Commutative algebra and modular representation theory (2025)

This Panorama Lecture Series will feature lectures by Prof Srikanth Iyengar on cohomological support varieties for modules over complete intersections, stratification of the bounded derived category of complete intersections and applications to modular representation theory of finite groups. Additionally, there will be preparatory lectures on stable module categories and group cohomology.

Prof Srikanth Iyengar

Prof. Srikanth Iyengar is a Professor of mathematics at the University of Utah. His research is in the homological aspects of commutative algebra and its relation to representation theory of groups and to number theory. He has received various honours for his research.

Recently, he has been announced as an invited speaker at the International Congress of Mathematicians 2026.

He is a Fellow of the American Mathematical Society, a Simons Fellow and has been a Research Professor at SLMath/MSRI.

He serves on the editorial board of several prominent journals such as the Journal of the London Mathematical Society and International Math. Research Notices and is a managing editor of Journal of Pure and Applied Algebra.

 

Participants are expected to be familiar with the following topics: basic homological methods in commutative algebra; derived category of the module category of a ring; basics of representations of finite groups.

 Convener(s)

 
Name: Sarang Sane Manoj Kummini
Mailing Address:

Assistant Professor
Indian Institute of Technology Madras

 Professor
Chennai Mathematical Institute
Email: sarangsanemath at gmail.com mkummini at cmi.ac.in

Dates: 

Monday, December 15, 2025 - 19:00 to Friday, December 19, 2025 - 19:00

Venue: 

Venue Address: 

Department of Mathematics, IIT Madras,
Chennai Tamilnadu 600 036.

Venue State: 

Venue City: 

PIN: 

600036

Syllabus: 

 

Speaker and affiliation Number of Lectures Detailed Syllabus
Srikanth Iyengar
University of Utah
USA		 5
  1. Perfect complexes and the theorem of Hopkins and Neeman;
  2. Complete intersections and the BGG correspondence;
  3. Support varieties for modules over complete intersections;
  4. Stratification for the bounded derived category of a complete intersection;
  5. The stable module category of a finite group.
Manoj Kummini
CMI		 1

Review of derived categories and DG algebras
Sarang Sane
IIT Madras		 2

Stable module categories. The stable module category of matrix factorizations.
Upendra Kulkarni
CMI		 2

Group algebras and group cohomology

 References

  1.  L. L. Avramov. Infinite free resolutions. In J. Elías, J. M. Giral, R. M. Miró-Roig, and S. Zarzuela, editors, Six lectures on commutative algebra, Papers from the Summer School (Ballaterra, 1996), Mod. Birkhäuser Class., pages 1–118. Birkhäuser/Springer,Basel, 1998.
  2.  L. L. Avramov, Modules of finite virtual projective dimension, Invent. Math. 96 (1989), 71-101.
  3.  L. L. Avramov, R.-O. Buchweitz, Support varieties and cohomology over complete intersections, Invent. Math. 142 (2000),285-318.
  4.  L. L. Avramov, R.-O. Buchweitz, S. B. Iyengar and C. Miller, Homology of perfect complexes, Advances in Math. 223 (2010),1731-1781. Corrigendum: Advances in Math. 225 (2010), 3576-3578.
  5.  L. L. Avramov and S. B. Iyengar, Constructing modules with prescribed cohomological support, Ill. Jour. Math. 51 (2007), 1-20.
  6.  L. L. Avramov and S. B. Iyengar, Restricting homology to hypersurfaces, Geometric and topological aspects of the representation theory of finite groups, 1–23, Springer Proc. Math. Stat., 242, Springer, Cham, ; MR3901154
  7.  D. J. Benson, Representations and Cohomology II: Cohomology of groups and modules, Cambridge Studies in Advanced Mathematics, vol. 31, Cambridge University Press, 1991, reprinted in paperback, 1998.
  8.  D. J. Benson, S. B. Iyengar, and H. Krause, Stratifying modular representations of finite groups, Annals of Math 174 (2011),1643-1684.
  9.  R.-O. Buchweitz, Maximal Cohen-Macaulay modules and Tate cohomology, Mathematical Surveys and Monographs, 262,Amer. Math. Soc., Providence, RI, [2021] ©2021; MR4390795
  10.  J. F. Carlson, Cohomology and induction from elementary abelian subgroups, Q. J. Math. 51 (2000), no. 2, 169–181;MR1765788
  11.  J. F. Carlson and S. B. Iyengar, Thick subcategories of the bounded derived category of a finite group, Trans. Amer. Math. Soc.367 (2015), no. 4, 2703–2717; MR3301878
  12.  D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math.Soc. 260 (1980), 35-64.
  13.  M. J. Hopkins, Global methods in homotopy theory, Homotopy Theory, Durham 1985, Lecture Notes in Mathematics, vol.117, Cambridge University Press, 1987.
  14.  S. Iyengar, Modules and Cohomology over Group Algebras: One Commutative Algebraist’s Perspective, Trends in Commutative Algebra, MSRI Publications, Volume 51, 2004, pp. 51–86
  15.  J. Tate. Homology of Noetherian rings and local rings. Illinois J. Math., 1:14–27, 1957.

