Harmonic Analysis (2019)

 
Name: Dr. Saurabh Shrivastava Dr. Rahul Garg
Mailing Address: Office-213, Academic Building 1,
IISER Bhopal,
Bhauri, Bhopal Bypass Road,
Bhopal, Madhya Pradesh 462 066		 Office-209, Academic Building 1,
IISER Bhopal,
Bhauri, Bhopal Bypass Road,
Bhopal, Madhya Pradesh 462 066.
Email: saurabhk at iiserb.ac.in rahulgarg at iiserb.ac.in

Please Note:  Participants have to arrange for their own travel.

This will be an advanced workshop in four different themes in harmonic analysis. First set of lectures will be by Professor Luca Fanelli on "Hardy inequalities and applications" , introducing a unified point of view through Quantum Mechanics, Functional Analysis and Fourier Analysis to describe Hardy inequalities as mathematical manifestations of the Uncertainty Principle. Later on, some useful applications to Spectral Theory and the study of Dispersive PDE’s will be discussed.

Second set of lectures will be by Professor Bent Orsted on "Branching problems for unitary representations and Poisson transforms". An interesting problem studied in the literature is to investigate how certain unitary representations of semi-simple Lie groups decompose when restricted to subgroups. This is known as Branching problem and it leads to structures that shed new light on certain elliptic boundary value problems. For example, for the groups O(1,n+1) and U(1,n+1) the branching theory leads to the well known Poisson transforms associated to symmetric spaces. Studying this problem in the general context one is led to Symmetric Breaking operators of Kobayashi and Speh providing new examples of Poisson transforms.

Third set of lectures will be on "Bochner-Riesz conjecture and related problems" by Prof. Sanghyuk Lee. The Bochner-Riesz conjecture is an attempt to understand the convergence of multidimensional Fourier series and integral, which is one of the most fundamental questions in the classical harmonic analysis. Though the conjecture is settled in 2-dimensions, it is still open in higher dimensions. As is well known to experts in this field, the progresses in the Bochner-Riesz conjecture are closely tied to those of Fourier restriction problems, where we have witnessed rapid developments in recent years. Bilinear and multilinear generalizations of linearestimates turned out to be the most efficient tools. In this series of lectureswe will cover developments in the Bochner-Riesz conjecture and its related problems in connection with the Fourier restriction problem.

The Fourth set of lectures will on the topic of "Noncommutative Harmonic Analysis" by Prof. Parasar Mohanty. This course will begin with an introduction to the noncommutative operator space structure of L^pspaces. We shall discuss several important examples and the main results in this direction. This allows us to formulate problems fromclassical harmonic analysis in the context of group von Neumann algebras. In particular, we shall develop the theory of Calderon-Zygmundoperators and completely bounded multipliers in generalon noncommutativeL^pspaces.

Dates: 

Tuesday, December 10, 2019 - 11:00 to Saturday, December 14, 2019 - 11:00

Venue: 

Venue Address: 

Department of Mathematics,
Academic Building 1, IISER Bhopal,
Bhopal Bypass Road, Bhauri,
Bhopal, Madhya Pradesh 462 066.

Venue State: 

Venue City: 

PIN: 

462066

Chrono Order: 

340

Syllabus: 

 

Name of the Speakers with affiliation.

No. of Lectures

Detailed Syllabus

Outstation Speakers

 

 

Dr. Luca Fanelli, SAPIENZA Università di Roma, Italy
(LF)

Five lectures and one tutorial
= 6.5 hrs

Hardy inequalities, Applications to Spectral Theory, Study of Dispersive PDE.

Prof. Bent Orsted, Aarhus University, Denmark
(BO)

Five lectures and one tutorial
= 6.5 hrs

Branching problems for unitary representations and Poisson transforms.

Prof. Sanghyuk Lee, Seoul National University, South Korea
(SL)

Five lectures and one tutorial
= 6.5 hrs

Bochner-Riesz conjecture and related problems.

Prof. Parasar Mohanty, IIT Kanpur, India
(PM)

Five lectures and two tutorials
8 hrs

Noncommutative Harmonic Analysis, Theory of Calderon-Zygmund operators and completely bounded multipliers on noncommutative L^p spaces.

 References:

Books:
1. Pisiser, Gilles, Introduction to Operator Spaces Theory, London Mathematical Society, Lecture notes Series 294.
2. Xu, Qunahua,Lecture notes on noncommutative L^p spaces.

