Representations of p-adic groups (2022)

Convener(s)

 
Name: Prof. Tanmay Deshpande Prof. Ravi Raghunathan Prof. Sandeep Varma
Mailing Address: TIFR Mumbai
School of Mathematics
Homi Bhabha Road, Colaba, Mumbai - 400005		 IIT Bombay
Department of Mathematics
IIT Bombay, Powai, Mumbai - 400076		 TIFR Mumbai
School of Mathematics
Homi Bhabha Road, Colaba, Mumbai - 400005
Email: tanmaynd2001 at gmail.com raviraghunathan at gmail.com sandeepvarmav at gmail.com

 The theory of admissible complex representations of p-adic groups is an important constituent of the Langlands program, and in particular informs research on various areas of number theory such as modular forms, arithmetic geometry etc., in addition to being a topic of intensive research in its own right.
We plan to have a basic (mini-)course on each of the following six topics that come under or is intimately tied to this broad area:

  1. Deligne-Lusztig theory of representations of finite groups of Lie type.
  2. Representation theory of general linear groups over p-adic fields.
  3. Bruhat-Tits theory.
  4. Types and construction of supercuspidal representations of p-adic groups (this will use Bruhat-Tits theory).
  5. Affine Deligne-Lusztig constructions, the representations of p-adic groups realized in the cohomology of affinne Deligne-Lusztig varieties. This is an evolving area in which much recent progress has been made by Charlotte Chan and her collaborators.
  6. Automorphic representations and L-functions (in which lies the origin of the p-adic theory, and which still gives rise to objects in it).

Three of the courses (Deligne-Lusztig theory, Bruhat-Tits theory and the construction of supercuspidal representations) will also serve as background material to let students follow the lectures on the fifth course mentioned above, namely the Affine Deligne-Lusztig constructions. We expect the lectures to be useful to mathematicians working across the country on a diverse set of topics related to the Langlands program, and especially so to the several graduate students, post doctoral researchers and young faculty whose main research interest is the theory of complex representations of p-adic groups.

 

Dates: 

Monday, May 23, 2022 - 19:00 to Saturday, June 4, 2022 - 19:00

Venue: 

Venue Address: 

 

Department of Mathematics,

 

IIT Bombay

 

Powai, Mumbai-400076.

 

 

Venue State: 

Venue City: 

PIN: 

400076

Chrono Order: 

387

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
CG Venketasubramanian   Bernstein-Zelevinsky theory including combinatorial classification of irreducible admissible representations of p-adic general linear groups in terms of supercuspidal representations and multisegments, the work of Lapid and Minguez on ladder representations.
Tanmay Deshpande   Realization of various supercuspidal representations of p-adic
reductive groups in the cohomology of affine Deligne-Lusztig varieties.
Manish Mishra   Compact induction, J.-K. Yu’s construction of supercuspidal repre-
sentations, Bushnell-Kutzko theory of types and covers.
Santosh Nadimpalli   Construction and analysis of representations of finite groups of
Lie type, Deligne-Lusztig theory.
Ravi Raghunathan   Modular and automorphic forms, connection between global and
local representation theory, L-functions and their integral representations.
Sandeep Varma   The Bruhat-Tits building, parahohoric groups, Moy-Prasad filtrations.

References:

  • Bump, Daniel Automorphic forms and representations. Cambridge Studies in Advanced Mathematics, 55. Cambridge University Press, Cambridge, 1997. xiv+574 pp.
  • Bushnell, Colin J.; Kutzko, Philip C. The admissible dual of GL(N) via compact open subgroups. Annals of Mathematics Studies, 129. Princeton University Press, Princeton, NJ, 1993. xii+313 pp.
  • Ottawa lectures on admissible representations of reductive p-adic groups. Lectures from the Field Institute Workshops held at the University of Ottawa, Ottawa, ON, May 2004 and January 2007. Edited by Cli↵ton Cunningham and Monica Nevins. Fields Institute Monographs, 26. American Mathematical Society.
  • Digne, Francois; Michel, Jean. Representations of Finite Groups of Lie Type. Cam-bridge University Press.

