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Associate Professor and Undergraduate Director
Illinois State University
Ph.D., Univ. of Washington (2005)
Research interests: Modular Representation theory, Tate Cohomology, Galois Cohomology, Number Theory, Triangulated Categories, and General Recreational Mathematics.
Office Phone: (309) 438 3893
Fax: (309) 540 5678 (Include my name)
email@example.com     (with the two "z"s removed)
Address: Department of Mathematics,
Illinois State University, Campus Box 4520, Normal, IL 61790. USA
I am an associate professor and the undergraduate director in the department of mathematics at
Illinois State University. I
also hold research assistant professor positions in the mathematics departments at UIUC, and at
A brief history of my time since 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 broad 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 lie in the
fields of Number theory, representation theory of groups,
Tate cohomology, and Galois cohomology. Visit my research page for more
information. My research is being currently supported by a grant from the National
Security Agency (NSA).
I am one of the organisers 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
algebra seminar homepage.
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
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
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),
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,
(AMS Journal) 15 (2011) 244-257.
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,
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, Math. Mag. Vol. 86, No. 2 (2013).
Detecting Fast solvability of equations via small powerful Galois groups joint with Minac and Quadrelli,
to appear in Transactions of the AMS
Characterizations of Mersenne primes and 2-rooted primes, joint with Lockridge and Yamskulna, 18 pages, submitted.
When is the multiplicative group of a field indecomposable? joint with Lockridge, 10 pages, submitted.
Galois p-groups and Galois modules, joint with Minac and Schultz, 27 pages, to appear in Rocky Mountain Journal of
Fuchs' problem for indecomposable abelian groups joint with Lockridge, 10 pages, submitted.
Witt's cancellation theorem seen as a cancellation, joint with McQuillan and Minac, 16 pages.
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
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
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.