Contact information

Affiliation Indian Institute of
	  Science   Assistant Professor in Mathematics, Indian Institute of Science
Analysis and Probability Research Group (APRG): Member;
currently also
Ramanujan Fellow of SERB
                                Apoorva Khare
                    CVs:   [Abridged]   |   [Detailed]
Office Room X-26 (top floor, X-wing), Mathematics department
Postal address    
Department of Mathematics
Indian Institute of Science
Bangalore – 560012, INDIA
Phone +91–80–2293–2514         (Fax +91–80–2360–0146)
Email (no quantum)
Ph.D.   University of
	  Chicago University of Chicago (Department of Mathematics)
	  University Research Associate in Mathematics and Statistics,
Stanford University

Selected international conference talks

Papers: Combinatorics, algebra, FPSAC; also Analysis (positivity, Schur polynomials, probability); also Representation theory.

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

  1. Matrix analysis and positivity preservers (PDF, 140+ pp.)
    Lecture notes from a topics graduate course (or for advanced undergraduates) taught in Spring 2018.
  2. (With Alexander Belton, Dominique Guillot, Mihai Putinar.)   A panorama of positivity, survey article (83 pages)   [arXiv] – split for publication:
  3. (With Alexander Belton, Dominique Guillot, Mihai Putinar.)   Matrix positivity preservers in fixed dimension. I, Advances in Mathematics 298,
    pages 325–368, 2016.   [arXiv]
  4. (With Dominique Guillot, Bala Rajaratnam.)   Preserving positivity for rank-constrained matrices, Transactions of the AMS 369 no. 9,
    pages 6105–6145, 2017.   [arXiv]
  5. (With Dominique Guillot, Bala Rajaratnam.)   Preserving positivity for matrices with sparsity constraints, Transactions of the AMS 368 no. 12,
    pages 8929–8953, 2016.   [arXiv]
  6. (With Dominique Guillot, Bala Rajaratnam.)   Critical exponents of graphs, Journal of Combinatorial Theory Series A 139, pages 30–58, 2016.   [arXiv]
  7. (With Alexander Belton, Dominique Guillot, Mihai Putinar.)   Moment-sequence transforms, preprint.   [arXiv]
  8. (With Alexander Belton, Dominique Guillot, Mihai Putinar.)   Total-positivity preservers, preprint.   [arXiv]
  9. (With Terence Tao.)   On the sign patterns of entrywise positivity preservers in fixed dimension, preprint.   [arXiv]

Selected publications – representation theory; algebraic combinatorics

  1. (With Carolina Benedetti, Rafael S. González D'León, Christopher R. H. Hanusa, Pamela E. Harris, Alejandro H. Morales, Martha Yip.)  
    A combinatorial model for computing volumes of flow polytopes, Transactions of the AMS 372 no. 5, pages 3369–3404, 2019.   [arXiv]
  2. Generalized nil-Coxeter algebras over discrete complex reflection groups, Transactions of the AMS 370 no. 4, pages 2971–2999, 2018.   [arXiv]
  3. (With Gurbir Dhillon.)   Faces of highest weight modules and the universal Weyl polyhedron, Advances in Mathematics 319, pages 111–152, 2017.   [arXiv]
  4. Standard parabolic subsets of highest weight modules, Transactions of the AMS 369 no. 4, pages 2363–2394, 2017.   [arXiv]
  5. Faces and maximizer subsets of highest weight modules, Journal of Algebra 455, pages 32–76, 2016.   [arXiv]
  6. (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.
  7. 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]
  8. (With Wee Liang Gan.)   Quantized symplectic oscillator algebras of rank one, Journal of Algebra 310 no. 2, pages 671–707, 2007.   [arXiv]
  9. (With Gurbir Dhillon.)   Characters of highest weight modules and integrability, preprint.   [arXiv]
  10. (With Projesh Nath Choudhury.)   Distance matrices of a tree: two more invariants, and in a unified framework, preprint.   [arXiv]

Selected publications – other (book, probability, graphons, Polymath(geometric group theory))

  1. (With Anna Lachowska.)   Beautiful, Simple, Exact, Crazy: Mathematics in the Real World (480 pp., book), Yale University Press, 2015.
  2. As D.H.J. Polymath (With Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, Terence Tao.)   Polymath14: Homogeneous length functions on groups, Algebra & Number Theory 12 no. 7, pages 1773–1786, 2018.   [arXiv]     [Blogpost 1]     [Polymath14 wiki]
  3. (With Bala Rajaratnam.)   The Hoffmann-Jørgensen inequality in metric semigroups, Annals of Probability 45 no. 6A, pages 4101–4111, 2017.   [arXiv]
  4. (With Peter Diao, Dominique Guillot, Bala Rajaratnam.)   Differential calculus on graphon space, Journal of Combinatorial Theory Series A 133,
    pages 183–227, 2015.   [arXiv]

Support (selected)

SERB, India Indian
Institute of Science International Centre for Mathematical Sciences
(SERB, Govt. of India) (IISc, Bangalore, India) (ICMS, Edinburgh, UK)
Foundation Tata
Trusts International Linear Algebra Society
(Infosys Foundation, India) (Tata Trusts, India) (ILAS, USA)
Taylor & Francis DARPA American Institute of
Mathematics National Science Foundation
(Taylor & Francis, USA) (DARPA, USA) (AIM and NSF, USA)