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)

[2017 Talks]    
[2016 Talks]     [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 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.

Publications by research interests; or list (PDF)

Representation theory Analysis: positivity, probability, graph limits
Combinatorics and discrete mathematics

Analysis: positivity, probability, graph limits     Back to top

(shares six papers with "Combinatorics and discrete mathematics" section)

arXiv Annals of Probability The Hoffmann-Jørgensen inequality in metric semigroups (with Bala Rajaratnam)
Annals of Probability, in press, 2017.
arXiv Transactions of the AMS Preserving positivity for rank-constrained matrices (with Dominique Guillot and Bala Rajaratnam)
Transactions of the American Mathematical Society, published online, 2017.
FPSAC 2017 The critical exponent: a novel graph invariant (with Dominique Guillot and Bala Rajaratnam)
(Extended abstract of following paper below)
29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC '17),
Séminaire Lotharingien de Combinatoire, in press, 2017.
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 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 '16),
DMTCS Proceedings BC, pages 155–166, 2016.
Poster
(Poster)
arXiv Transactions of the AMS Preserving positivity for matrices with sparsity constraints (with Dominique Guillot and Bala Rajaratnam)
Transactions of the American Mathematical Society 368 no. 12, pages 8929–8953, 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 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 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 Preprint Moment-sequence transforms (with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Preprint, 2016.
arXiv Preprint The Khinchin–Kahane inequality and Banach space embeddings for metric groups (with Bala Rajaratnam)
Preprint, 2016.
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, 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.

Combinatorics and discrete mathematics (and connections to algebra, geometry, analysis)     Back to top

FPSAC 2017 The Weyl–Kac weight formula (with Gurbir Dhillon)
(Extended abstract of the paper "Characters of highest weight modules and integrability")
Talk at 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC '17);
Séminaire Lotharingien de Combinatoire, in press, 2017.
arXiv Transactions of the AMS Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society 369 no. 4, pages 2363–2394, 2017.
arXiv Final version Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property
AMS Contemporary Mathematics 688, pages 139–168, 2017.
FPSAC 2017 The critical exponent: a novel graph invariant (with Dominique Guillot and Bala Rajaratnam)
(Extended abstract of following paper below)
29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC '17),
Séminaire Lotharingien de Combinatoire, in press, 2017.
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 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 '16),
DMTCS Proceedings BC, pages 155–166, 2016.
Poster
(Poster)
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 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 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 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 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.
FUEJUM Divisibility tests
Furman University Electronic Journal of Undergraduate Mathematics (FUEJUM) 3, pages 1–5, 1997.
arXiv Preprint Faces of highest weight modules and the universal Weyl polyhedron (with Gurbir Dhillon)
Preprint, 2016.
arXiv Preprint A Carlitz–von Staudt type theorem for finite rings (with Akaki Tikaradze)
Preprint, 2016.
arXiv Preprint Generalized nil-Coxeter algebras over discrete complex reflection groups
Preprint, 2016.

Representation theory     Back to top

(shares four papers with "Combinatorics and discrete mathematics" section)

FPSAC 2017 The Weyl–Kac weight formula (with Gurbir Dhillon)
(Extended abstract of the paper "Characters of highest weight modules and integrability")
Talk at 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC '17),
Séminaire Lotharingien de Combinatoire, in press, 2017.
arXiv Transactions of the AMS Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society 369 no. 4, pages 2363–2394, 2017.
arXiv Journal of Algebra Faces and maximizer subsets of highest weight modules
Journal of Algebra 455, pages 32–76, 2016.
arXiv Journal of Algebra On Category $\mathcal{O}$ over triangular generalized Weyl algebras (with Akaki Tikaradze)
Journal of Algebra 449, pages 687–729, 2016.
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 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 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 Journal of Algebra Quantized symplectic oscillator algebras of rank one (with Wee Liang Gan)
Journal of Algebra 310 no. 2, pages 671–707, 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.
arXiv Preprint Faces of highest weight modules and the universal Weyl polyhedron (with Gurbir Dhillon)
Preprint, 2016.
arXiv Preprint Characters of highest weight modules and integrability (with Gurbir Dhillon)
Preprint, 2016.
arXiv Preprint Axiomatic framework for the BGG Category $\mathcal{O}$
Preprint, 2015.

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