Secondary references

  1. L. L. Avramov and S. B. Iyengar, Cohomology over complete intersections via exterior algebras, Triangulated categories (Leeds,2006), London Math. Soc. Lecture Note Ser. 375, Cambridge Univ. Press, Cambridge, 2010, 52-75.
  2. D. J. Benson, Representations and Cohomology II: Cohomology of groups and modules, Cambridge Studies in Advanced Mathematics, vol. 31, Cambridge University Press, 1991, reprinted in paperback, 1998.
  3. D. J. Benson, J. F. Carlson and J. Rickard, Thick subcategories of the stable module category, Fund. Math. 153 (1997), no. 1, 59–80; MR1450996
  4. T. H. Gulliksen and G. Levin. Homology of local rings. Number 20 in Queen’s Papers in Pure and Applied Mathematics. Queen’s University, Kingston, Ont., 1969.
  5. H. Krause, Homological theory of representations, Cambridge Studies in Advanced Mathematics, 195, Cambridge Univ. Press, Cambridge, 2022; MR4327095
  6. M. Hovey, J. H. Palmieri, and N. P. Strickland, Axiomatic stable homotopy theory, Mem. AMS, vol. 128, American Math.Society, 1997.

Time Table: 

 

Day Date Lecture 1
9.30–11.00 		  Lecture 2
11.30–1.00 		  Tutorial
2.30–3.30 		  Tutorial
4.00-5.00 		 
Mon 15/12/2025 MK

T
e
a

 SI L
u
n
c
h

MK, T1, T2 T
e
a

 

 SI, T1, T3

S
n
a
c
k
s
Tue 16/12/2025 SS SI SS, T2, T3 SI, T1, T2
Wed 17/12/2025 SS SI SS, T1, T3 SI, T2, T3
Thu 18/12/2025 UK SI UK, T1, T2 SI, T1, T3
Fri 19/12/2025 UK SI UK, T2, T3 SI, T1, T2

 

SI : Srikanth Iyengar
UK : Upendra Kulkarni
MK : Manoj Kummini
SS : Sarang Sane

 

Selected Applicants: 

 

