I am an assistant professor at the University of Connecticut. My research interests include metric geometry, functional analysis, geometric measure theory, and harmonic analysis. Before Connecticut, I was a L.E. Dickson Instructor at the University of Chicago, and I received my Ph.D. from the Courant Institute at NYU under the supervision of Professor Assaf Naor.
Papers
Notions of null sets in infinite-dimensional Carnot groups (with N. Eldredge, M. Gordina, and E. Le Donne), submitted. arXiv.
The strong geometric lemma for the Heisenberg group (with V. Chousionis and R. Young), submitted. arXiv.
The Riesz transform on intrinsic Lipschitz graphs in the Heisenberg group (with V. Chousionis and R. Young), submitted. arXiv.
Identifying 1-rectifiable measures in Carnot groups (with M. Badger and S. Zimmerman), submitted. arXiv.
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups (with V. Chousionis and R. Young), J. Reine Angew. Math., 2022 (2022), no. 784, 251--274. arXiv.
Singular integrals on C^{1,\alpha} regular curves in Carnot groups (with V. Chousionis and S. Zimmerman), J. Anal. Math. 147 (2022), 299--32. arXiv.
Stratified β-numbers and traveling salesman in Carnot groups, J. London Math. Soc., 106 (2022), no. 2, 662--703. arXiv.
Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces (with V. Chousionis, V. Vellis, and S. Zimmerman), Ann. Acad. Sci. Fenn. Math., 45 (2020), no. 2, 931--955. arXiv.
Gâteaux differentiability on infinite-dimensional Carnot groups (with E. Le Donne and T. Moisala), J. Geom. Anal. 31 (2019), 1756--1785. arXiv.
The traveling salesman theorem on Carnot groups (with V. Chousionis and S. Zimmerman), Calc. Var. Partial Differ. Equ. 58 (2019), no. 14. arXiv.
Nonnegative kernels and 1-rectifiability in the Heisenberg group (with V. Chousionis), Anal. PDE. 10 (2017), no. 6, 1407-1428. arXiv.
Some remarks on the Lipschitz regularity of Radon transforms (with J. Azzam and J. Hickman), Proc. Amer. Math. Soc., 146 (2018). arXiv.
Separated nets in nilpotent groups (with T. Dymarz, M. Kelly, and A. Lukyanenko), Indiana Univ. Math. J. 67 (2016), no. 3, 1143-1183. arXiv.
Quantitative affine approximation for UMD targets (with T. Hytönen and A. Naor), Discrete Anal. (2016), no. 6, 37pp. arXiv.
Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces (with E. Le Donne and T. Rajala), Proc. London Math. Soc. 115 (2017), no. 2, 348-380. arXiv.
Differentiability and Poincaré-type inequalities in metric measure spaces (with D. Bate), Adv. Math. 333 (2018), 868-930. arXiv.
BiLipschitz decomposition of Lipschitz maps between Carnot groups, Anal. Geom. Metr. Spaces 3, 231--243, 2015. arXiv.
Characterizations of rectifiable metric measure spaces (with D. Bate), Ann. Sci. Éc. Norm. Supér. 50(1), 1--37, 2017. arXiv.
Markov convexity and nonembeddability of the Heisenberg group, Ann. Inst. Fourier 66(4), 1615--1651, 2016. arXiv.
An upper bound for the length of a traveling salesman path in the Heisenberg group (with R. Schul), Rev. Mat. Iberoam. 32(2), 391-417, 2016. arXiv.
The traveling salesman problem in the Heisenberg group: upper bounding curvature (with R. Schul), Trans. Amer. Math. Soc. 368(7), 4585--4620, 2016. arXiv.
Coarse differentiation and quantitative nonembeddability for Carnot groups, J. Funct. Anal. 266, 4616--4704, 2014. arXiv.
Discretization and affine approximation in high dimensions (with A. Naor), Israel J. Math. 197(1), 107--129, 2013. arXiv.
Compression bounds for wreath products, Proc. Amer. Math. Soc. 138(8), 2701--2714, 2010. arXiv.
Collaborators: Jonas Azzam, Matthew Badger, David Bate, Vasilis Chousionis, Tullia Dymarz, Nathaniel Eldredge, Maria Gordina, Jonathan Hickman, Tuomas Hytönen, Enrico Le Donne, Michael Kelly, Anton Lukyanenko, Terhi Moisala, Assaf Naor, Tapio Rajala, Raanan Schul, Vyron Vellis, Robert Young, Scott Zimmerman.
Non-mathematical
RunningAHEAD - My running log.