I am an L.E. Dickson Instructor at the University of Chicago. My research interests include metric geometry, functional analysis, geometric measure theory, and harmonic analysis. I received my Ph.D. from the Courant Institute at NYU under the supervision of Professor Assaf Naor. Papers*Nonnegative kernels and 1-rectifiability in the Heisenberg group*(with V. Chousionis), Anal. PDE, accepted. arXiv.*Some remarks on the Lipschitz regularity of Radon transforms*(with J. Azzam and J. Hickman), submitted. arXiv.*Separated nets in nilpotent groups*(with T. Dymarz, M. Kelly, and A. Lukyanenko), Indiana Univ. Math. J., accepted. 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., accepted. arXiv.*Differentiability and Poincaré-type inequalities in metric measure spaces*(with D. Bate), submitted. 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.
TeachingHere are notes I have developed for the introductory analysis classes I have taught at Chicago. I have not checked them for spelling/technical errors. Caveat emptor! - 20300 Analysis I - Construction of real numbers, metric spaces, abstract vector spaces.
- 20400 Analysis II - Multivariable differentiation and integration on R.
- 20500 Analysis III - Multivariable integration and introductory differential forms.
Non-mathematicalRunningAHEAD - My running log. |