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Sunil K. Chebolu Assistant Professor Ph.D., Univ. of Washington (2005) Research interests: Homotopy theory, modular and geometric representation theory, support varieties, affine group schemes, spectra, triangulated categories, derived categories, Galois cohomology, Quadratic forms, Bloch-Kato conjecture, and K-theory. Office: Stevenson 303B. Office Phone: (309) 438 3893 Fax: (309) 540 5678 (Include my name) E-mail: szchebol@ilstu.eduz     (with the two "z"s removed) Address: Department of Mathematics, Illinois State University, Campus Box 4520, Normal, IL 61790. USA

About me

Papers

Thesis


• Refinements of chromatic towers and Krull-Schmidt decompositions in stable homotopy categories, Ph.D. thesis, University of Washington, 2005.

Published papers:


• Refining thick subcategory theorems, Fundamenta Mathematicae 189 (2006) 61-97.
  


• Thick subcategories of stable homotopy theory, Oberwolfach Report 8 (2006) 12-20.
  


• Krull-Schmidt decompositions for thick subcategories, Journal of Pure and Applied Algebra 210 (2007) 11-27.
  


• Abelian subcategories closed under extensions: K-theory and decompositons, Communications in Algebra 35 (2007) 807-819.
  


• The generating hypothesis for the stable module category of a p-group, joint with Benson, Christensen and Minac, Journal of Algebra 310 (2007) 428-433.
  


• Groups which do not admit ghosts, joint with Christensen and Minac, Proc. Amer. Math. Soc. 136 (2008), 1171-1179.


• Ghosts in modular representation theory, joint with Christensen and Minac, Advances in Mathematics 217 (2008), 2782-2799


• Auslander-Reiten sequences for homotopists and arithmeticians, joint with Minac, Annales des sciences math´ematiques du Qu´ebec. 32 (2008), no 2, 19 pages.


• Freyd's generating hypothesis with almost split sequences, joint with Carlson and Minac, Proc. Amer. Math. Soc. 137 (2009), 2575-2580.


• Absolute Galois groups viewed from small quotients and the Bloch-Kato conjecture, joint with Minac, Topology and Geometry monographs 16 (2009) 31-47.


• Classifying subcategories of modules over a PID, JP Journal of Algebra, Number Theory and Applications 2 (2009) 211 - 220.


• Reciprocity laws for representations of finite groups, joint with Jan Minac and Clive Reis, preprint 2010, 21 pages, to appear in Annales des sciences math´ematiques du Qu´ebec.


• Finite generation of Tate cohomology, joint with Jon Carlson and Jan Minac, preprint 2010, 17 pages, to appear in Representation theory (AMS Journal).


• Freyd's generating hypothesis for groups with periodic cohomology, joint with Christensen and Minac, 12 pages, to appear in Canadian Mathematical Bulletin
  


Preprints:


• Quotients of absolute Galois groups which determine entire Galois cohomology cohomology, joint with Ido Efrat and Jan Minac, preprint 2009, 14 pages, Submitted.
  
  
• Counting irreducible polynomials over finite fields, joint with Jan Minac, preprint 2010, 3 pages, Submitted.
  
  
• Bloch-Kato pro-p groups and a refinement of the Bloch-Kato conjecture, joint with Benson, Minac and Swallow, 13 pages, preprint 2008.
  
  

Work in progress: (Manuscripts available upon request for starred items)


• Decomposing Serre subcategories of finitely presented modules, in preparation.
  
  
• Refining the chromatic tower for the stable module category, in preparation.
  
  
• Representations of the Klein four group and Galois theory, joint with Minac and Swallow, in preparation.(*)
  
  
• On Jennings sequences for p-groups, joint with Minac and Dhillon, in preparation. (*)
  
  
• Group extensions and Galois modules for the bicyclist, joint with Minac, Schultz and Swallow, in preparation. (*)

PDF Slides of some talks

1. Progress report on the generating hypothesis AMS special session on Homotopy theory and Geometric aspects of algebraic topology, Univ. of Kentucky, Lexington, Mar 27-29, 2010.
2. The unreasonably beautiful world of numbers, Presentation in Math Club, Illinois State University, March 3rd 2010.
3. Cohomology of Bloch-Kato profinite groups AMS special session on Homotopy theory, Penn. State Univ., State College, Oct 24-25, 2009.
4. Cohomology with stones and sticks, Plenary talk at MAA meetings, Bradley univeristy, Peoria, February 2009.
5. Strongly regular graphs, Discrete Math Seminar, Oct 14th 2008. (Page 10 is missing, here it is Page 10.)
6. A new interpretation of the quadratic closure of a field, AMS meetings in Vancouver, BC, Oct 3-4, 2008.
7. A new perspective on groups with periodic cohomology, CMS meetings in London, ON, Dec. 10, 2007.
8. Towards a refinement of the Bloch-Kato conjecture, CMS meetings in London, ON, Dec. 9, 2007.
9. Finite generation of Tate cohomology and Freyd's generating hypothesis, AMS meetings in Murfreesboro, TN, Nov. 3, 2007.
10. Diagrammatic methods in representation theory and cohomology, Graduate student seminar, UWO, London, July 23rd, 2007.
11. Tate cohomology often fails to detect null homotopy, AMS meetings in Davidson, NC, March 3-4, 2007.
12. Which finite p-groups are like a finite product of fields?, CMS Winter 2006 meetings, Toronto, December 10, 2006.
13. Stable homotopy theory -- A gateway to Modern Mathematics, Indian Institute of Science (IISc) and the Indian Statistical Institute (ISI), Bangalore, May 2006
14. Thick subcategories in stable homotopy theory (work of Devinatz, Hopkins, Smith) at a workshop on thick subcategories, Oberwolfach, Germany, February 2006.
15. My final examination at the University of Washington, Seattle, May 11 (on my birthday!) 2005.
16. A Brave New World in homotopy theory, Graduate student topology conference, Northwestern University, Evanston, April 2005
17. A Krull-Schmidt theorem for wide subcategories of modules, Joint Meetings of the AMS, Atlanta, January 2005

Conferences

MATH VIDEOS

• How Mathematics Could Save Romeo and Juliet! This is an amazing play by Prof. Jan Minac and his wife Leslie. Absolutely terrific, highly original and hilarious!
• More to be added to soon.