NCMW - Representations of p-adic groups (2022)

Speakers and 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).

Week 1

Week 2

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

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