 References (Research articles).

  • Bernstein, I. N. and Zelevinsky, A.V. Representations of the group GL(n, F), where F is a local non-Archimedean field. Uspehi Mat. Nauk 31 (1976). Available at: http://www.math.tau.ac.il/⇠bernstei/Publication list/Publication list.html
  • Bruhat, F; Tits, J. Groupes rductifs sur un corps local. Inst. Hautes Etudes Sci.  ́ Publ. Math. No. 41 (1972), 5-251-.
  • Bruhat, F; Tits, J. Groupes rductifs sur un corps local. II Sch ́emas en groupes.Existence d’une donn ́ee radicielle valu ́ee. Inst. Hautes Etudes Sci. Publ. Math.  ́ No. 60 (1984), 197-376.
  • Lapid, Erez; Mnguez, Alberto On a determinantal formula of Tadi ́c. Amer. J. Math 136 (2014), no. 1, 111-142.
  • Moy, Allen; Prasad, Gopal. Unrefined minimal K-types for p-adic groups. Invent. Math. 116 (1994), no. 1-3, 393-408.
  • Bushnell, Colin J.; Kutzko, Philip C. Smooth representations of reductive p-adic groups: structure theory via types. Proc. London Math. Soc. (3) 77 (1998), no. 3, 582-634.
  • Jacquet, H.; Piatetskii-Shapiro, I. I.; Shalika, J. A. Rankin-Selberg convolutions. Amer. J. Math. 105 (1983), no. 2, 367-464.
  • Gelbart, Stephen S. Automorphic forms on adle groups. Annals of Mathematics Studies, No. 83. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. x+267 pp.

Tentative Schedule

  • Course 1 - Representations of Finite Groups of Lie Type: by Santosh Nadimpalli (SN).
  • Course 2 - Representations of General Linear Groups over p-adic Fields: by CG Venketasubramanian (CGV).
  • Introductory lectures; and Course 3 - Bruhat-Tits theory: by Sandeep Varma (SV).
  • Course 4 - Types and Construction of Supercuspidal Representations: by Manish Mishra (MM).
  • Course 5 - Realizing representations of p-adic groups using affine Deligne-Lusztig varieties: by Tanmay Deshpande (TD).
  • Course 6 - Automorphic Representations and L-functions (by RR).

Time Table: 

 Week 1

Day Date 9:30-10:45 11:15-12:30 14:15-15:30 16:00-17:00
(Tutorial)
M May 23 SV
(Introductory)		 SN SV
(Introductory)		 Tutorial (Course 1)
T May 24 SN CGV SV Tutorial (Course 2)
W May 25 SN CGV SV Tutorial (Course 3)
Th May 26 SN CGV SV Tutorial (Course 1)
F May 27 SN CGV SV Tutorial (Course 2)
S May 28 SN CGV SV Tutorial (Course 3)

 

 Week 2

Day Date 9:30-10:45 11:15-12:30 14:15-15:30 16:00-17:00
(Tutorial)
M May 30 MM TD RR Tutorial (Course 4)
T May 31 MM TD RR Tutorial (Course 5)
W June 1 MM RR TD Tutorial (Course 6)
Th June 2 MM TD RR Tutorial (Course 4)
F June 3 MM TD RR Tutorial (Course 5)
S June 4 MM RR TD Tutorial (Course 6)

 10:45 - 11:15 and 15:30 - 16:00 will be tea breaks, while 12:30 - 14:15 will be a lunch break.

Selected Applicants: 

 All selected applicants will receive an email from the organizers asking them to confirm their participation in the workshop by 30th March 2022.

