Department of Mathematics at Illinois State University

Faculty

Chebolu

Sunil Kumar Chebolu

Associate Professor
Undergraduate Director

Office Address: Stevenson 303B
Office Phone: (309) 438-3893
Office Hours:
Email: Contact Sunil Chebolu (schebol)
Website: Visit Sunil Chebolu’s Website
Teaching Schedule:
Teaching Interests:
I enjoy teaching a wide range of courses in mathematics at various levels. Although my own research interests lie in algebra, number theory, and  topology, I am constantly looking for the opportunity to teach undergraduate courses in other branches as well -- combinatorics, graph theory, probability, statistics, analysis, and set theory, to mention a few. I enjoy working with students. If you are a student who is interested in doing an Honors project, or a Masters thesis/project or an independent study in some area of Mathematics under my supervison please contact me. I will be happy to guide you.
Research Interests:
My research interests lie in the fields of Algebraic topology, Representation theory, and Arthimetic. Specifically, I am intersted in interactions between these fields which are inspired by cohomology theories and triangulated structures, among others. For example, I like to think about homotopy theoretic questions in algebraic subjects like the derived categories of homological algebra and the stable module categories of modular representation theory. In my thesis (at the University of Washington under the supervision of John Palmieri) I have studied the refinements of chromatic towers and Krull-Schmidt type decompositions in various stable homotopy categories including the derived categories of rings, the stable homotopy category of spectra and the stable modules categories of group schemes. More recently, in several joint projects with my collaborators Benson, Carlson, Minac, Swallow, and Ido Efrat, I have been working on several problems in Galois cohomology, modular representation theory (which are inspired from stable homotopy theory).
For more information please visit:  http://math.illinoisstate.edu/schebol/research.html
Education:
Spring 2005 :  Ph.D. in Mathematics, University of Washington, Seattle, USA.
Spring 2002 : Master of Science, Mathematics, University of Washington, Seattle, USA.
Spring 2000 :  Master of Statistics, Indian Statistical Institute, Bangalore, India.
Spring 1998 : Bachelor of Statistics, Indian Statistical Institute, Calcutta, India.
Selected Publications:
      All these papers are available from my author page of the arXiv.

      Publications:

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

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

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

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

      5. 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.

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

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

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

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

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

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

      12. Reciprocity laws for representations of finite groups, joint with Jan Minac and Clive Reis Annales des sciences math´ematiques du Qu´ebec 34 (2010), no 1, 37-61.

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

      14. On a small quotient of the big absolute Galois group, (joint work with Efrat and Minac) Oberwolfach Report, July 2010 (to appear).

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

      Preprints:
      1. Quotients of absolute Galois groups which determine entire Galois cohomology cohomology, joint with Ido Efrat and Jan Minac, preprint 2009, 14 pages, Submitted.

      2. Counting irreducible polynomials over finite fields, joint with Jan Minac, preprint 2010, 3 pages, Submitted.