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. Beautiful, Simple, Exact, Crazy: 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.

Publications

Papers in analysis: positivity and graph limits

25 arXiv Transactions of the AMS Preserving positivity for matrices with sparsity constraints (with Dominique Guillot and Bala Rajaratnam)
Transactions of the American Mathematical Society, in press.
24 arXiv Journal of Combinatorial
Theory Series A Differential calculus on graphon space (with Peter Diao, Dominique Guillot, and Bala Rajaratnam)
Journal of Combinatorial Theory, Series A 133 (July 2015), pages 183-227.
23 arXiv Journal of Mathematical
Analysis and Applications Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity (with Dominique Guillot and Bala Rajaratnam)
Journal of Mathematical Analysis and Applications 425 No. 1 (May 2015), pages 489-507.
22 arXiv Linear Algebra and its
Applications The critical exponent conjecture for powers of doubly nonnegative matrices (with Dominique Guillot and Bala Rajaratnam)
Linear Algebra and its Applications 439 No. 8 (October 2013), pages 2422-2427.
21 arXiv Preprint Critical exponents of graphs (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2015.
20 arXiv Preprint Differential calculus on the space of countable labelled graphs (with Bala Rajaratnam)
Preprint, 2014.
19 arXiv Preprint Preserving positivity for rank-constrained matrices (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2014.
18 arXiv Preprint On fractional Hadamard powers of positive block matrices (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2014.

Papers in representation theory

17 arXiv Transactions of the AMS Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society, in press.
16 arXiv TRIM Representations of complex semi-simple Lie groups and Lie algebras
Connected at Infinity II: A Selection of Mathematics by Indians (R. Bhatia, C.S. Rajan, and A.I. Singh, Eds.),
Texts and Readings in Mathematics (TRIM), Hindustan Book Agency (2013), pages 85-129.
15 arXiv TRIM Faces of polytopes and Koszul algebras (with Vyjayanthi Chari and Tim Ridenour)
Journal of Pure and Applied Algebra 216 No. 7 (July 2012), pages 1611-1625.
14 arXiv Algebras and
Representation Theory Faces of weight polytopes and a generalization of a theorem of Vinberg (with Tim Ridenour)
Algebras and Representation Theory 15 No. 3 (June 2012), pages 593-611.
13 arXiv Communications in
Algebra Center and representations of infinitesimal Hecke algebras of sl_2 (with Akaki Tikaradze)
Communications in Algebra 38 No. 2 (February 2010), pages 405-439.
12 arXiv Communications in
Algebra Functoriality of the BGG Category O
Communications in Algebra 37 No. 12 (December 2009), pages 4431-4475.
11 arXiv Journal of Algebra Quantized symplectic oscillator algebras of rank one (with Wee Liang Gan)
Journal of Algebra 310 No. 2 (April 2007), pages 671-707.
10 arXiv Journal of Pure and Applied
Algebra Category O over a deformation of the symplectic oscillator algebra
Journal of Pure and Applied Algebra 195 No. 2 (January 2005), pages 131-166; erratum.
  9 arXiv Preprint Axiomatic framework for the BGG Category O
Preprint, 2015 (updated with major revisions from an earlier version).
  8 arXiv Preprint Faces and maximizer subsets of highest weight modules
Preprint, 2013.
Here is a related announcement, which computes 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.

Papers: other

  7 arXiv Axioms 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").
  6 arXiv Axioms Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order (with Avinash Khare and Avadh Saxena)
Pramana 79 No. 3 (September 2012), pages 377-392.
  5 arXiv Linear Algebra and its
Applications Vector spaces as unions of proper subspaces
Linear Algebra and its Applications 431 No. 9 (October 2009), pages 1681-1686.
  4 arXiv JPANTA Divisibility tests and recurring decimals in Euclidean domains (final section with Peter Moree)
JP Journal of Algebra, Number Theory, and Applications (JPANTA) 7 No. 1 (February 2007), pages 1-32.
  3 FUEJUM Divisibility tests
Furman University Electronic Journal of Undergraduate Mathematics (FUEJUM) 3 (1997), pages 1-5.
  2 arXiv Preprint The covering problem for Chinese rings
Preprint (under revision).
  1 arXiv Preprint Drinfeld-Hecke algebras over cocommutative algebras
Preprint (under revision).

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Conference Organization




This page was last modified on Thu Apr 16 2015, 06:04:34 PM PDT.