Serial SID Full Name Gender Affiliation Position Year of Passing M.Sc./M.A Ph.D. Degree Date
1 38202 Ms. Shubhanshi Gupta Female Institute of Infrastructure, Technology, Research And Management PhD 2019  
2 38373 Mr. Basudev Pattanayak Male IISER Pune PhD Student 2016  
3 38383 Dr. Saurabh Kumar Singh Male Indian Institute of Technology Kanpur Assistant Professor 2010 09/09/2015
4 38423 Mr. Hariom Sharma Male IIT ROORKEE PhD 2019  
5 38431 Mr. Prem Dagar Male IIT ROORKEE Ph.D STUDENT 2017  
6 38441 Mr. Asfak Ahamad Soneji Male (IITRAM) PhD Student 2018  
7 38455 Ms. Ankita Parashar Female IIT Delhi PhD 2019  
8 38462 Dr. Kumar Balasubramanian Male IISER Bhopal Assistant Professor 2005 11/06/2012
9 38464 Dr. Mahendra Kumar Verma Male IIT Roorkee Assistant Professor 2005 31/08/2015
10 38473 Mr. Narayanan P Male Indian Institute of Science Education and Research-Pune (IISER-Pune) Int Ph.D. Student Appeared  
11 38497 Mr. Sabyasachi Dhar Male INDIAN INSTITUTE OF TECHNOLOGY, KANPUR PhD 2018  
12 38500 Mr. Sanjeev Kumar Pandey Male Indian Institute of Science Education and Research (IISER)Tirupati PhD 2015  
13 38505 Mr Rajat Kumar Mishra Male Indian Institute of Technology, Gandhinagar PhD 2019  
14 38525 Dr. Amiya Kumar Mondal Male IISER Berhampur Assistant Professor 2007 01/04/2015
15 38526 Ms. Himanshi Khurana Female Indian Institute of Science Education and Research Bhopal Integrated PhD Student 2021  
16 38527 Ms Harshitha C Female IISER Tirupati PhD student 2018  
17 38532 Mr. Mayank Kumar Bijay Male TIFR ICTS PhD 2018  
18 38540 Mr Arghya Sadhukhan Male University of Maryland, College Park PhD Student 2017  
19 38544 Mr. Darshan Prafulbhai Nasit Male IISER Pune PhD 2019  
20 38547 Mr. Prashant Shivaji Arote Male Indian Institute of Science, Education and Research Postdoc 2015 24/12/2021
21 38548 Mr. Arindam Jana Male Tata Institute of Fundamental Research, Mumbai Visiting Fellow 2012 20/08/2020
22 38553 Mr. Praneel Samanta Male University of Iowa PhD student, 5th year 2016  
23 38564 Ms Saniya Hari Wagh Female Tata Institute of Fundamental Research PhD student 2018  
24 38581 Dr. Gautam Borisagar Male Institute of Infrastructue, Technology, Research And Management Asst. Prof. 2003 09/08/2014
25 38593 Ms. Ekta Tiwari Female University of Ottawa PhD student 2020  
26 38605 Mr Paul Chalakuzhy Mammen Male Chennai Mathematical Institute BSc Student    
  Without accommodation
     
1 38477 Mr. Manodeep Raha Male Tata Institute of Fundamental Research PhD 2021  
2 38489 Mr. Niladri Sekhar Patra Male TATA INSTITUTE OF FUNDAMENTAL RESEARCH RESEARCH SCHOLAR 2019  
3 38558 Mr. Soumyadip Sahu Male Tata Institute of Fundamental Research PhD 2018  
4 38572 Mr. Ankit Rai Male Indian Institute of Technology, Bombay Postdoctoral fellow 2014 16/10/2020
5 38574 Mr. Anand Uday Chitrao Male Tata Institute of Fundamental Research, Mumbai PhD Student    
6 38578 Mr. Akash Yadav Male Indian Institute of Technology, Bombay PhD 2019  
7 38587 Mr. Sameer Kulkarni Male Tata Institute of Fundamental Research, Mumbai PhD student 2016  
8 38589 Mr. Mohammed Saad Qadri Male IIT Bombay Integrated Msc Phd Student 2020  
9 38594 Mr Sagar Shrivastava Male Tata Institute of Fundamental Research PhD 2016  

 

 

How to Reach: 

TBA

School Short Name: 

rpag

Last Date Application: 

Wednesday, April 15, 2020

School Type: 

NCMW

Separate faculty form: 

0