Articles:

  1. D'Ancona, Piero; Fanelli, Luca,Lp-boundedness of the wave operator for the one dimensional Schrödinger operator, Comm. Math. Phys. 268 (2006), no. 2, 415-438.
  2. D'Ancona, Piero; Fanelli, Luca; Vega, Luis; Visciglia, Nicola, Endpoint Strichartz estimates for the magnetic Schrödinger equation, J. Funct. Anal. 258 (2010), no. 10, 3227-3240.
  3. Möllers, Jan; Ørsted, Bent; Oshima, Yoshiki, Knapp-Stein type intertwining operators for symmetric pairs, Adv. Math. 294 (2016), 256-306.
  4. Möllers, Jan; Ørsted, Bent; Zhang, Genkai, Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups, J. Geom. Anal. 26 (2016), no. 1, 118-142.
  5. Möllers, Jan; Ørsted, Bent; Zhang, Genkai,On boundary value problems for some conformally invariant differential operators, Comm. Partial Differential Equations 41 (2016), no. 4, 609-643.
  6. Lee, Sanghyuk., Square function estimates for the Bochner-Riesz means, Anal. PDE 11 (2018), no. 6, 1535-1586.
  7. Bak, Jong-Guk; Lee, Jungjin; Lee, Sanghyuk, Bilinear restriction estimates for surfaces of codimension bigger than 1, Anal. PDE 10 (2017), no. 8, 1961-1985.
  8. Lee, Sanghyuk, Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators, Duke Math. J. 122 (2004), no. 1, 205-232.

 

Time Table: 

 

Day

Date

Lecture 1

(9.30
to
10.30)

Tea

(10.30 to
10.50)

Lecture 2

(10.50
to
11.50)

Lecture 3

(12.00
to
13.00)

Lunch

(13.00 to
14.30)

Lecture 4

(14.30
to
15.30)

Snacks

(15.30
to
16.00)

Discussion/Tutorial

(16.00
to
17.30)

 

 

Name of the speaker)

 

Name of the speaker)

Name of the speaker)

 

Name of the speaker)

 

 

Name of the speaker)

Tue

10/12/2019

LF

BO

SL

PM

PM

Wed

11/12/2019

PM

LF

BO

SL

SL

Thu

12/12/2019

SL

PM

LF

BO

BO

Fri

13/12/2019

BO

SL

PM

LF

LF

Sat

14/12/2019

LF

BO

SL

PM

PM

  • LF: Luca Fanelli (SAPIENZA Università di Roma, Italy)

  • PM: ParasarMohanty (IIT Kanpur, India)

  • SL: Sanghyuk Lee (Seoul National University, South Korea)

  • BO: Bent Orsted (Aarhus University, Denmark)

 

 

Selected Applicants: 

 

