A complete renormalization group trajectory between two fixed points, *Comm. Math. Phys.* 276(3) (2007), 727-772. preprint version arXiv:math-ph/0610018

Brill-Gordan loci, transvectants and an analogue of the Foulkes conjecture, *Adv. Math.* 208(2) (2007), 491-520 (with J. Chipalkatti). preprint version arXiv:math.AG/0411110

Twin Buildings and Applications to S-Arithmetic Groups, *Lecture Notes in Mathematics* 1641, Springer (1996).

*Buildings: Theory and Applications*, Graduate Texts in Mathematics 248, Springer (2008) (with Ken Brown).

F. Di Plinio and C. Thiele, *Endpoint bounds for the bilinear Hilbert transform*, Trans Amer. Math. Soc. 368 (2016), no. 6, 3931–3972. MR 3453362

F. Di Plinio and Y. Ou, *A modulation invariant Carleson embedding theorem outside local **L**2*, preprint arXiv:1510.06433, to appear in J. Anal. Math

Property (T) for noncommutative universal lattices (with Andrei Jaikin-Zapirain), *Inventiones Mathematicae 179(2) (*2010), 303-347.

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Kazhdan quotients of Golod-Shafarevich groups (with appendices by Andrei Jaikin-Zapirain),* Proceedings of the London Mathematical Society *102(4)* (*2011), 599-636.

The fluid limit of a heavily loaded processor sharing queue, *Annals of Applied Probability* 12 (2002), 797-859 (with A. L. Puha and R. J. Williams).

Diffusion approximation of a processor sharing queue in heavy traffic, *Annals of Applied Probability* 14 (2004), 555-611.

Coherent vortex structures and 3D enstrophy cascade (with R. Dascaliuc), Comm. Math. Phys. 317 (2013), 547-561.

A geometric measure-type regularity criterion for solutions to the 3D Navier-Stokes equations, Nonlinearity 26 (2013), 289-296.

Decay of eigenfunctions of elliptic PDEs I (with E. Skibsted), Adv. Math. 270, (2015), 138--180.

Decay of eigenfunctions of elliptic PDEs II (with E. Skibsted), arXiv 1504.07128.

The Beurling-Selberg extremal functions for a ball in Euclidean space, *Duke Math. J.* 83, no. 1 (1996), 203-247 (with J. D. Vaaler).

Commutative algebra was born out of three classical fields: number theory, algebraic geometry, and invariant theory, but now is used to study many other topics in mathematics. My own focus is the study of solutions of polynomial or power series equations in many variables. I am especially interested in a method called "reduction to characteristic p." Here are a few of my papers:

The structure of linkage (with B. Ulrich), Annals of Math. 126 (1987), 277-334.

Tight closure, invariant theory, and the Briançon-Skoda theorem (with M. Hochster), J. Amer. Math. Soc. 3 (1990), 31-116.

Infinite integral extensions and big Cohen-Macaulay algebras (with M. Hochster), Annals of Math 135 (1992), 53-89.

Direct methods for primary decomposition (with D. Eisenbud and W. Vasconcelos), Inventiones Math. 110 (1992), 207-236.

Uniform bounds in noetherian rings, Inventiones Math. 107 (1992), 203-223.

Comparison of symbolic and ordinary powers of ideals (with M. Hochster), Invent. Math. 147 (2002), 349-369.

The regularity of Tor and graded Betti numbers (with D. Eisenbud and B. Ulrich), Amer. J. Math. 128 (2006), 573-605.

