. 

5. Multiplier theorems: Marcinkiewicz multiplier theorem, Mihlin–Hormander multiplier theorem.

Suparna Sen

(University of Calcutta)

6

Harmonic Analysis on the Heisenberg Group:

1. The group Fourier transform on the Heisenberg group. 

2. Spectral theory of the sublaplacian. 

3. Bochner-Riesz means for the sublaplacian. 

4. A multiplier theorem for the Fourier transform.

Mousami Bhakta 

(IISER Pune)

6

Elliptic PDEs

1. Weak Formulation and elliptic PDEs (Lax-Milgram theorem and its application, inhomogeneous boundary data problems).

2. Well-posedness of elliptic PDEs with lower order perturbations (Fredholm alternatives).

3. Boundary and Interior regularity of solutions of Elliptic PDEs.

4. Unique Continuation Principles (UCP) of solution of Elliptic PDEs (if time permits).

Sombuddha Bhattacharyya 

(IISER Bhopal)

6

Inverse Problems

1. Calderón problem (Recovering a zeroth order perturbation of the Laplacian operator from the boundary Dirichlet-Neumann map).

2. An inverse problem for the Magnetic Schrödinger Operator (Assuming the Carleman estimates).

3. Boundary and Interior Carleman estimates.

4. Ray transformation of functions: Fourier slice theorem and explicit inversion of Ray transformation.

Jotsaroop Kaur 

(IISER Mohali)

6

Restriction Theorems for the Fourier Transform

1. Certain generalized functions and their Fourier transforms. 

2. Restriction problems, Stein-Tomas restriction theorem, Strichartz theorems on restrictions of Fourier transforms to the quadratic surface. 

3. Applications of restriction theorems to PDE (Strichartz’s inequalities), and some recent developments.

S. No.

Name

Affiliation

1 

Ms. Nishta Garg 

IISER Bhopal

2

Mr. Surya Kanta Rana

IISER Bhopal

3

Ms. Manisa Maity

IISER Bhopal

4

Mr. Tuhin Mondal

IISER Bhopal

5

Mr. Paramananda Das

IISER Pune

6

Mr. Aniket Sen

IISER Pune

7

Mr. Basil Paul

BITS Pilani K K Birla Goa Campus

8

Dr. Pradeep Boggarapu

BITS Pilani K K Birla Goa Campus

9

Dr. Aswin Govindan Sheri

IISER Berhampur