ATMW Commutative Algebra (2011)

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 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.

Link to how to reach