Homepage of Apoorva Khare
|Research Associate (joint in Mathematics
Littlefield Center, Room 334
390 Serra Mall,
Stanford, CA - 94305
|khare AT university-name DOT edu
University of Chicago; Advisor: Victor Ginzburg
- Mathematics in the Real World, with Anna Lachowska,
forthcoming from Yale University Press, 2015. 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.
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.
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.
symplectic oscillator algebras of rank one, joint with Wee
Liang Gan; Journal
of Algebra Volume 310 No. 2 (April 2007), pages
- 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
- Center and
representations of infinitesimal Hecke algebras of sl_2,
joint with Akaki Tikaradze, Communications
in Algebra Volume 38 No. 2 (February 2010), pages
- 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),
- Faces of polytopes
and Koszul algebras, joint with Vyjayanthi Chari and Tim
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
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,
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.
- Preserving positivity for rank-constrained
matrices, joint with Dominique Guillot and Bala Rajaratnam;
- On fractional Hadamard powers of
positive block matrices, joint with Dominique Guillot and
Bala Rajaratnam; preprint, math.FA/1404.6839.
- 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.
- Complete characterization of
Hadamard powers preserving Loewner positivity, monotonicity, and
convexity, joint with Dominique Guillot and Bala
Rajaratnam; preprint, math.FA/1311.1581.
- Differential calculus on graphon
space, joint with Peter Diao, Dominique Guillot, and Bala
Rajaratnam; preprint, math.CO/1403.3736.
- Standard parabolic subsets of
highest weight modules; preprint, math.RT/1409.4133.
- Faces and maximizer subsets of highest
weight modules; preprint, math.RT/1301.1140.
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
preprint, math.RT/0811.2080 (under revision).
- The covering problem for Chinese
preprint, math.AC/0906.1023 (under revision).
- Drinfeld-Hecke algebras over cocommutative
preprint, math.RA/0705.2067 (under revision).
- My research at Stanford has been supported by a DARPA grant
(DARPA YFA N66001-11-1-4131).
- AMS Special Session on Positivity and Matrix
Inequalities, AMS-MAA 2015 Joint Mathematics Meetings
(San Antonio), January 13, 2015. Co-organizing with Dominique
Guillot and Bala Rajaratnam (Stanford).
- AMS Special Session on Limits of Discrete
Structures, AMS-MAA 2015 Joint Mathematics Meetings (San
Antonio), January 12, 2015. Co-organizing with Peter Diao,
Dominique Guillot, and Bala Rajaratnam (Stanford).
- 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
- 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
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
This page was last modified on Sat Oct 04 2014, 04:44:20 PM PDT.