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 |
Name | Jugal Verma | Anurag Singh | Srikanth Iyengar |
Mailing Address | Prof., Department of Mathematics IIT Bombay, Mumbai 400 076 |
- | - |
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
- Basic Notions: algebraic sets, dimension theory, regular rings.
- Injective Modules: structure theorem, Matlis duality.
- Resolutions and derived functors.
- Depth: Koszul complex, regular sequences, depth, Cech complex.
- Local Cohomology: torsion functor, direct limit of Ext modules, direct limit of Koszul cohomology modules.
- Regular rings: ﬁniteness of global dimension, Auslander-Buchsbaum formula, complete regular local rings.
- Cohomological Dimension: depth, nonvanishing theorem.
- Arithmetic rank: examples, set-theoretic complete intersections.
- Cohen-Macaulay Rings: intersection multiplicities, invariant theory.
- Gorenstein Rings: Bass numbers, injective resolutions, local duality.
- Sheaf Cohomology: Sheaves, Cech cohomology, ﬂasque sheaves, local cohomology and sheaf cohomology.
- Projective Varieties: graded local cohomology, sheaves on projective varieties, global sections and cohomology.
- The Hartshorne-Lichtenbaum Vanishing Theorem.
- Connectedness: Mayer-Vietoris sequence, punctured spectra.
- Duality: Poincare duality, Grothendieck duality, local duality, global canonical modules.
- D-modules: Weyl algebra, holonomic modules, Bernstein-Sato polynomials.
- Algorithmic Aspects: local cohomology as a D-module.
- The Frobenius Endomorphism: homological properties, Frobenius action on local cohomology, a vanishing theorem.
- More on Frobenius: Lyubeznik’s vanishing theorem, dependence of local cohomology on characteristic.
- Finiteness properties: Hartshorne’s example, associated primes.
- Parafactoriality: Samuel’s conjecture via local cohomology.
- Big Cohen-Macaulay algebras: the Huneke-Lyubeznik theorem.
- Local cohomology with respect to ideals of minors of generic matrices
- Connections with topology: work of Dwyer, Greenlees, and Iyengar.
Selected Participants
List of Selected Candidates (Final)
All selected candidates are requested to confirm their participation by sending email to verma.jugal@gmail.com 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 | 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 |