Representation Theory and Harmonic Analysis

Convener(s)

 
Name: Dr. Pratyoosh Kumar Dr. Jitendriya Swain
Mailing Address:  Associate Professor
Department of Mathematics
Indian Institute of Technology Guwahati		 Associate Professor
Department of Mathematics
Indian Institute of Technology Guwahati
Email:  pratyoosh at iitg.ac.in  jitumath at iitg.ac.in

This workshop is organized on the occasion of the centenary birth year of Harish-Chandra.  The main aim of this AIS is to introduce the works of Harish-Chandra and their importance in the various areas of current research in mathematics. This program is intended for Ph.D. students, post-doctoral fellows, and young teachers interested in working in representation theory and harmonic analysis.  The overall theme of this workshop will be the representation theory of semi-simple Lie groups and harmonic analysis of related symmetric spaces and their applications. These topics have a profound interaction with numerous areas of mathematics and physics. 

Dates: 

Monday, December 11, 2023 - 19:00 to Saturday, December 16, 2023 - 19:00

Venue: 

Venue Address: 

Department of Mathematics
Indian Institute of Technology Guwahati
Guwahati, Pin code 781039
Assam (India)
                                              

 

Venue State: 

Venue City: 

PIN: 

781039

Syllabus: 

 

 Syllabus to be covered in terms of modules of 6 lectures each:

Name of the Speakers with their affiliation.

No. of Lectures

Detailed Syllabus

Simon Marshall

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA

3 Hours

Periods and restrictions of eigenfunctions on locally symmetric spaces: A brief introduction to Hecke theory for SL(2,Z), and describe the method of arithmetic amplification, which uses Hecke operators to give improved bounds for periods and L^p restrictions.

Toshiyuki Kobayashi

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan

6 Hours

Harish-Chandra’s tempered representations and geometry and Harish-Chandra’s admissibility theorem and beyond.

Amos Nevo

Technion-Israel Institute of Technology, Haifa, 32000 Israel

 

 

6 Hours

Representation theory, Harmonic analysis, and intrinsic Diophantine approximation on homogeneous varieties.  The spectral approach to Diophantine approximation averaging operators in dynamical systems, unitary representations, spectral estimates, and operator norm bounds. 

A brief introduction to some aspects of the representation theory of semisimple algebraic groups and the integrability of their matrix coefficients. The spectral transfer principle and effective ergodic theorems. The automorphic representation associated with a lattice subgroup, and effective counting of lattice points. Best possible spectral estimates for subgroup actions.  

Lattice actions on homogeneous spaces and fast equidistribution of dense lattice orbits. Intrinsic Diophantine approximation on homogeneous algebraic varieties, and best possible exponent for tempered subgroups. The effective duality principle on homogeneous spaces.  

Bernhard Krötz

Institute für Mathematik, Universität Paderborn, Germany

 

 

6 Hours

Plancherel theory for real spherical spaces: Harish-Chandra's Plancherel formula for real reductive groups G. Harish-Chandra's Plancherel formula up to the formal degrees of the discrete series as well as the theorem of Delorme and van den Ban-Schlichtkrull for symmetric spaces.

Jyoti Sengupta

Department of Mathematics, Indian Association for the Cultivation Of Science, Kolkata 700032, India

6 Hours

The Fourier transform on semisimple Lie Algebras and Lie groups. Ramifications and Applications.

 

 

 

 

Time Table: 

 

Day Date Lecture 1
(9.30-11.00)

Tea
11.05

to
11.25

 Lecture 2
(11.30-1.00)

(1.05

to

1.55)

 Lecture 3
(2.00–3.30)

3.35

to

3.55

 Discussion
(4.00-5.00)

5.05

to

5.35
    (name of the speaker)

T

E

A

 

B

R

E

A

K

  (name of the speaker)

L

U

N

C

H

 

B

R

E

A

K  

  (name of the speaker)

T

E

A

 

B

R

E

A

K

      

  (name of the speaker)

S

N

A

C

K

S 
Mon 11 Dec TK BK  JS  BK+TK
Tues 12 Dec TK  BK  JS   BK+JS
Wed 13 Dec TK  BK  TK  TK+JS
Thu 14 Dec AN  BK  AN  SM+AN
Fri 15 Dec AN  JS  SM  JS+SM
Sat 16 Dec AN  JS  SM  AN+SM

 

Full forms for the abbreviations of speakers and tutors:

 

 

 

AN: Amos Nevo

 

BK: Bernhard Krötz

 

SM: Simon Marshall

 

TK: Toshiyuki Kobayashi

 

JS: Jyoti Sengupta

 

 

 

 

Selected Applicants: 

 

