1  Matrix analysis and entrywise positivity preservers (Book),
2022. Vol. 471 in London Mathematical Society Lecture Note Series, Cambridge University Press, xxii+292 pp. and Vol. 82 in Texts and Readings In Mathematics (TRIM Series), Hindustan Book Agency, xxii+339 pp. 
(CUP book cover) (TRIM book cover) 

2  A panorama of positivity (83 pp., with Alexander Belton,
Dominique Guillot, and Mihai Putinar) Survey article, 2018 – split into two parts for publication: 

Part 1: Dimension free – in
Analysis of Operators on Function Spaces (the Serguei Shimorin
Memorial Volume) A. Aleman, H. Hedenmalm, D. Khavinson, M. Putinar, Eds., pages 117–165, Trends in Mathematics, Birkhauser, 2019. 

Part 2: Fixed dimension – in
Complex Analysis and Spectral Theory (in honor of Thomas
Ransford) Proceedings of the CRM Workshop held at Laval University, QC, May 21–25, 2018; G. Dales, D. Khavinson, J. Mashreghi, Eds. CRM Proceedings, AMS Contemporary Mathematics 743, pages 109–150, 2020. 

3  Matrix analysis, Pólya frequency functions, and preservers
of (total) positivity
(PDF, 320+ pp.) Expanded lecture notes from a topics graduate course (or for advanced undergraduates) taught in Spring 2018 and Autumn 2019. 

4  Beautiful, Simple, Exact, Crazy: Mathematics in the Real World
(Book, 480 pp., with Anna Lachowska)
Yale University Press, 2015.


5  Invited survey article: Representations of complex semisimple 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.), Texts and Readings in Mathematics (TRIM), Hindustan Book Agency, pages 85–129, 2013. 
Representation theory  Combinatorics, discrete mathematics, and algebra 
(including FPSAC extended abstracts)  
Analysis: positivity, Schur polynomials, probability, graph limits 
Totally positive kernels, Pólya frequency functions, and
their transforms
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Journal d'Analyse Mathématique, in press. 

The pnorm of circulant matrices
(with Ludovick Bouthat, Javad Mashreghi, and Frédéric
MorneauGuérin) Linear and Multilinear Algebra, in press. 

Momentsequence transforms
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Journal of the European Mathematical Society 24 no. 9, pages 3109–3160, 2022. 

Matrix compression along isogenic blocks
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Acta Scientiarum Mathematicarum (Szeged) 88 nos. 1–2, 100th anniversary special issue, pages 417–448, 2022. 

Smooth entrywise positivity preservers, a Horn–Loewner
master theorem, and symmetric function identities
Transactions of the American Mathematical Society 375 no. 3, pages 2217–2236, 2022. 

Blowup polynomials and deltamatroids of graphs
(with Projesh Nath Choudhury) (Extended abstract of the paper The blowuppolynomial of a metric space: connections to stable polynomials, graphs and their distance spectra) Talk at 34th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2022), Séminaire Lotharingien de Combinatoire 86B, Article #42, 2022. 

Hirschman–Widder densities
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Applied and Computational Harmonic Analysis 60, pages 396–425, 2022. 

Preservers of totally positive kernels and Pólya frequency
functions
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Mathematics Research Reports 3, pages 35–56, 2022. [Joint announcement – via a unified, probabilitythemed narrative – of many results from the three works arXiv:2006.16213, arXiv:2008.05121, and arXiv:2101.02129.] 

On the sign patterns of entrywise positivity preservers in fixed
dimension
(with Terence Tao)
American Journal of Mathematics 143 no. 6, pages 1863–1929, 2021. 

Sharp nonzero lower bounds for the Schur product theorem
Proceedings of the American Mathematical Society 149 no. 12, pages 5049–5063, 2021. (Summary: Refines results by Schur in Crelle 1911 and Vybíral in Adv. Math. 2020, with an application to numerical integration.) 

Sign nonreversal property for totally nonnegative and totally
positive matrices, and testing total positivity of their interval
hull
(with Projesh Nath Choudhury and M. Rajesh Kannan) Bulletin of the London Mathematical Society 53 no. 4, pages 981–990, 2021. (Summary: Novel characterization of total positivity, using only sign nonreversal; novel test for total positivity of interval hull.) 

On an asymptotic characterisation of Griffiths semipositivity
(with Vamsi Pritham Pingali)
Bulletin des Sciences Mathématiques 167, article 102956 (7 pp.), 2021. 

Differential calculus on the space of countable labelled
graphs (with Bala Rajaratnam)
Advances in Operator Theory 6 no. 1, article 12 (28 pp.), 2021. 

