Contact information

Affiliation Indian Institute of
	  Science   Assistant Professor in Mathematics, Indian Institute of Science
and
Analysis and Probability Research Group (APRG): Member
                                Apoorva Khare
Office Room R23, Mathematics department
 
Postal address    
Department of Mathematics
Indian Insitute of Science
Bangalore – 560012, INDIA
Phone +91–80–2293–3214     (Fax +91–80–2360–0146)
Email khare@iisc.ac.qin (no quantum)
Ph.D.   University of
	  Chicago University of Chicago
Previous
affiliation
Stanford
	  University Research Associate in Mathematics and Statistics,
Stanford University

Selected international conference talks

Selected publications – positivity (and analysis, combinatorics, Schur polynomials)

  1. (With Alexander Belton, Dominique Guillot, Mihai Putinar.)   Matrix positivity preservers in fixed dimension. I, Advances in Mathematics 298,
    pages 325–368, 2016.   [arXiv]
  2. (With Dominique Guillot, Bala Rajaratnam.)   Preserving positivity for rank-constrained matrices, Transactions of the AMS 369 no. 9,
    pages 6105–6145, 2017.   [arXiv]
  3. (With Dominique Guillot, Bala Rajaratnam.)   Preserving positivity for matrices with sparsity constraints, Transactions of the AMS 368 no. 12,
    pages 8929–8953, 2016.   [arXiv]
  4. (With Dominique Guillot, Bala Rajaratnam.)   Critical exponents of graphs, Journal of Combinatorial Theory Series A 139, pages 30–58, 2016.   [arXiv]
  5. (With Alexander Belton, Dominique Guillot, Mihai Putinar.)   Moment-sequence transforms, preprint.   [arXiv]
  6. (With Terence Tao.)   On the sign patterns of entrywise positivity preservers in fixed dimension, preprint.   [arXiv]

Selected publications – representation theory

  1. (With Gurbir Dhillon.)   Faces of highest weight modules and the universal Weyl polyhedron, Advances in Mathematics, accepted, 2017.   [arXiv]
  2. Standard parabolic subsets of highest weight modules, Transactions of the AMS 369 no. 4, pages 2363–2394, 2017.   [arXiv]
  3. Faces and maximizer subsets of highest weight modules, Journal of Algebra 455, pages 32–76, 2016.   [arXiv]
  4. (With Akaki Tikaradze.)   On Category $\mathcal{O}$ over triangular generalized Weyl algebras, Journal of Algebra 449, pages 687–729, 2016.   [arXiv]
    Summary: Blocks of $\mathcal{O}$ categorify Young tableaux.
  5. Invited survey article: Representations of complex semi-simple Lie groups and Lie algebras, in Connected at Infinity II: A Selection of Mathematics by Indians (R. Bhatia, C.S. Rajan, and A.I. Singh, Eds.), pages 85–129, Texts and Readings in Mathematics (TRIM), Hindustan Book Agency, 2013.   [arXiv]
  6. (With Wee Liang Gan.)   Quantized symplectic oscillator algebras of rank one, Journal of Algebra 310 no. 2, pages 671–707, 2007.   [arXiv]
  7. (With Gurbir Dhillon.)   Characters of highest weight modules and integrability, preprint.   [arXiv]

Selected publications – other (book, probability, graphons)

  1. (With Anna Lachowska.)   Beautiful, Simple, Exact, Crazy: Mathematics in the Real World (480 pp., book), Yale University Press, 2015.
  2. (With Bala Rajaratnam.)   The Hoffmann-Jørgensen inequality in metric semigroups, Annals of Probability, in press, 2017.   [arXiv]
  3. (With Peter Diao, Dominique Guillot, Bala Rajaratnam.)   Differential calculus on graphon space, Journal of Combinatorial Theory Series A 133,
    pages 183–227, 2015.   [arXiv]