Sr. SID Full Name Gender Affiliation Position in College/ University Univ./Inst. M.Sc./ M.A. Year of Passing M.Sc. / M.A Ph.D. Deg. Date
1 28332 Mr. Pritam Ganguly Male Indian Institute of Science. Int. Ph.D. student Indian Institute of Science, Bangalore 2018  
2 28909 Mr Partha Sarathi Patra Male IISER Bhopal Postdoctoral Fellow Guru Ghasidas University 2012 05/08/2018
3 29043 Mr. Jayanta Sarkar Male Indian Statistical Institute PhD Indian Institute of Technology Madras 2015  
4 29096 Mr. Yasser K.T Male NIT Calicut PhD NIT Calicut 2015  
5 29181 Mr Muna Naik Male Indian Statistical Institute PhD   2013  
6 29291 Mr. Ramesh Manna Male TIFR CAM Post Doctoral Fellow IIT Madras 2010 27/04/2017
7 29376 Mr. Santanu Debnath Male University of Calcutta PhD IIT Kanpur 2016  
8 29492 Mr. Arun Kumar Bhardwaj Male IIT Guwahati PhD Patna University 2015  
9 29559 Mr. Shubham Rameshsingh Bais Male IIT Hyderabad PhD Pondicherry University, Puducherry 2017  
10 29619 Mr. Duranta Chutia Male Tezpur University PhD Tezpur University 2017  
11 29722 Mr. Md Nurul Molla Male Indian Statistical Institute PhD Student University of Calcutta 2016  
12 29798 Mr. Dhiraj Patel Male Indian Institute of Technology Delhi PhD Indian Institute of Technology Kanpur 2017  
13 29849 Mr. Anoop V P Male Indian Institute of Science Banglore Research Associate University of Hyderabad 2012  
14 30031 Mr Somnath Ghosh Male IIT Guwahati PhD IIT Guwahati 2015  
15 30061 Mr. Rupak Kumar Dalai Male Indian Institute of Technology Guwahati PhD University of Hyderabad, 2015  
16 30115 Mr Shyam Swarup Mondal Male IIT Guwahati PhD IIT Guwahati 2016  
17 30136 Mr. Naman Kumar Male IIT Kanpur PhD Student IIT Kanpur    
18 30163 Mr Rattan Lal Lal Male IIT Delhi PhD IIT Delhi 2015  
19 30208 Mr. Sewook Oh Male Seoul national university Graduate student Seoul national university    
20 30214 Mr Juyoung Lee Male Seoul National University PhD student      
21 30226 Ms. Surbhi   Female University of Delhi Ph.D. University of Delhi 2018  
22 30229 Mr Manoj Kumar Male IIT Delhi PhD IIT Kanpur 2015  
23 30234 Mr. Arup Kumar Maity Male HRI,Allahabad PhD IIEST,Shibpur 2016  
24 30246 Mr. Ryu Jae Hyeon Male Seoul national university PhD Student      
25 30261 Mr. Salman Ashraf Male IIT Mandi Ph.D. IIT Madras 2016  
26 30288 Ms. Hyerim Ko Female Seoul National University Post Doctor Seoul National University 2013 29/08/2019
27 30289 Dr. Chuhee Cho Female Department of Mathematics/ Seoul National University Postdoc Korea University 2005 25/08/2010
28 30303 Mr Tapendu Rana Male Indian Institute of Technology, Bombay PhD IIT Kanpur 2016  
29 30304 Mr. Ankit Bhojak Male IIT Kanpur PhD Student IIT Kanpur 2016  
30 30307 Mr. Rajesh Kumar Singh Male Harish-Chandra Research Institute, Post Doctoral IIT Kanpur 2011 28/06/2018
31 30308 Dr. Kanailal Mahato Male Banaras Hindu University Assistant Professor IIT Delhi 2012 14/01/2017
32 30390 Mr. Sumit Kumar Rano Male Indian Institute of Technology Guwahati PhD Indian Institute of Technology Madras 2015  
33 30399 Mr. Santi Ranjan Das Male IIT MADRAS PhD IIT Madras 2016  
34 30413 Mr. Md Hasan Ali Biswas Male IIT Madras PhD IIT Madras 2017  
35 30419 Mr. Yehyun Kwon Male KIAS research fellow Seoul National University 2012 26/02/2019
36 30431 Dr. Anupam Gumber Female Indian Institute of Science Post Doctoral Fellow Guru Nanak Dev University, Amritsar/ Lyallpur Khalsa College, Jalandhar 2007 19/11/2018
37 30439 Mr. Shubham Namdeo Male IIT Indore PhD IISER Bhopal 2017  
38 30466 Mr. Abhishek Ghosh Male Indian Institute of Technology Kanpur PhD scholar Indian Institute of Technology Kanpur 2013  
39 30531 Dr. Eunhee Jeong Female Korea Institute for Advanced Study postdoc      
40 30538 Dr. Choiti Bandyopadhyay Female University of Manitoba Post Doctoral Fellow Indian Institute of Science 2012 18/12/2017
 Local participants       
1 29015 Mr Kalachand Shuin Male IISER BHOPAL PhD IIT Kanpur 2015  
2 29027 Mr Riju Basak Male IISER Bhopal IPhD student IISER Bhopal 2018  
3 29236 Prof Manisha Udit Jain Female vellore Institute of Technology, Bhopal Associate Professor Govt. Auto. Science College, Jabalpur 1996 30/03/2011
4 29307 Dr. Neha Choubey Female VIT Bhopal University Assistant Professor Barkatullah 2006 03/07/2017
5 30381 Mr. Muzammil Khan Male Maulana Azad National Institute of Technology PhD Bundelkhand University 2018  
6 30462 Mr. Sonu Kurmi Male Maulana Azad National institute of technology, bhopal Phd Institute For Excellence in Higher Education, Bhopal 2018  
 Waiting list       
1 30238 Mr. Sudipta Sarkar Male IIT Indore PhD IIT Kanpur 2016  
2 29412 Mr. Vidya Sagar Male IIT Delhi PhD IIT JODHPUR, KARWAR, RAJASTHAN 2018  
3 29898 Ms. Ritika Singhal Female IIT Delhi PhD INDIAN INSTITUTE OF TECHNOLOGY DELHI Appeared / Awaiting Result  
4 29978 Mr Suman Mukherjee Male NISER, Bhubaneswar PhD Student University Of Calcutta 2018  
5 30095 Ms. Shivani Goel Female Indraprastha Institute of Information Technology Delhi PhD Chaudhary Charan Singh University, Meerut 2018  
6 30420 Mr. Abhinav Kumar Mishra Male IIT Mandi PhD IIT GUWAHATI Appeared / Awaiting Result  
7 30559 Mr Rohan Joy Male Indian Institute of Technology Madras PhD Indian Institute for Technology Hyderabad 2018  
8 28529 Ms. Pratibha Pandey Female University of Allahabad Ph. D. Student University of Allahabad 2015  
9 30564 Mr. Shesh Kumar Pandey Male Department of Mathematics, University of Delhi,Delhi PhD University of Delhi, Delhi 2014  
10 30511 Mr. Nitin Sharma Male University Of Delhi PhD scholar University Of Delhi 2016  
11 30015 Mr. Satyapriya   Male University of Delhi PhD Student University of Delhi 2018  
12 30200 Ms Ruchi Bhardwaj Female University of Delhi Ph.D Student University of Delhi 2017  
13 30491 Ms. Dipa Ghosh Female IIIT Delhi PhD IIT Madras 2014  
14 30195 Ms. Divya Jindal Female University of Delhi M.Phil Student University of Delhi 2017  
15 30019 Mr. Sunder Deep Male University of Delhi MPhil Student IIT Madras, Chennai 2017  
16 30532 Ms Kamna Laghate Female Indian Institute of Technology Indore Junior Research Fellow Dr B A M University, Aurangabad 2016  
17 30344 Mr Soumitra Daptari Male IIT Hyderabad PhD IIT Madras 2017  

 

 

How to Reach: 

Click here to download Map1

Click here to download Map2

School Short Name: 

ha

Last Date Application: 

Sunday, April 21, 2019

School Type: 

NCMW