Probability inequalities and tail estimates for metric
semigroups (with Bala Rajaratnam)
Advances in Operator Theory 5 no. 3, pages 779–795, 2020. (Special issue in honor of Rajendra Bhatia) 

Simultaneous kernels of matrix Hadamard powers
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Linear Algebra and its Applications 576, pages 142–157, 2019. 

Polymath14: Homogeneous length functions on groups (as D.H.J. Polymath, with Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, and Terence Tao) Algebra & Number Theory 12 no. 7, pages 1773–1786, 2018. [Blogpost 1] (Summary: Provides novel characterizations from analysis and geometry, of abelian, torsionfree groups.) 



The HoffmannJørgensen inequality in metric semigroups
(with Bala Rajaratnam)
Annals of Probability 45 no. 6A, pages 4101–4111, 2017. 

Preserving positivity for rankconstrained matrices
(with Dominique Guillot and Bala Rajaratnam)
Transactions of the American Mathematical Society 369 no. 9, pages 6105–6145, 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 2017), Séminaire Lotharingien de Combinatoire 78B, Article #62, 2017. 

Critical exponents of graphs
(with Dominique Guillot and Bala Rajaratnam)
Journal of Combinatorial Theory, Series A 139, pages 30–58, 2016. 

Matrix positivity preservers in fixed dimension. I
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Advances in Mathematics 298, pages 325–368, 2016. 

Schur polynomials and matrix positivity preservers
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)


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. 

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. 

Differential calculus on graphon space
(with Peter Diao, Dominique Guillot, and Bala Rajaratnam)
Journal of Combinatorial Theory, Series A 133, pages 183–227, 2015. 

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. 

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. 

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. 

The blowuppolynomial of a metric space: connections to stable
polynomials, graphs and their distance spectra
(with Projesh Nath Choudhury)
Preprint, 2021. 

Multivariate blowuppolynomials of graphs
(with Projesh Nath Choudhury)
Preprint, 2021. 

Multiply positive functions, critical exponent phenomena, and the
Jain–Karlin–Schoenberg kernel
Preprint, 2020. 

The noncompact normed space of norms on a finitedimensional
Banach space
Preprint, 2018. 

The Khinchin–Kahane inequality and Banach space embeddings
for metric groups (with Bala Rajaratnam)
Preprint, 2016. 

Modelfree consistency of graph partitioning
(with Peter Diao, Dominique Guillot, and Bala Rajaratnam)
Preprint, 2016. 

Integration and measures on the space of countable labelled
graphs (with Bala Rajaratnam)
Preprint, 2015. 

On fractional Hadamard powers of positive block matrices
(with Dominique Guillot and Bala Rajaratnam)
Preprint, 2014. 
Smooth entrywise positivity preservers, a Horn–Loewner
master theorem, and symmetric function identities
Transactions of the American Mathematical Society 375 no. 3, pages 2217–2236, 2022. 

Hirschman–Widder densities
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Applied and Computational Harmonic Analysis 60, pages 396–425, 2022. 

Covering modules by proper submodules (with Akaki Tikaradze)
Communications in Algebra 50 no. 2, pages 498–507, 2022. 

On the sign patterns of entrywise positivity preservers in fixed
dimension
(with Terence Tao)
American Journal of Mathematics 143 no. 6, pages 1863–1929, 2021. [FPSAC 2018 abstract] 

A combinatorial model for computing volumes of flow polytopes
(with Carolina Benedetti, Rafael S. González D'León,
Christopher R. H. Hanusa, Pamela E. Harris, Alejandro H. Morales, and
Martha Yip).
Transactions of the American Mathematical Society 372 no. 5, pages 3369–3404, 2019. [FPSAC 2018 abstract] 

A Carlitz–von Staudt type theorem for finite rings (with
Akaki Tikaradze)
Linear Algebra and its Applications 568, pages 106–126, 2019. 

Generalized nilCoxeter algebras over discrete complex reflection
groups
Transactions of the American Mathematical Society 370 no. 4, pages 2971–2999, 2018. [FPSAC 2018 abstract] 

Faces of highest weight modules and the universal Weyl
polyhedron (with Gurbir Dhillon)
Advances in Mathematics 319, pages 111–152, 2017. 

Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society 369 no. 4, pages 2363–2394, 2017; erratum. 

