Homepage of Apoorva Khare

Contact information


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

Recent talks (with links to abstracts)

[2015 Talks]     [2014 Talks]     [2013 Talks]    

Books; invited chapters/monographs

1 Yale University Press Beautiful, Simple, Exact, Crazy: Mathematics in the Real World (480 pp., with Anna Lachowska)
Yale University Press, 2015.
  • The book title is inspired from a talk by Israel Moiseevich Gelfand.
  • The course which I developed and taught in Spring 2011 at Yale, and which led to the book.
  • The announcements from Yale Mathematics and from Yale University.
2 Entry on the BGG Category $\mathcal{O}$, for the Encyclopedia of Mathematics (Michiel Hazewinkel, Editor), Kluwer Academic Publishers, 2005.

Publications by research interests; or list (PDF)

Papers in representation theory and algebra

arXiv Advances in Mathematics Matrix positivity preservers in fixed dimension. I (with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Advances in Mathematics 298, pages 325–368, 2016.
arXiv FPSAC 2016 Schur polynomials and matrix positivity preservers (with Alexander Belton, Dominique Guillot, and Mihai Putinar)
(Extended abstract of preceding paper above)
28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC),
DMTCS Proceedings BC, pages 155–166, 2016.
Poster
(Poster)
arXiv Final version Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property
AMS Contemporary Mathematics (Proceedings of International Conference for Passman), in press, 2016.
arXiv Transactions of the AMS Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society, published online, 2016.
arXiv Journal of Algebra Faces and maximizer subsets of highest weight modules
Journal of Algebra 455, pages 32–76, 2016.
(Here is an older, related announcement of some of the results.)
arXiv Journal of Algebra On Category $\mathcal{O}$ over triangular generalized Weyl algebras (with Akaki Tikaradze)
Journal of Algebra 449, pages 687–729, 2016.
Final version Comptes Rendus Mathematique Matrix positivity preservers in fixed dimension (with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Comptes Rendus Mathematique de l'Académie des Sciences 354 no. 2, pages 143–148, 2016.
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, pages 85–129, 2013.
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, pages 1611–1625, 2012.
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, pages 593–611, 2012.
arXiv Axioms The sum of a finite group of weights of a Hopf algebra
Axioms 1 no. 3, pages 259–290, 2012.
(Special issue on: "Hopf Algebras, Quantum Groups and Yang-Baxter Equations")
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, pages 377–392, 2012.
arXiv Communications in
Algebra Center and representations of infinitesimal Hecke algebras of $\mathfrak{sl}_2$ (with Akaki Tikaradze)
Communications in Algebra 38 no. 2, pages 405–439, 2010.
arXiv Communications in
Algebra Functoriality of the BGG Category $\mathcal{O}$
Communications in Algebra 37 no. 12, pages 4431–4475, 2009.
arXiv Linear Algebra and its
Applications Vector spaces as unions of proper subspaces
Linear Algebra and its Applications 431 no. 9, pages 1681–1686, 2009.
arXiv Journal of Algebra Quantized symplectic oscillator algebras of rank one (with Wee Liang Gan)
Journal of Algebra 310 no. 2, pages 671–707, 2007.
arXiv JPANTA Divisibility tests and recurring decimals in Euclidean domains (final section with Pieter Moree)
JP Journal of Algebra, Number Theory, and Applications (JPANTA) 7 no. 1, pages 1–32, 2007.
Thesis Category $\mathcal{O}$ over the symplectic oscillator algebra
Ph.D. Thesis, University of Chicago, 2006.
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, pages 131–166, 2005; erratum.
FUEJUM Divisibility tests
Furman University Electronic Journal of Undergraduate Mathematics (FUEJUM) 3, pages 1–5, 1997.
arXiv Preprint Highest weight modules to first order (with Gurbir Dhillon)
Preprint, 2016.
arXiv Preprint A Carlitz–von Staudt type theorem for finite rings (with Akaki Tikaradze)
Preprint, 2016.
arXiv Preprint On the classification of finite-dimensional nil-Coxeter algebras over complex reflection groups
Preprint, 2016.
arXiv Preprint Axiomatic framework for the BGG Category $\mathcal{O}$
Preprint, 2015 (significant additions and major revisions to an earlier version).

Papers in analysis: positivity, combinatorics, and probability

Preprint The Hoffmann-Jørgensen inequality in metric semigroups (with Bala Rajaratnam)
Annals of Probability, under minor revision, 2016.
arXiv Transactions of the AMS Preserving positivity for rank-constrained matrices (with Dominique Guillot and Bala Rajaratnam)
Transactions of the American Mathematical Society, available online, 2016.
arXiv Transactions of the AMS Preserving positivity for matrices with sparsity constraints (with Dominique Guillot and Bala Rajaratnam)
Transactions of the American Mathematical Society, published online, 2016.
arXiv Journal of Combinatorial
Theory Series A Critical exponents of graphs (with Dominique Guillot and Bala Rajaratnam)
Journal of Combinatorial Theory, Series A 139, pages 30–58, 2016.
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, pages 183–227, 2015.
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, pages 489–507, 2015.
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, pages 2422–2427, 2013.
arXiv Preprint Model-free consistency of graph partitioning (with Peter Diao, Dominique Guillot, and Bala Rajaratnam)
Preprint, 2016.
arXiv Preprint Probability inequalities and tail estimates for metric semigroups (with Bala Rajaratnam)
Preprint (under revision), 2015.
arXiv Preprint Integration and measures on the space of countable labelled graphs (with Bala Rajaratnam)
Preprint, 2015.
arXiv Preprint Differential calculus on the space of countable labelled graphs (with Bala Rajaratnam)
Preprint, 2014.
arXiv Preprint On fractional Hadamard powers of positive block matrices (with Dominique Guillot and Bala Rajaratnam)
Preprint, 2014.

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