My work focuses primarily on Asymptotic Geometric Analysis, a field at the interface of functional analysis and convex geometry, employing tools from optimal transport, probability theory, information theory, combinatorics, and harmonic analysis.

In particular, I study high-dimensional convex sets and their asymptotic behaviour as the dimension tends to infinity. I am also interested in duality phenomena in convex geometry, especially the duality of finite-dimensional normed spaces, often represented through the duality of their unit balls. Such dualities underlie many elegant results in the field, and I am interested in related geometric inequalities as well as their functional counterparts.

Papers and preprints:

• Uncentered Blaschke-Santaló inequalities for the Gaussian measure
  (with S. Artstein-Avidan and M. Fradelizi)
  arXiv:2609.18472
• A Renyi entropy interpretation of anti-concentration and noncentral sections of convex bodies
  (with J. Melbourne and T. Tkocz)
  arXiv:2406.04200 (Communications in Contemporary Mathematics (2025))
• 60 years of cyclic monotonicity: a survey (with A. Kausamo and L. De Pascale)
  arXiv:2308.07682 (Journal of Convex Analysis volume 32 (2025); special issue in honor of R.T. Rockafellar)
• A Sharp Gaussian Tail Bound for Sums of Uniforms (with X. He and T. Tkocz)
  arXiv:2305.06235 (Israel Journal of Mathematics (2025))
• Stability of polydisc slicing (with N. Glover and T. Tkocz)
  arXiv:2303.16896 (Mathematika, volume 66 (2023))
• A Zoo of Dualities (with S. Artstein-Avidan and S. Sadovsky)
  arXiv:2110.11308 (Journal of Geometric Analysis, volume 33 (2023))
• A counterexample to a strengthening of a question of V. D. Milman (with W. T. Gowers)
  arXiv:2110.03023 (Annales Henri Lebesgue, volume 6 (2023), pp. 427-448.)
• Optimal measure transportation with respect to non-traditional costs (with S. Artstein-Avidan and S. Sadovsky)
  arXiv:2104.04838 (Calculus of Variations and Partial Differential Equations, volume 62 (2022))
• A Rockafellar-type theorem for non-traditional costs (with S. Artstein-Avidan and S. Sadovsky)
  arXiv:2011.13263 (Advances in Mathematics, volume 395 (2022))
• Corrigendum to “A Rockafellar-type theorem for non-traditional costs” (with S. Artstein-Avidan and S. Sadovsky)
  Advances in Mathematics, 2025
• High-dimensional tennis balls (with W. T. Gowers)
  arXiv:1912.10679 (Combinatorial Theory, volume 2 (2022))

PhD Thesis:

• My PhD thesis titled "Topics in high-dimensional geometry and optimal transport" can be found here.

See also:

• A note on my research on mathinstitutes.org titled "Optimal Transport and a Unified Perspective on Set Dualities" available here.
• A short article about my research featured in ICERM's Newsletter (Spring 2023, p. 12) titled "A unified perspective on Set Dualities" can be found here.
• An Oberwolfach Report No. 59/2021 for "Convex Geometry and its Applications" meeting is available here.