### Books, monographs, and surveys

 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. The book title is inspired from a talk by Israel Moiseevich Gelfand. The course which I developed and taught in Spring 2011 at Yale, and which led to the book. The announcements from Yale Mathematics and from Yale University. 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.), Texts and Readings in Mathematics (TRIM), Hindustan Book Agency, pages 85–129, 2013.

## Analysis: positivity, Schur polynomials, probability, graph limits

(shares fourteen papers with "Combinatorics, discrete mathematics, and algebra" section)

Totally positive kernels, Pólya frequency functions, and their transforms (with Alexander Belton, Dominique Guillot, and Mihai Putinar)
Journal d'Analyse Mathématique, in press.
The p-norm of circulant matrices (with Ludovick Bouthat, Javad Mashreghi, and Frédéric Morneau-Guérin)
Linear and Multilinear Algebra, in press.
Moment-sequence 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 delta-matroids of graphs (with Projesh Nath Choudhury)
(Extended abstract of the paper The blowup-polynomial 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, probability-themed 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 non-reversal property for totally non-negative 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 non-reversal; 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, torsion-free groups.)
 Schur polynomials, entrywise positivity preservers, and weak majorization (with Terence Tao) Extended abstract of the paper On the sign patterns of entrywise positivity preservers in fixed dimension, 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2018), Séminaire Lotharingien de Combinatoire 80B, Article #14, 2018. (Poster)
The Hoffmann-Jørgensen inequality in metric semigroups (with Bala Rajaratnam)
Annals of Probability 45 no. 6A, pages 4101–4111, 2017.
Preserving positivity for rank-constrained 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)
 (Extended abstract of preceding paper above) 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings BC, pages 155–166, 2016. (Poster)
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 blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra (with Projesh Nath Choudhury)
Preprint, 2021.
Multivariate blowup-polynomials of graphs (with Projesh Nath Choudhury)
Preprint, 2021.
Multiply positive functions, critical exponent phenomena, and the Jain–Karlin–Schoenberg kernel
Preprint, 2020.
The non-compact normed space of norms on a finite-dimensional Banach space
Preprint, 2018.
The Khinchin–Kahane inequality and Banach space embeddings for metric groups (with Bala Rajaratnam)
Preprint, 2016.
Model-free 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.

## Combinatorics, discrete mathematics (including Schur functions), and algebra     (also FPSAC)

 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 nil-Coxeter 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 nil-Coxeter 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 Yang-Baxter 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 nil-Hecke algebras over real and complex reflection groups (with Sutanay Bhattacharya) Preprint, 2021. The blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra (with Projesh Nath Choudhury) Preprint, 2021.                 [FPSAC 2022 abstract] Multivariate blowup-polynomials 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.

## FPSAC publications (International conference on Formal Power Series and Algebraic Combinatorics)

Blowup polynomials and delta-matroids of graphs (with Projesh Nath Choudhury)
Extended abstract of the paper The blowup-polynomial 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.
 Schur polynomials, entrywise positivity preservers, and weak majorization (with Terence Tao) Extended abstract of the paper On the sign patterns of entrywise positivity preservers in fixed dimension, Séminaire Lotharingien de Combinatoire 80B, Article #14, 2018. (Poster)
 Generalized nil-Coxeter algebras Extended abstract of the paper Generalized nil-Coxeter algebras over discrete complex reflection groups, Séminaire Lotharingien de Combinatoire 80B, Article #29, 2018. (Poster)
 The volume of the caracol polytope (with Carolina Benedetti, Rafael S. González D'León, Christopher R. H. Hanusa, Pamela E. Harris, Alejandro H. Morales, and Martha Yip) Extended abstract of the paper A combinatorial model for computing volumes of flow polytopes, Séminaire Lotharingien de Combinatoire 80B, Article #87, 2018. (Poster)
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.
 Schur polynomials and matrix positivity preservers (with Alexander Belton, Dominique Guillot, and Mihai Putinar) Extended abstract of the paper Matrix positivity preservers in fixed dimension. I, DMTCS Proceedings BC, pages 155–166, 2016. (Poster)

## Representation theory

(shares five papers with "Combinatorics, discrete mathematics, and algebra" section)

 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 weight-formula 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.