Branched polymers and dimensional reduction, *Annals of Mathematics*, 158 (2003), 1019-1039 (with D. Brydges). arXiv:math-ph/0107005

On Many-Body Localization for Quantum Spin Chains, http://arxiv.org/pdf/1403.7837.pdf

Embedability between right-angled Artin groups. Joint with Sang-hyun Kim. (Geom. Topol. 17 (2013), no. 1, 493-530)

Anti-trees and right-angled Artin subgroups of planar braid groups. Joint with Sang-hyun Kim. (Geom. Topol. 19 (2015), no. 6, 3289-3306)

Quotients of surface groups and homology of finite covers via quantum representations. Joint with Ramanujan Santharoubane. (Invent. Math. (2016))

A counterexample to the strong version of Freedman's conjecture, *Annals of Mathematics* 168 (2008), 675-693. Preprint version: http://arxiv.org/PS_cache/math/pdf/0610/0610865v2.pdf (.pdf)

Tutte chromatic identities from the Temperley-Lieb algebra, *Geometry and Topology* 13 (2009), 709-741 (with Paul Fendley). Preprint version: http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0016v3.pdf (.pdf)

Localization of Andre-Quillen-Goodwillie towers, and the periodic homology of infinite loopspaces, *Advances in Math.* 201 (2006), 318-378.

Primitives and central detection numbers in group cohomology, *Advances in Math.* 216 (2007), 387-442.

Product formulae for Ozsvath-Szabo 4-manifold invariants, *Geom. Topol.* 12 (2008), 1557-1651 (with S. Jabuka).

On the Heegaard Floer homology of a surface times a circle, *Adv. Math.* 218 (2008), 728-761 (with S. Jabuka).

Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups (with F. Baudoin and M. Gordina), *Transactions of the AMS*, 365, 4313-4350, 2013.

Heat kernel analysis on semi-infinite Lie groups, *J. Functional Analysis* 257(11) (2009), 3552-3592.

Cyclic extensions and the local lifting problem (with S. Wewers), *Ann. of Math. 180*, No. 1 (2014), 233--284.

Fields of moduli of three-point G-covers with cyclic p-Sylow, I, *Algebra Number Theory 6, *No. 5 (2012), 833--883.

A new approach to the Koszul property in representation theory (with L. Scott),* J. Inst. Math. Jussieu 12 *(2013), 153-197.

Cohomology of quantum groups via the geometry of the nullcone (with C. Bendel, D. Nakano, and C. Pillen), *Memoirs of the Amer. Math. Soc. ***229** (2014), 93 pages.

*James Joseph Sylvester: Jewish Mathematician in a Victorian World,* Baltimore: Johns Hopkins University Press, 2006.

*Episodes in the History of Modern Algebra 1800-1950*, HMATH, vol. 32, Providence: American Mathematical Society and London: London Mathematical Society, 2008 (co-edited with Jeremy J. Gray).

- Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes (2012), arXiv:1202.3901 [math.PR].
*Probability Theory and Related Fields*, 160 (2014), no. 3, 429–487. - (with Alexei Borodin) Integrable probability: From representation theory to Macdonald processes,
*Probability Surveys*, 11 (2014), 1-58, arXiv:1310.8007 [math-ph]. - (with Ivan Corwin) Stochastic higher spin vertex models on the line (2015), arXiv:1502.07374 [math.PR]. To appear in Comm. Math. Phys.

Anomalies in the Foundations of Ridge Regression, *International Statistical Review*, 76, 89-105 (2008) (with D. Jensen). http://arxiv.org/abs/math.ST/0703551

Anomalies in the Analysis of Calibrated Data, *Journal of Statistical Computation and Simulation* 79(3)(2009), 299-314 (with D. Jensen). http://arxiv.org/abs/math.ST/0703550

Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable, *J. Amer. Math. Soc.* 15 (2002), 929-978 (with Y. Segev and G. Seitz).

Weakly commensurable arithmetic groups and isospectral locally symmetric spaces, *Publ. Math. IHES *109(2009), 113-184.

Unitary orbits of normal operators in von Neumann algebras, *Journal für die Reine und Angewandte Mathematik* 605 (2007), 95-132.

Model theory of operator algebras I: Stability, *Bull. London Math. Soc*., to appear (with Ilijas Farah and Bradd Hart).

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Super duality and irreducible characters of ortho-symplectic Lie superalgebras, *Inventiones Mathematicae* 183 (2011), 189-224 (with Shun-Jen Cheng and Ngau Lam).

Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras (with Shun-Jen Cheng and Ngau Lam), Duke J. Math. 164 (2015), 617-695.