ATMW Commutative Algebra (2011)

Venue: Indian Institute of Technology Bombay, Mumbai
Dates: 1 July - 12 July, 2011


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name Jugal Verma   Anurag Singh Srikanth Iyengar
Mailing Address Prof., Department of Mathematics
IIT Bombay, Mumbai 400 076
- -


Speakers and Syllabus 

Workshop speakers:

  • Krishna Hanumanthu, Kansas University
  • Ananth Hariharan, University of Nebraska
  • Srikanth Iyengar, University of Nebraska
  • Manoj Kummini, Purdue University
  • Tony Puthenpurakal, IIT Bombay
  • Anurag Singh, University of Utah
  • Wenliang Zhang, University of Michigan

Conference speakers:

  • Manuel Blickle, Universität Mainz
  • Holger Brenner, Universität Osnabrück
  • Ananth Hariharan, University of Nebraska
  • Gennady Lyubeznik, University of Minnesota
  • Vikram Mehta, TIFR Mumbai
  • Suresh Nayak, Chennai Math Institute
  • Pramath Sastry, Chennai Math Institute
  • Vijaylaxmi Trivedi, TIFR Mumbai
  • Jugal Verma, IIT Bombay
  • Uli Walther, Purdue University

Tentative Lectures Plan

  1. Basic Notions: algebraic sets, dimension theory, regular rings.
  2. Injective Modules: structure theorem, Matlis duality.
  3. Resolutions and derived functors.
  4. Depth: Koszul complex, regular sequences, depth, Cech complex.
  5. Local Cohomology: torsion functor, direct limit of Ext modules, direct limit of Koszul cohomology modules.
  6. Regular rings: finiteness of global dimension, Auslander-Buchsbaum formula, complete regular local rings.
  7. Cohomological Dimension: depth, nonvanishing theorem.
  8. Arithmetic rank: examples, set-theoretic complete intersections.
  9. Cohen-Macaulay Rings: intersection multiplicities, invariant theory.
  10. Gorenstein Rings: Bass numbers, injective resolutions, local duality.
  11. Sheaf Cohomology: Sheaves, Cech cohomology, flasque sheaves, local cohomology and sheaf cohomology.
  12. Projective Varieties: graded local cohomology, sheaves on projective varieties, global sections and cohomology.
  13. The Hartshorne-Lichtenbaum Vanishing Theorem.
  14. Connectedness: Mayer-Vietoris sequence, punctured spectra.
  15. Duality: Poincare duality, Grothendieck duality, local duality, global canonical modules.
  16. D-modules: Weyl algebra, holonomic modules, Bernstein-Sato polynomials.
  17. Algorithmic Aspects: local cohomology as a D-module.
  18. The Frobenius Endomorphism: homological properties, Frobenius action on local cohomology, a vanishing theorem.
  19. More on Frobenius: Lyubeznik’s vanishing theorem, dependence of local cohomology on characteristic.
  20. Finiteness properties: Hartshorne’s example, associated primes.
  21. Parafactoriality: Samuel’s conjecture via local cohomology.
  22. Big Cohen-Macaulay algebras: the Huneke-Lyubeznik theorem.
  23. Local cohomology with respect to ideals of minors of generic matrices
  24. Connections with topology: work of Dwyer, Greenlees, and Iyengar.

Selected Applicants

Selected Participants

List of Selected Candidates (Final)

All selected candidates are requested to confirm their participation by sending email to by May 16 2011.


No. Name   Affiliation Gender
1 B. Baskara Rao RS Univ. of Pondicherry M
2 K. Premkumar RS Univ. of Pondicherry M
3 R. Athimoolam RS Pondicherry Engg. College M
4 Abhishek Parab RS Institute of Mathematical Sciences, Chennai M
5 Krishanu Dan RS Institute of Mathematical Sciences, Chennai M
6 Ramakrishnan Nanduri RS IIT Madras M
7 R. Balakrishnan RS IIT Madras M
8 SarithaViswanathan RS IIT Madras F
9 Susobhan Mazumdar RS IIT Madras M
10 Neena Gupta RS Indian Statistical Institute, Kolkata F
11 Md. Ali Zinna RS Indian Statistical Institute, Kolkata M
12 Gaurab Tripathi RS Jadavpur University, Kolkata M
13 Raj Bhattacharyya AP Dinabandhu Andrews College, Kolkata M
14 Joydip Saha RS RKMV University, Belur Math M
15 Ajay Kumar RS IISER Mohali M
16 Rabeya Basu AP IISER, Pune F
17 Surjeet Kour RS IIT Kanpur F
18 Ashok Kumar RS Science College, Jammu M
19 Anjan Gupta RS TIFR, Mumbai M
20 Devika Sharma RS TIFR Mumbai F
21 Anand Sawant RS TIFR Mumbai M
22 Viji Thomas PDF TIFR Mumbai M
23 Sagar Kolte RS TIFR, Mumbai M
24 Papri Dey RS IIT Bombay F
25 Vivek Sadhu RS IIT Bombay M
26 H. Parvez Sarwar RS IIT Bombay M
27 Shreedevi Masuti RS IIT Bombay F
28 Alpesh Dhorajia RS IIT Bombay M
29 Swapnil Lokhande RS IIT Bombay M
30 Mousumi Mandal RS IIT Bombay F
31 Sarang Sane -- TIFR, MUmbai M

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