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Sunil K. Chebolu

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About me

I am an associate professor and the undergraduate director in the department of mathematics at Illinois State University. I am also an affliate member in the department of mathematics at the University of Western Ontario as an adjunct research professor.

A brief history of my time after college: From 1995 to 2000, I attended the Indian Statistical Institute (Kolkatta) where I got my Bachelors and Masters degrees in Statistics with a specialisation in Advanced Probability. Under the supervision of John Palmieri I got my Ph.D. in Mathematics at the University of Washington, Seattle in 2005. My thesis was in the area of stable homotopy theory. After completing my Ph.D., I had a 3-year postdoctoral fellowship at the University of Western Ontario, Canada. I joined the Illinois State University in Fall 2008.

My interests include Mathematics, Music, Physics, Astronomy, Cosmology, Games, Logic, Computing, Philosophy, and the History of Intellectual Thought.

My current Erdos number is 3: Erdos ---> John Conway ---> Dave Benson ---> Me. You can read about the Erdos number here. The homotopy type of my known mathematical genealogy is a wedge of three circles.

I love working with students. If you are a student who is interested in doing an Honors project, a Masters thesis/project or an independent study/research in some area of Mathematics under my supervision please contact me. I will be very happy to guide you.

I work on a bunch of different areas. Current interests like in the fields of representation theory of groups, Tate cohomology, Galois cohomology. Visit my research page for more information. My research is being supported by grants from the National Security Agency (NSA).

I am the organiser of the algebra seminar at Illinois State. If you would like to give a talk in the seminar please let me know. We meet on Tuesdays from 2:00 - 3:00. Please check out our algebra seminar homepage. I am the faculty advisor for the Math Club at ISU. Math Club is a great nice place to meet other math students and take part in fun activities including, potluck, games night, movie night, puzzles night, etc. Let me know if you would like to be part of it. Please visit our website ISU Math Club. I am also the in-charge of the Putnam Mathematical Competition at ISU. If you are an undergraduate student who loves solving math problems, you should definitely take part in Putnam. For more information visit ISU Putnam homepage.

NEWS : I received the Illinois State University Research Initiative Award (2011). For more about it, read the CAS newsletter. I also won the mathematics department Teaching Initiative Award (2011).

Papers

Thesis

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

Publications:

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, Geometry and Topology 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 Annales des sciences math´ematiques du Qu´ebec 34 (2010), no 1, 37-61.

On a small quotient of the big absolute Galois group, (joint work with Efrat and Minac) Oberwolfach Report 32 (2010) 14-17.

Finite generation of Tate cohomology, joint with Jon Carlson and Jan Minac, Representation theory (AMS Journal) 15 (2011) 244-257.

Counting irreducible polynomials over finite fields using the inclusion-exclusion principle, joint with Jan Minac, Math. Mag 84 (2011), No. 5, 369-371.

Quotients of absolute Galois groups which determine entire Galois cohomology cohomology, joint with Ido Efrat and Jan Minac, Math. Annalen 352 (2012), 205-221.

Freyd's generating hypothesis for groups with periodic cohomology, joint with Christensen and Minac, Canadian Mathematical Bulletin 55 (2012), 48-59

What is special about the divisors of 24?, Math. Mag. Vol. 85, No. 5 (2012).

Representations of the Miraculous Klein group, joint with Jan Minac, Ramanujan Mathematics Society Newsletter 22 (2012), No. 1, 135-145.

What is special about the divisors of 12?, with Michael Mayers, to appear in Math. Mag.

Preprints:

Witt's cancellation theorem seen as a cancellation, joint with McQuillan and Minac.
Groups which do not admit strong ghosts, joint with Carlson and Minac
Ghost maps and groups with periodic cohomology, joint with Carlson and Minac
Group extensions and Galois modules for the bicyclist, joint with Minac, Schultz and Swallow, 13 pages,
Bloch-Kato pro-p groups and a refinement of the Bloch-Kato conjecture, joint with Benson, Minac and Swallow, 13 pages

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. (*)

PDF Slides of some talks

What is special about the divisors of 24? Discrete Mathematics seminar, Illinois State Univ., April 21, 2011.
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.
The unreasonably beautiful world of numbers, Presentation in Math Club, Illinois State University, March 3rd 2010.
Cohomology of Bloch-Kato profinite groups AMS special session on Homotopy theory, Penn. State Univ., State College, Oct 24-25, 2009.
Cohomology with stones and sticks, Plenary talk at MAA meetings, Bradley univeristy, Peoria, February 2009.
Strongly regular graphs, Discrete Math Seminar, Oct 14th 2008. (Page 10 is missing, here it is Page 10.)
A new interpretation of the quadratic closure of a field, AMS meetings in Vancouver, BC, Oct 3-4, 2008.
A new perspective on groups with periodic cohomology, CMS meetings in London, ON, Dec. 10, 2007.
Towards a refinement of the Bloch-Kato conjecture, CMS meetings in London, ON, Dec. 9, 2007.
Finite generation of Tate cohomology and Freyd's generating hypothesis, AMS meetings in Murfreesboro, TN, Nov. 3, 2007.
Diagrammatic methods in representation theory and cohomology, Graduate student seminar, UWO, London, July 23rd, 2007.
Tate cohomology often fails to detect null homotopy, AMS meetings in Davidson, NC, March 3-4, 2007.
Which finite p-groups are like a finite product of fields?, CMS Winter 2006 meetings, Toronto, December 10, 2006.
Stable homotopy theory -- A gateway to Modern Mathematics, Indian Institute of Science (IISc) and the Indian Statistical Institute (ISI), Bangalore, May 2006
Thick subcategories in stable homotopy theory (work of Devinatz, Hopkins, Smith) at a workshop on thick subcategories, Oberwolfach, Germany, February 2006.
My final examination at the University of Washington, Seattle, May 11 (on my birthday!) 2005.
A Brave New World in homotopy theory, Graduate student topology conference, Northwestern University, Evanston, April 2005
A Krull-Schmidt theorem for wide subcategories of modules, Joint Meetings of the AMS, Atlanta, January 2005

Conferences

Keir Lockridge and I have organised an AMS special session on "Triangulated categories and their associated cohomology theories" at University Park, PA on October 24-25, 2009.
George Seelinger and I have organised the Fall Midwest Topology Seminar at ISU on Saturday, October 8th, 2011.

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 amazing videos of Prof. Jan Minac Video 1 Video 2.