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.
Collaborators:
Jonas Azzam,
David Bate,
Vasilis Chousionis,
Tullia Dymarz,
Jonathan Hickman,
Tuomas Hytönen,
Enrico Le Donne,
Michael Kelly,
Anton Lukyanenko,
Assaf Naor,
Tapio Rajala,
Raanan Schul.
Teaching
Here 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-mathematical
RunningAHEAD - My running log.
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