Homepage of Apoorva Khare

Contact information


Affiliation Visiting Assistant Professor, University of California at Riverside
Address University of California at Riverside,
Department of Mathematics,
900 University Avenue, Surge 228,
Riverside, CA - 92521
Phone 951-827-3120 (Office)
Fax 951-827-7314 (Office)
Email apoorva AT math DOT ucr DOT edu
Ph.D. University of Chicago; Advisor: Victor Ginzburg
Curriculum vitae PDF
Personal web page http://www.math.ucr.edu/~apoorva/personal/

Teaching

In the Fall of 2008, I am teaching a section of Math 8B - for which you have to go to ilearn or WebAssign as well - and a section of Math 10B. Here are the links to Math 10B - Calculus: Several Variables - II, Section 1, and Math 8B - Introduction to College Mathematics for Sciences, Section 30 .


Publications and preprints

  1. Divisibility Tests, Furman University Electronic Journal of Undergraduate Mathematics FUEJUM Volume 3 (1997), pages 1-5. PDF
  2. Category O over a deformation of the symplectic oscillator algebra. Journal of Pure and Applied Algebra, Volume 195 No. 2 (15 January, 2005), pages 131-166; math.RT/0309251. Here is the PDF without the errata.
    (The erratum appeared in the same JPAA, in Volume 199 (1 July, 2005), pages 319-320.)
  3. Divisibility tests and recurring decimals in Euclidean domains, JP Journal of Algebra, Number Theory, and Applications JPANTA, Volume 7 No. 1 (February 2007), pages 1-32;
    preprint, math.NT/0406025. Here is the PDF.
  4. Quantized symplectic oscillator algebras of rank one, joint with Wee Liang Gan. Journal of Algebra Volume 310 No. 2 (15 April 2007), pages 671-707; math.RT/0405176. Here is the PDF.
  5. Axiomatic framework for the BGG Category O; preprint, math.RT/0502227. Here is the PDF that is currently undergoing revision.
  6. Functoriality of the BGG Category O; accepted for publication in Communications in Algebra; preprint (unrevised), math.RT/0504371. Here is the version that is currently undergoing significant revision.
  7. The sum of a finite group of weights of a Hopf algebra, preprint, math.RA/0701467 v2. Here is the PDF, that is currently being revised.
  8. Drinfeld-Hecke algebras over cocommutative algebras, preprint, arxiv:0705.2067 (math.RA). Here is the PDF.
  9. Vector spaces, modules over Chinese rings, and monoids as unions of proper subobjects, preprint, arxiv:0803.2746 (math.AC). Here is the PDF.
  10. Center and representations of infinitesimal Hecke algebras of sl_2, joint with Akaki Tikaradze. Accepted for publication in Communications in Algebra; arxiv:0807.4776 (math.QA). Here is the PDF.
  11. I have also been asked to write an entry, titled The BGG Category O, for the Encyclopedia of Mathematics (Michiel Hazewinkel, Editor), Kluwer Academic Publishers. (I have submitted the same.)

Talks at conferences

  1. Here are the transcripts of a talk I gave at Claremont McKenna College, at the 2008 Spring AMS Western Section Meeting, in May 2008 - the slides.
  2. Here are the transcripts of a talk I gave at Louisiana State University, at the 2008 Spring AMS Southeastern Sectional Meeting, in March 2008 - the slides.
  3. Here are the transcripts of a talk that I gave at the University of Arkansas, Fayetteville, at the 2006 Fall AMS Southeastern Sectional Meeting, in the Special Session on Combinatorial Representation Theory, in November 2006.
  4. Here are the transcripts of a talk I gave in the conference in hono(u)r of J. Leposwki and R. Wilson, in NCSU, Raleigh, in May 2005 - here are the transparencies.

Other documents

  1. Here is my topic proposal, titled Semisimple Lie algebras and their representations from 2002; I went through the text and the problems of Introduction to Lie algebras and representation theory (Graduate Texts in Mathematics, Volume 9, Springer Verlag), by James E. Humphreys.
  2. Here are some notes on various things, thanks to various people. They talk about simple modules and complete reducibility over products of algebras, and also about block decomposition using central characters.
  3. I participated in the Directed Reading Program in Fall 2005. This was a one-on-one interaction with an undergraduate; I was paired with Philip Brunetti, and we studied Mobius functions on partially ordered sets. Here are some notes we made.

Quantum Gravity Seminar

    I was taking (TeXing!) notes for the Cohomology and Quantization module of Professor John Baez's Quantum Gravity Seminar in 2006-07.

    These notes are only a preliminary version; they have to be polished up, edited, and figures added. In the meantime, here they are. (Note that each new lecture will start on a new page, so it's convenient for "updating".)

  1. Fall 2006
  2. Winter 2007
  3. Spring 2007


More methods of lion-hunting that are accessible to graduate students. This is joint with Jayadev Athreya (Princeton University).