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 (with links to abstracts)

[Upcoming]    
[2015]     [2014]    

Books; invited chapters/monographs in books

1 Yale University Press Beautiful, Simple, Exact, Crazy: Mathematics in the Real World (480 pp., with Anna Lachowska)
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. (The book title is inspired from a talk by Israel Moiseevich Gelfand.)
2 Entry on the BGG Category O, for the Encyclopedia of Mathematics (Michiel Hazewinkel, Editor), Kluwer Academic Publishers.

Publications

Papers in analysis: positivity and graph limits

29 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.
28 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 (2015), pages 183-227.
27 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 (2015), pages 489-507.
26 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 (2013), pages 2422-2427.
25 arXiv Preprint Probability inequalities and tail estimates for metric semigroups (with Bala Rajaratnam)
Preprint, 2015.
24 arXiv Preprint Integration and measures on the space of countable labelled graphs (with Bala Rajaratnam)
Preprint, 2015.
23 arXiv Preprint Schoenberg's positivity theorem in fixed dimension (with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Preprint, 2015.
22 arXiv Preprint Critical exponents of graphs (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2015.
21 arXiv Preprint Differential calculus on the space of countable labelled graphs (with Bala Rajaratnam)
Preprint, 2014.
20 arXiv Preprint Preserving positivity for rank-constrained matrices (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2014.
19 arXiv Preprint On fractional Hadamard powers of positive block matrices (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2014.

Papers in representation theory and algebra

18 arXiv Transactions of the AMS Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society, in press.
17 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.
16 arXiv Journal of Pure and Applied
Algebra Faces of polytopes and Koszul algebras (with Vyjayanthi Chari and Tim Ridenour)
Journal of Pure and Applied Algebra 216 No. 7 (2012), pages 1611-1625.
15 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 (2012), pages 593-611.
14 arXiv Axioms The sum of a finite group of weights of a Hopf algebra
Axioms 1 No. 3 (2012), pages 259-290 (Special issue on: "Hopf Algebras, Quantum Groups and Yang-Baxter Equations").
13 arXiv Pramana Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order (with Avinash Khare and Avadh Saxena)
Pramana 79 No. 3 (2012), pages 377-392.
12 arXiv Communications in
Algebra Center and representations of infinitesimal Hecke algebras of $\mathfrak{sl}_2$ (with Akaki Tikaradze)
Communications in Algebra 38 No. 2 (2010), pages 405-439.
11 arXiv Communications in
Algebra Functoriality of the BGG Category $\mathcal{O}$
Communications in Algebra 37 No. 12 (2009), pages 4431-4475.
10 arXiv Linear Algebra and its
Applications Vector spaces as unions of proper subspaces
Linear Algebra and its Applications 431 No. 9 (2009), pages 1681-1686.
  9 arXiv Journal of Algebra Quantized symplectic oscillator algebras of rank one (with Wee Liang Gan)
Journal of Algebra 310 No. 2 (2007), pages 671-707.
  8 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 (2007), pages 1-32.
  7 arXiv Journal of Pure and Applied
Algebra Category $\mathcal{O}$ over a deformation of the symplectic oscillator algebra
Journal of Pure and Applied Algebra 195 No. 2 (2005), pages 131-166; erratum.
  6 FUEJUM Divisibility tests
Furman University Electronic Journal of Undergraduate Mathematics (FUEJUM) 3 (1997), pages 1-5.
  5 arXiv Preprint On Category $\mathcal{O}$ over triangular Generalized Weyl Algebras (with Akaki Tikaradze)
Preprint, 2015.
  4 arXiv Preprint Axiomatic framework for the BGG Category $\mathcal{O}$
Preprint, 2015 (updated with major revisions from an earlier version).
  3 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.
  2 arXiv Preprint The covering problem for Chinese rings
Preprint (under revision), 2009.
  1 arXiv Preprint Drinfeld-Hecke algebras over cocommutative algebras
Preprint (under revision), 2007.

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This page was last modified on Wed Aug 26 2015, 10:48:53 AM PDT.