Affiliation |
Research Associate (joint in Mathematics and Statistics), Stanford University |

Address |
Sequoia Hall, 390 Serra Mall, Stanford, CA - 94305 |

Office |
Sequoia 234 |

Phone |
650-723-2957 (Office) |

Fax |
650-725-8977 (Office) |

Email |
khare AT university-name DOT edu |

Ph.D. |
University of Chicago; Advisor: Victor Ginzburg |

Curriculum vitae |

*Mathematics in the Real World*, with Anna Lachowska, forthcoming from Yale University Press, 2014. See here for more information on the course which led to the book.- Entry on the BGG
Category O, for the
*Encyclopedia of Mathematics*(Michiel Hazewinkel, Editor), Kluwer Academic Publishers, 2005.

*Divisibility Tests*, Furman University Electronic Journal of Undergraduate Mathematics FUEJUM Volume**3**(1997), pages 1-5.*Category O over a deformation of the symplectic oscillator algebra*, Journal of Pure and Applied Algebra, Volume**195**No. 2 (January 2005), pages 131-166;*erratum*.*Category O over the symplectic oscillator algebra*, Ph.D. Thesis, University of Chicago, June 2006.*Divisibility tests and recurring decimals in Euclidean domains*(final section with Pieter Moree), JP Journal of Algebra, Number Theory, and Applications (JPANTA), Volume**7**No. 1 (February 2007), pages 1-32.*Quantized symplectic oscillator algebras of rank one*, joint with Wee Liang Gan; Journal of Algebra Volume**310**No. 2 (April 2007), pages 671-707.*Vector spaces as unions of proper subspaces*, Linear Algebra and its Applications Volume**431**No. 9 (1 October 2009), pages 1681--1686.*Functoriality of the BGG Category O*, Communications in Algebra Volume**37**No. 12 (December 2009), pages 4431-4475.*Center and representations of infinitesimal Hecke algebras of sl_2*, joint with Akaki Tikaradze, Communications in Algebra Volume**38**No. 2 (February 2010), pages 405-439.*Faces of weight polytopes and a generalization of a theorem of Vinberg*, joint with Tim Ridenour, Algebras and Representation Theory Volume**15**No. 3 (June 2012), pages 593-611.*Faces of polytopes and Koszul algebras*, joint with Vyjayanthi Chari and Tim Ridenour, Journal of Pure and Applied Algebra Volume**216**No. 7 (July 2012), pages 1611-1625.*Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order*, joint with Avinash Khare and Avadh Saxena, Pramana Volume**79**No. 3 (September 2012), pages 377-392.*The sum of a finite group of weights of a Hopf algebra*, Axioms**1**No. 3 (October 2012), pages 259-290 (Special issue on: "Hopf Algebras, Quantum Groups and Yang-Baxter Equations").*Representations of complex semi-simple Lie groups and Lie algebras*, in Connected at Infinity II: On the work of Indian mathematicians (R. Bhatia and C.S. Rajan, Eds.), Texts and Readings in Mathematics (TRIM), Hindustan Book Agency (2013), pages 85-129. Here is the PDF.*The critical exponent conjecture for powers of doubly nonnegative matrices*, joint with Dominique Guillot and Bala Rajaratnam, in Linear Algebra and its Applications Volume**439**No. 8 (October 2013), pages 2422-2427.

*Preserving positivity for matrices with sparsity constraints*, joint with Dominique Guillot and Bala Rajaratnam; preprint,`math.FA/1406.3408`(submitted).*Preserving positivity for rank-constrained matrices*, joint with Dominique Guillot and Bala Rajaratnam; preprint,`math.FA/1406.0042`(submitted).*On fractional Hadamard powers of positive block matrices*, joint with Dominique Guillot and Bala Rajaratnam; preprint,`math.FA/1404.6839`(submitted).*Differential calculus on graphon space*, joint with Peter Diao, Dominique Guillot, and Bala Rajaratnam; preprint,`math.CO/1403.3736`(submitted).*Loewner positive entrywise functions, and classification of measurable solutions of Cauchy's functional equations*, joint with Dominique Guillot and Bala Rajaratnam; preprint,`math.FA/1312.6297`(submitted).*Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity*, joint with Dominique Guillot and Bala Rajaratnam; preprint,`math.FA/1311.1581`(submitted).*Faces and maximizer subsets of highest weight modules*; preprint,`math.RT/1301.1140`(submitted).

Here is a related announcement, where I compute 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`.*Axiomatic framework for the BGG Category O*; preprint,`math.RT/0811.2080`(under revision).*The covering problem for Chinese rings*; preprint,`math.AC/0906.1023`(under revision).*Drinfeld-Hecke algebras over cocommutative algebras*; preprint,`math.RA/0705.2067`(under revision).

- My research at Stanford has been supported by a DARPA grant (DARPA YFA N66001-11-1-4131).

- Positivity, graphical models, and modeling of complex multivariate dependencies, American Institute of Mathematics (Palo Alto), October 13-17, 2014. Co-organizing with Dominique Guillot and Bala Rajaratnam (Stanford) and Helene Massam (York).
- Lie Theory Workshop on Quantum Groups, Stanford University, February 1-2, 2014. Co-organized with Daniel Bump and Persi Diaconis (Stanford).
- Young Researchers Meet (Mathematics and Computer Science), Stanford University, May 26-27, 2012. Co-organized with Govindan Rangarajan (Indian Institute of Science, India).
- Lie Theory Workshop on Quantum Groups, Stanford University, February 4-5, 2012. Co-organized with Daniel Bump (Stanford) and Anne Schilling (UC Davis).

More methods of lion-hunting that are accessible to graduate students. This is joint with Jayadev Athreya (University of Illinois, Urbana-Champaign).

This page was last modified on Tue Sep 09 2014, 04:10:40 PM PDT.