Homepage of Apoorva Khare

Contact information

Affiliation Research Associate (joint in Mathematics and Statistics), Stanford University
Office Littlefield Center, Room 334
Postal address Sequoia Hall,
390 Serra Mall,
Stanford, CA - 94305
Phone 650-723-2957 (Office)
Fax 650-725-8977 (Office)
Email khare AT university-name DOT edu
Ph.D. University of Chicago

Recent and upcoming talks

Books; invited chapters/monographs in books

  1. Mathematics in the Real World, with Anna Lachowska, forthcoming from Yale University Press, 2015. See here for more information on the course which I developed and taught in Spring 2011 at Yale, and which led to the book.
  2. Entry on the BGG Category O, for the Encyclopedia of Mathematics (Michiel Hazewinkel, Editor), Kluwer Academic Publishers, 2005.


  1. Preserving positivity for matrices with sparsity constraints, joint with Dominique Guillot and Bala Rajaratnam,
    Transactions of the American Mathematical Society, in press, 2015; math.FA/1406.3408.
  2. Differential calculus on graphon space, joint with Peter Diao, Dominique Guillot, and Bala Rajaratnam,
    Journal of Combinatorial Theory, Series A Volume 133 (July 2015), pages 183-227 -- available for download courtesy Elsevier, until April 25.
  3. Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity, joint with Dominique Guillot and Bala Rajaratnam,
    Journal of Mathematical Analysis and Applications Volume 425 No. 1 (May 2015), pages 489-507.
  4. The critical exponent conjecture for powers of doubly nonnegative matrices, joint with Dominique Guillot and Bala Rajaratnam,
    Linear Algebra and its Applications Volume 439 No. 8 (October 2013), pages 2422-2427.
  5. Representations of complex semi-simple Lie groups and Lie algebras,
    in Connected at Infinity II: On the work of Indian mathematicians (R. Bhatia, C.S. Rajan, and A.I. Singh, Eds.),
    Texts and Readings in Mathematics (TRIM), Hindustan Book Agency (2013), pages 85-129.
  6. The sum of a finite group of weights of a Hopf algebra, Axioms 1 No. 3 (October 2012), pages 259-290 (Special issue on: "Hopf Algebras, Quantum Groups and Yang-Baxter Equations").
  7. Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order, joint with Avinash Khare and Avadh Saxena, Pramana Volume 79 No. 3 (September 2012), pages 377-392.
  8. Faces of polytopes and Koszul algebras, joint with Vyjayanthi Chari and Tim Ridenour,
    Journal of Pure and Applied Algebra Volume 216 No. 7 (July 2012), pages 1611-1625.
  9. Faces of weight polytopes and a generalization of a theorem of Vinberg, joint with Tim Ridenour,
    Algebras and Representation Theory Volume 15 No. 3 (June 2012), pages 593-611.
  10. Center and representations of infinitesimal Hecke algebras of sl_2, joint with Akaki Tikaradze,
    Communications in Algebra Volume 38 No. 2 (February 2010), pages 405-439.
  11. Functoriality of the BGG Category O,
    Communications in Algebra Volume 37 No. 12 (December 2009), pages 4431-4475.
  12. Vector spaces as unions of proper subspaces,
    Linear Algebra and its Applications Volume 431 No. 9 (October 2009), pages 1681-1686.
  13. Quantized symplectic oscillator algebras of rank one, joint with Wee Liang Gan;
    Journal of Algebra Volume 310 No. 2 (April 2007), pages 671-707.
  14. Divisibility tests and recurring decimals in Euclidean domains (final section with Pieter Moree),
    JP Journal of Algebra, Number Theory, and Applications (JPANTA), Volume 7 No. 1 (February 2007), pages 1-32.
  15. Category O over the symplectic oscillator algebra, Ph.D. Thesis, University of Chicago, June 2006.
  16. Category O over a deformation of the symplectic oscillator algebra,
    Journal of Pure and Applied Algebra, Volume 195 No. 2 (January 2005), pages 131-166; erratum.
  17. Divisibility Tests, Furman University Electronic Journal of Undergraduate Mathematics
    FUEJUM Volume 3 (1997), pages 1-5.


Preprints in analysis and positivity

  1. Preserving positivity for rank-constrained matrices, joint with Dominique Guillot and Bala Rajaratnam; math.FA/1406.0042.
  2. On fractional Hadamard powers of positive block matrices, joint with Dominique Guillot and Bala Rajaratnam; math.FA/1404.6839.

Preprints in graph theory

  1. Differential calculus on the space of countable labelled graphs, joint with Bala Rajaratnam; math.CO/1410.6214.

Preprints in algebra

  1. Axiomatic framework for the BGG Category O; math.RT/1502.06706 (updated with major revisions).
  2. Standard parabolic subsets of highest weight modules; math.RT/1409.4133.
  3. Faces and maximizer subsets of highest weight modules; math.RT/1301.1140.
    Here is a related announcement, where I compute the weights of all simple highest weight modules (and others) over a complex semisimple Lie algebra:
    Weights of simple highest weight modules over a complex semisimple Lie algebra, math.RT/1305.4104.
  4. The covering problem for Chinese rings; math.AC/0906.1023 (under revision).
  5. Drinfeld-Hecke algebras over cocommutative algebras; math.RA/0705.2067 (under revision).


Conference Organization

This page was last modified on Fri Mar 06 2015, 07:35:37 AM PST.