Assistant Professor of Mathematics
Department of Mathematics
Massachusetts Institute of Technology

Email:

Office: 2-271

Mail:
MIT Department of Mathematics
77 Massachusetts Ave, Bldg 2-271
Cambridge, MA 02139, USA

Research interests: Combinatorics (extremal, probabilistic, additive, graph theory, discrete geometry)

Co-organizer of MIT Combinatorics Seminar

Current PhD students: Aaron Berger, Ashwin Sah, Mehtaab Sawhney, Jonathan Tidor

Former PhD students: Benjamin Gunby (Harvard PhD ‘21 → Rutgers postdoc)

Teaching

• 18.225 Graph Theory and Additive Combinatorics (grad), Fall 2021 Book project OCW videos YouTube
• 18.A34 Mathematical Problem Solving (Putnam Seminar), Fall 2021
• 18.226 Probabilistic Methods in Combinatorics (grad), Fall 2020 Notes
• 18.211 Combinatorial Analysis, Fall 2018
• Polynomial Method in Combinatorics (grad), Trinity Term 2016, Oxford
• Math Olympiad training handouts

Selected publications

• Joints of varieties (with Jonathan Tidor and Hung-Hsun Hans Yu)
• Testing linear-invariant properties (with Jonathan Tidor)
  FOCS 2020.
• Equiangular lines with a fixed angle (with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang)
  Annals of Mathematics 195 (2022), to appear.
• A reverse Sidorenko inequality (with Ashwin Sah, Mehtaab Sawhney, and David Stoner)
  Inventiones Mathematicae 221 (2020), 665–711.
• An $L^p$ theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions (with Christian Borgs, Jennifer T. Chayes, and Henry Cohn)
  Transactions of the American Mathematical Society 372 (2019), 3019–3062.
• Upper tails and independence polynomials in random graphs (with Bhaswar B. Bhattacharya, Shirshendu Ganguly, and Eyal Lubetzky)
  Advances in Mathematics 319 (2017), 313–347.
• A relative Szemerédi theorem (with David Conlon and Jacob Fox)
  Geometric and Functional Analysis 25 (2015), 733–762.
• Sphere packing bounds via spherical codes (with Henry Cohn)
  Duke Mathematical Journal 163 (2014), 1965–2002.

Slides

• Extremal problems in discrete geometry
• The joints problem for varieties
• Equiangular lines, spherical two-distance sets, and spectral graph theory
• Popular common difference
• Regularity method for sparse graphs and its applications
• A reverse Sidorenko inequality: independent sets, colorings, and graph homomorphisms
• Large deviations in random graphs
• Pseudorandom graphs, relative Szemerédi theorem and the Green-Tao Theorem

Videos

• The joints problem for varieties, Big Seminar by Laboratory of Combinatorial and Geometric Structures, Aug 2020
• Equiangular lines, spherical two-distance sets, and spectral graph theory, DIMAP, Dec 2020
• Popular common difference, Webinar in Additive Combinatorics, May 2020
• Equiangular lines with a fixed angle, Banff International Research Station, Sep 2019
• Large deviations and exponential random graphs, Northeastern University Network Science Institute, May 2018
• Large deviations for arithmetic progressions, Simons Institute, Berkeley, Apr 2017
• Sparse graph regularity tutorial, Simons Institute, Berkeley, Jan 2017
• Green–Tao theorem and a relative Szemerédi theorem, Simons Institute, Berkeley, Dec 2013

Short CV

• NSF CAREER award, 2021
• Sloan Research Fellowship, 2019
• Dénes König Prize, 2018
• Ph.D. Mathematics, MIT, 2015 (Advisor: Jacob Fox)
• M.A.St. Mathematics with Distinction, Cambridge, 2011
• S.B. Mathematics, MIT, 2010
• S.B. Computer Science and Engineering, MIT, 2010
• Previous affiliations: Oxford, Berkeley, Stanford, Microsoft Research