Generalized nilCoxeter algebras, cocommutative algebras, and the
PBW property
AMS Contemporary Mathematics 688, pages 139–168, 2017. (Proceedings of International Conference on Groups, Rings, Group Rings, and Hopf Algebras (in honor of Donald S. Passman)) 

Critical exponents of graphs
(with Dominique Guillot and Bala Rajaratnam)
Journal of Combinatorial Theory, Series A 139, pages 30–58, 2016. [FPSAC 2017 abstract] 

Matrix positivity preservers in fixed dimension. I
(with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Advances in Mathematics 298, pages 325–368, 2016. [FPSAC 2016 abstract] 

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. 

Differential calculus on graphon space
(with Peter Diao, Dominique Guillot, and Bala Rajaratnam)
Journal of Combinatorial Theory, Series A 133, pages 183–227, 2015. 

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. 

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 YangBaxter Equations") 

Vector spaces as unions of proper subspaces
Linear Algebra and its Applications 431 no. 9, pages 1681–1686, 2009. 

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. 

Divisibility tests
Furman University Electronic Journal of Undergraduate Mathematics (FUEJUM) 3, pages 1–5, 1997. 

From Cauchy's determinant formula to bosonic and fermionic
immanant identities
(with Siddhartha Sahi)
Preprint, 2022. 

The lattice of nilHecke algebras over real and complex reflection
groups (with Sutanay Bhattacharya)
Preprint, 2021. 

The blowuppolynomial of a metric space: connections to stable
polynomials, graphs and their distance spectra
(with Projesh Nath Choudhury)
Preprint, 2021. [FPSAC 2022 abstract] 

Multivariate blowuppolynomials of graphs
(with Projesh Nath Choudhury)
Preprint, 2021. 

Distance matrices of a tree: two more invariants, and in a unified
framework (with Projesh Nath Choudhury).
Preprint, 2019. 
Blowup polynomials and deltamatroids of graphs
(with Projesh Nath Choudhury) Extended abstract of the paper The blowuppolynomial of a metric space: connections to stable polynomials, graphs and their distance spectra Talk at FPSAC 2022; Séminaire Lotharingien de Combinatoire 86B, Article #42, 2022. 







The Weyl–Kac weight formula
(with Gurbir Dhillon) Extended abstract of the paper The weights of simple modules in Category $\mathcal{O}$ for Kac–Moody algebras, Talk at FPSAC 2017; Séminaire Lotharingien de Combinatoire 78B, Article #77, 2017. 

The critical exponent: a novel graph invariant
(with Dominique Guillot and Bala Rajaratnam) Extended abstract of the paper Critical exponents of graphs, Séminaire Lotharingien de Combinatoire 78B, Article #62, 2017. 


The weights of simple modules in Category $\mathcal{O}$ for
Kac–Moody algebras (with Gurbir Dhillon)
Journal of Algebra 603, pages 164–200, 2022. [FPSAC 2017 abstract] 

The Weyl–Kac weight formula
(with Gurbir Dhillon) (Extended abstract of preceding paper above) Talk at 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2017); Séminaire Lotharingien de Combinatoire 78B, Article #77, 2017. 

Faces of highest weight modules and the universal Weyl
polyhedron (with Gurbir Dhillon)
Advances in Mathematics 319, pages 111–152, 2017. 

Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society 369 no. 4, pages 2363–2394, 2017; erratum. 

Faces and maximizer subsets of highest weight modules
Journal of Algebra 455, pages 32–76, 2016. 

On Category $\mathcal{O}$ over triangular generalized Weyl
algebras (with Akaki Tikaradze)
Journal of Algebra 449, pages 687–729, 2016. (Summary: Blocks of $\mathcal{O}$ categorify Young tableaux.) 

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. 

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. 

Center and representations of infinitesimal Hecke algebras of
$\mathfrak{sl}_2$ (with Akaki Tikaradze)
Communications in Algebra 38 no. 2, pages 405–439, 2010. 

Functoriality of the BGG Category $\mathcal{O}$
Communications in Algebra 37 no. 12, pages 4431–4475, 2009. 

Quantized symplectic oscillator algebras of rank one
(with Wee Liang Gan)
Journal of Algebra 310 no. 2, pages 671–707, 2007. 

Category $\mathcal{O}$ over the symplectic oscillator algebra,
Ph.D. Thesis, University of Chicago, 2006. 

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. 

A weightformula for all highest weight modules, and a higher
order parabolic category $\mathcal{O}$
(with G. Krishna Teja)
Preprint, 2022. 

From Cauchy's determinant formula to bosonic and fermionic
immanant identities
(with Siddhartha Sahi)
Preprint, 2022. 

Axiomatic framework for the BGG Category $\mathcal{O}$
Preprint, 2015. 