Harmonic Analysis and PDE

Convener(s)

 
Name:  Dr. Rahul Garg Dr. Pradeep Boggarapu  Prof. Monojit Bhattacharjee 
Mailing Address: Associate Professor
Department of Mathematics,
IISER Bhopal
Bhopal, India.
Assistant Professor,
Department of Mathematics,
BITS Pilani, K K Birla Goa Campus 
Assistant Professor
Department of Mathematics,
BITS Pilani, K K Birla Goa Campus 
Email: rahulgarg at iiserb.ac.in pradeepb at goa.bits-pilani.ac.in monojitb at goa.bits-pilani.ac.in 

The proposed AIS on "Harmonic Analysis and PDEs" offers an in-depth exploration of some important topics in modern mathematical research. Over the past few decades, Harmonic Analysis has significantly evolved, finding applications in PDEs, Number Theory, Physics, and Signal Processing, among other fields. This 3-week workshop is structured to provide an introduction to some fundamental aspects of the subject. For the same, we plan to teach topics in Distribution Theory, Fourier Analysis on the Euclidean spaces, Harmonic Analysis on the Heisenberg Group, Elliptic PDEs, Inverse Problems and Restriction Theorems for the Fourier Transform.

Dates: 

Monday, June 8, 2026 - 09:00 to Saturday, June 27, 2026 - 21:00

Venue: 

Venue Address: 

 

 

 

Department of Mathematics,

 

BITS Pilani, KBirla Goa Campus NH-17B, Zuarinagar

 

Goa-403726

 

 

 

 

 

 

Venue State: 

Venue City: 

PIN: 

403726

Syllabus: 

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.

  Tutorial Assistants:

S. No.

Name

Affiliation

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

 

Time Table: 

    Time-Table (with names of speakers and course associates/tutors):

 

Day

Date

Lecture 1

(9.30–11.00)

Tea

(11.05 –11.25)

Lecture 2

(11.30–1.00)

Lunch

(1.05–2.25)

Tutorial

(2.30–3.30)

Tea

(3.35-3.55)

Tutorial

(4.00-5.00)

Snacks

5.05-5.30

Mon

8th June

SPK

 

ST

 

SPK+AGS+BP

 

ST+AGS+SKR

 

Tues

9th June

SPK

 

ST

 

SPK+AGS+BP

 

ST+AGS+SKR

 

Wed

10th June

SPK

 

ST

 

SPK+AGS+BP

 

ST+AGS+SKR

 

Thu

11th June

SPK

 

ST

 

SPK+AGS+BP

 

ST+AGS+SKR

 

Fri

12th June

SPK

 

ST

 

SPK+AGS+BP

 

ST+AGS+SKR

 

Sat

13th June

SPK

 

ST

 

SPK+AGS+BP

 

ST+AGS+SKR

 

SUNDAY: OFF

Mon

15th June

SS

 

MB

 

SS+NG+SKR

 

MB+PD+AS

 

Tues

16th June

SS

 

MB

 

SS+NG+SKR

 

MB+PD+AS

 

Wed

17th June

SS

 

MB

 

SS+NG+SKR

 

MB+PD+AS

 

Thu

18th June

SS

 

MB

 

SS+NG+SKR

 

MB+PD+AS

 

Fri

19th June

SS

 

MB

 

SS+NG+SKR

 

MB+PD+AS

 

Sat

20th June

SS

 

MB

 

SS+NG+SKR

 

MB+PD+AS

 

SUNDAY: OFF

Mon

22nd June

SB

 

JK

 

SB+MM+TM

 

JK+PB+BP

 

Tues

23rd June

SB

 

JK

 

SB+MM+TM

 

JK+PB+BP

 

Wed

24th June

SB

 

JK

 

SB+MM+TM

 

JK+PB+BP

 

Thu

25th June

SB

 

JK

 

SB+MM+TM

 

JK+PB+BP

 

Fri

26th June

SB

 

JK

 

SB+MM+TM

 

JK+PB+BP

 

Sat

27th June

SB

 

JK

 

SB+MM+TM

 

JK+PB+BP

 

Full forms for the abbreviations of speakers and tutors: 
AGS: Aswin Govindan Sheri
AS: Aniket Sen
BP: Basil Paul
JK: Jotsaroop Kaur
MB: Mousomi Bhakta
MM: Manisa Maity
NG: Nishta Garg
PB: Pradeep Boggarapu
PD: Paramananda Das
SB: Sombuddha Bhattacharyya
SKR: Surya Kanta Rana 
SPK: Sanjay P. K. 
SS: Suparna Sen 
ST: Sundaram Thangavelu
TM: Tuhin Mondal

 

Selected Applicants: 

 

 

 

 

How to Reach: 

TBA

School Short Name: 

hap

Last Date Application: 

Monday, March 31, 2025

School Type: 

AIS

Separate faculty form: 

0