Sr. SID Full Name Gender Affiliation Position in College/ University University/Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 51174 Mr. Shubhankar Ghosh Male University of Calcutta Ph.D. Student VISVA-BHARATI 2020  
2 51177 Mr. Vaishakh K J Male Cochin University of Science and Technology PhD Cochin University of Science and Technology 2022  
3 51183 Mr. Samya Kumar Ray Male Indian Statistical Institute Kolkata INSPIRE Faculty IISc Bangalore 2012 04/10/18
4 51198 Mr. P.Jitendra Kumar Senapati Male BITS Pilani, K K Birla Goa Campus PhD Khallikote Autonomous College, Berhampur 2014  
5 51233 Mr. Arvish Dabra Male Indian Institute of Technology Delhi PhD Student Indian Institute of Technology Delhi 2021  
6 51245 Dr. Santosh Kumar Nayak Male National Institute of Science Education and Research Post-doc Fellow Utkal University 2015 22/03/23
7 51247 Mr. Aniruddha Vishwas Deshmukh Male Indian Institute of Technology Indore PhD Sardar Vallabhbhai National Institute of Technology Surat 2020  
8 51251 Mr. Uday Sureshkumar Patel Male Harish-Chandra Research Institute PhD Student (SRF) Sardar Patel University    
9 51275 Mr. Sivashankar B Male Indian Institute of Technology Madras PhD University of Madras 2017  
10 51278 Mr Muna Naik Male Harish-Chandra Research Institute INSPIRE faculty NISER, Bhubaneswar    
11 51283 Mr. Manish Chaurasia Male IIT (BHU) Ph.D. IIT Bhubaneswar 2018  
12 51299 Ms. Rabeetha V Female Indian Institute of Technology Madras Ph.D Manonmaniam Sundaranar University, Tirunelveli, India. 2016  
13 51313 Mr. Promod Sharma Male Indian Institute of Technology (BHU) Varanasi PhD Assam University Silchar 2017  
14 51322 Ms. Athulya P Female SRM University Andhra Pradesh PhD Cochin University of Science and Technology, Kalamassery 2020  
15 51323 Ms Umamahswari S Female SRM UNIVERSITY AP Ph.D Scholar BHARATHIDASAN UNIVERSITY 2020  
16 51357 Mr Suman Mukherjee Male NISER, Bhubaneswar PhD Student University of Calcutta 2018  
17 51373 Ms. Ritika Singhal Female Indian Institue of Technology Delhi Research Scholar Indian Institue of Technology Delhi 2019  
18 51397 Mr. Joydwip Singh Male Indian Institute of Science Education and Research Kolkata PhD Indian Institute of Technology Kanpur 2020  
19 51400 Mr. Subham De Male IIT Delhi, India Graduate Student IIT Delhi Appeared / Awaiting Result  
20 51408 Mr. Navneet Navneet Male IIT Indore Phd M.Sc. 2019  
21 51494 Mr. Shubham Rameshsingh Bais Male The Institute of Mathematical Sciences Postdoctoral Fellow Pondicherry University, Puducherry 2017 15/07/23
22 51509 Mr K N Sridharan Namboodiri Male Indian Institute of Technology, New Delhi PhD Student Amrita Vishwa Vidyapeetham 2019  
23 51750 Mr. Rishabh Goswami Male North-Eastern Hill University PhD Student M.Sc. 2021  
24 52105 Mr. Sumit Parashar Male Indian institute of technology mandi PhD Students University of Delhi 2019  
25 52592 Mr. Sourav Dutta Male IIT Mandi PhD The University of Burdwan 2020  
26 52729 Mr Amal Das Male IIT BOMBAY Phd IIT Kanpur 2022  
27 52747 Dr. Jyoti Saikia Female Tingkhong College Assistant Professor NORTH EASTERN REGIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY 2018 23/01/23
28 52762 Mr. Satyajyoti Achar Male NISER, Bhubaneswar Ph.D Presidency University Kolkata 2021  
29 52943 Ms. Shubhanshi Gupta Female Institute of Infrastructure, Technology, Research And Management (IITRAM) PhD Student The Maharaja Sayajirao University of Baroda, Vadodara 2019  
30 53437 Ms. Mitali Sharma Female National Institute of Science Education and Research Int MSc student HBNI    
Local Participant
1 51633 Mr. Mandeep Singh Male IIT Guwahati PhD IIT Kanpur 2020  
2 53153 Ms Manali Sajjan Female IIT Guwahati PhD University of Calcutta 2017  
Waiting List
1 51571 Dr. Pritam Ganguly Male Paderborn University Postdoc Indian Institute of Science, Bangalore 2018 18/04/22
2 51767 Mr Tapendu Rana Male Ghent University, Belgium Postdoctoral Fellow IIT Kanpur 2016 09/01/23
3 51784 Dr. Manoj Kumar Male IISc Bangalore Postdoc M.Sc. 2015 23/02/21
4 51817 Dr. Jayanta Sarkar Male IISER Kolkata INSPIRE Faculty IIT Madras 2015 25/02/22
5 51899 Mr Somnath Ghosh Male Indian Institute of Science Postdoctoral fellow IIT Guwahati 2015 30/06/21
6 52064 Mr. Elanchearan R S Male Indian Institute of Technology Madras PhD Indian Institute of Technology Madras 2020  
7 52085 Mr. Sourav Das Male Department of Mathematics and Statistics, IIT Kanpur Ph.D. Student IIT Hyderabad 2019  
8 52518 Dr. Sudipta Sarkar Male Stat-Math unit, ISI Kolkata Visiting Scientist IIT Kanpur 2016 30/06/23
9 51417 Ms. Prerna Gulia Female Indian Institute of Technology Delhi PhD Indian Institute of Technology Kanpur 2022  
10 51486 Mr. Sahil Kalra Male IIT Indore PhD University of Delhi 2019  

 

How to Reach: 

TBA

School Short Name: 

rtha

Last Date Application: 

Monday, August 15, 2022

School Type: 

NCMW

Separate faculty form: 

0