Sr.n 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 65516 Mr Aryaman Maithani Male University of Utah PhD NA    
2 65544 Mr Arnab Kundu Male Harish-Chandra Research Instituite PhD Student Ramakrishna Mission Vivekananda Educational and Research Institute 2021  
3 65596 Ms. Mansi Mittal Female IIT PATNA PhD BHU/ M.Sc. 2019  
4 65608 Mr. Subhadip Bhowmick Male Indian Institute of Technology Kharagpur PhD Indian Institute of Technology Kharagpur 2023  
5 65613 Mr. Tapas Kumar Roy Male Indian Institute of Technology Kharagpur PhD Jadavpur University, Kolkata 2019  
6 65617 Ms. Mouma Samanta Female IIT Kharagpur PhD IIT Kharagpur 2022  
7 65656 Mr. Siddhartha Pramanik Male IIT Kharagpur PhD Student IIT Madras 2022  
8 65668 Mr. Manav Batavia Male Purdue University PhD Indian Institute of Technology Bombay 2022  
9 65726 Ms. Lisa Mandal Female IISER Kolkata. PhD Indian Institute of Technology Madras. 2023  
10 65739 Mr. Aniruddha Saha Male INDIAN INSTITUTE OF TECHNOLOGY HYDERABAD PhD University of Hyderabad 2018  
11 65782 Mr. Mifron Fernandes Male University of Missouri PhD IIT Madras 2023  
12 65814 Mrs Antonia Kekkou Female University of Utah PhD student N/A    
13 65822 Dr. Mitra Koley Female IISER Thiruvananthapuram Asst. Prof. IIT Guwahati 2011 28/07/2018
14 65830 Mr. Russell Dcruz Male N/A N/A Tata Institue of Fundamental Research, Mumbai Appearedl  
15 65856 Mr. Amit Phogat Male IIT Gandhinagar PhD IIT Madras 2023  
16 65874 Mr Nikhil Purushottam Zade Male Visvesvaraya National Institute of Technology PhD Visvesvaraya National Institute of Technology, Nagpur 2020  
17 65878 Prof. Chudamani Pranesachar Anil Kumar Male Krea University Associate Professor The Ohio State University 2002 01/08/2014
18 65881 Ms. Sudipa Das Female Harish-Chandra Research Institute PhD RKMVERI, Belur 2021  
19 65887 Prof Suresh Nayak Male ISI Bangalore Associate Professor Purdue University USA 1997 01/12/1998
20 65888 Mr. Florian Hartmut Tecklenburg Male Bielefeld University Ph.D. student Rheinische Friedrich-Wilhelms-Universität Bonn 2023  
21 65897 Mr. Suhas Vadan Gondi Male University of California San Diego PhD Student Indian Statistical Institute, Kolkata 2022  
22 65913 Mr Adhavan S V Male Indian Institute of Science, Bangalore MSc Student      
23 65936 Mr. Subham Jaiswal Male Tata Institute of Fundamental Research Phd Indian Statistical Institute 2024  
24 65941 Ms Chitra Venugopal Female Indian Institute of Technology Hyderabad Project Associate - I Cochin University of Science and Technology 2018 19/07/2025
25 65951 Dr. Dipankar Ghosh Male IIT Kharagpur Asst. Prof. M.Sc 2011 13/08/2016
26 65969 Mr. Soumik Mukherjee Male IIT Kharagpur PhD student IIT Kharagpur 2023  
27 65985 Mr. Samuel Alvite Male Universidade de Santiago de Compostela PhD Student Universidade de Santiago de Compostela 2022  
28 66006 Mr. Anjan Gupta Male IISER Bhopal Asst. Professor ISI Kolkata 2008 06/02/2015
29 66012 Mr. Anmol Anmol Male Indian Institute of Science Student Indian Institute of Science Appeared  
30 66030 Dr Rishi Vyas Male Krea University Assistant Professor of Mathematics University of Cambridge 2008 27/04/2013
31 66043 Dr. Vaibhav Pandey Male Purdue University Golomb Visiting Assistant Professor NISER, Bhubaneswar 2016 05/08/2022
  Local   Participants 
1 65531 Prof Anwesh Ray Male Chennai Mathematical Institute Asst. Prof. Chennai Mathematical Institute 2015 01/04/2020
2 65545 Dr. Manohar Kumar Male Indian Institute of Technology Madras PostDoc M.Sc. 2020 20/06/2025
3 65603 Dr. Prashanth Sridhar Male University of Alabama Assistant Professor Centre for Excellence in Basic Sciences 2015 01/08/2021
4 65625 Mr. Ganapathy K Male IIT Madras PhD student IIT Madras 2021  
5 65632 Mr. Abhiram Subramanian Male Chennai Mathematical Institute PhD Chennai Mathematical Institute, M.Sc. 2022  
6 65698 Mr Kesavan Mohana Sundaram Male University of Nebraska Lincoln Graduate Teaching Assistant Indian Institute of Technology Madras 2023  
7 65702 Mr. Velmurugan S Male The Institute of Mathematical Sciences PhD student University of Madras 2021  
8 65843 Mr Omkar Deepak Javadekar Male Chennai Mathematical Institute Postdoctoral Fellow IIT Bombay 2020 22/08/2025
9 65976 Dr Chi Trung Chau Male Chennai Mathematical Institute Postdoc Not applicable   01/08/2024
10 66027 Ma. Aditya Dwivedi Male Indian Institute of Technology, Bombay PhD Indian Institute of Technology Bombay 2025  

 

 

 

 

How to Reach: 

TBA

School Short Name: 

camrt

Last Date Application: 

Monday, August 15, 2022

School Type: 

PL

Separate faculty form: 

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