Omer Friedland

Research

My research is in functional analysis and geometric analysis, with a primary focus on asymptotic geometric analysis, convex geometry, and quantitative analytic inequalities.

A central part of my work concerns the geometry of high-dimensional normed spaces and convex bodies. Another direction focuses on quantitative inequalities for analytic functions and the geometric complexity of algebraic and analytic sets. These questions are closely connected to high-dimensional probability, concentration and anti-concentration, approximation, and metric entropy.

I have also worked on problems in spectral analysis and elliptic partial differential equations, particularly quantitative properties of eigenfunctions and quasimodes.

Preprints

• 2026The sharp exponent for the Banach–Mazur distance to the cube · Submitted
• 2026The equality case in Godbersen’s inequality and its generalizations (with E. Putterman and M. Szusterman) · Submitted
• 2026On partition functions of Gaussian random variables (with O. Guédon and F. Souli) · Submitted
• 2026Product-profile anti-concentration for block-structured multi-affine polynomials (with E. Abakumov and Y. Yomdin) · Submitted
• 2026On the Banach–Mazur radius of ℓ_∞ⁿ (with A. Naor and P. Youssef) · Submitted
• 2026A 5/8 Lower Bound on the Banach–Mazur Distance to the Cross-Polytope · Preprint
• 2026A Log-Free Lower Bound for the Number of Facets of 0/1-Polytopes · Submitted
• 2026A Disk-Growth Remez Principle and a Modular Proof of the Measurable Turán–Nazarov Inequality · Submitted
• 2026On the inner radius of the nonvanishing set for eigenfunctions of complex elliptic operators (with H. Ueberschär) · Preprint
• 2026An improved lower bound on the Banach–Mazur distance to the cross-polytope · Submitted
• 2026Geometry-Driven Conditioning of Multivariate Vandermonde Matrices in High-Degree Regimes (with Y. Yomdin) · Accepted for publication in Geometric Aspects of Functional Analysis (GAFA Seminar, Lecture Notes in Mathematics, Springer)
• 2024Local ℓ^∞ bounds for eigenfunctions of complex elliptic operators via diophantine problems (with H. Ueberschär) · Submitted

Publications

• 2022Superscarred quasimodes on flat surfaces with conical singularities (with H. Ueberschär) · Studia Mathematica 264:241–262 (2022)
• 2021Remez-Type Inequalities and Their Applications · Extended Abstracts Fall 2019: Spaces of Analytic Functions, pp. 73–79 (2021)
• 2021Doubling coverings via resolution of singularities and preparation (with R. Cluckers and Y. Yomdin) · Communications in Contemporary Mathematics 23(2):2050018 (2021)
• 2020Exponential Taylor domination (with G. Goldman and Y. Yomdin) · Operator Theory: Advances and Applications, Vol. 280 (2020)
• 2020Doubling chains on complements of algebraic hypersurfaces (with Y. Yomdin) · Journal d’Analyse Mathématique 140(2):617–636 (2020)
• 2019Approximating matrices and convex bodies through Kadison-Singer (with P. Youssef) · International Mathematics Research Notices 2019(8):2519–2537
• 2017Inverse Littlewood–Offord problems for quasi-norms (with O. Giladi and O. Guédon) · Discrete & Computational Geometry 57(1):231–255 (2017)
• 2017Doubling coverings of algebraic hypersurfaces (with Y. Yomdin) · Pure and Applied Functional Analysis 2(2):221–241 (2017)
• 2017(s,p)-valent functions (with Y. Yomdin) · Geometric Aspects of Functional Analysis, LNM 2169, Springer (2017)
• 2016Small ball estimates for quasi-norms (with O. Giladi and O. Guédon) · Journal of Theoretical Probability 29(4):1624–1643 (2016)
• 2015Sampling, metric entropy, and dimensionality reduction (with D. Batenkov and Y. Yomdin) · SIAM Journal on Mathematical Analysis 47(1):786–796 (2015)
• 2014Vitushkin-type theorems (with Y. Yomdin) · Geometric Aspects of Functional Analysis, LNM 2116, Springer (2014)
• 2013An observation on the Turán–Nazarov inequality (with Y. Yomdin) · Studia Mathematica 218(1):27–39 (2013)
• 2013Sparsity and non-Euclidean embeddings (with O. Guédon) · Israel Journal of Mathematics 197(1):329–345 (2013)
• 2013A simple observation on random matrices with continuous diagonal entries (with O. Giladi) · Electronic Communications in Probability 18(53) (2013)
• 2011Random embedding of ℓ_pⁿ into ℓ_r^N (with O. Guédon) · Mathematische Annalen 350(4):953–972 (2011)
• 2008Kahane–Khinchin type averages · Proceedings of the American Mathematical Society 136(10):3639–3645 (2008)
• 2007Bounds on the concentration function in terms of the Diophantine approximation (with S. Sodin) · C. R. Math. Acad. Sci. Paris 345(9):513–518 (2007)
• 2007An extension of a Bourgain–Lindenstrauss–Milman inequality (with S. Sodin) · Journal of Functional Analysis 251(2):492–497 (2007)
• 2007Geometric applications of Chernoff-type estimates (with S. Artstein-Avidan and V. Milman) · Geometric Aspects of Functional Analysis, LNM 1910, Springer (2007)
• 2006Polynomial bounds for large Bernoulli sections of ℓ₁^N (with S. Artstein-Avidan, V. Milman, and S. Sodin) · Israel Journal of Mathematics 156:141–155 (2006)
• 2006Geometric applications of Chernoff-type estimates and a zigzag approximation for balls (with S. Artstein-Avidan and V. Milman) · Proceedings of the American Mathematical Society 134(6):1735–1742 (2006)

Graduate Courses

• 2026–2027 — Convexité en grande dimension I
• 2020–2022 — Uncertainty Principles
• 2019–2020 — Random Matrices
• 2018–2019 — Random Matrices and their Applications

Doctoral supervision

• 2025–present — Léonard Walaszek.
• 2021–2023 — Maud Szusterman (co-supervision).
• 2020–2024 — Yiyu Tang (co-supervision).

Academic service

Undergraduate pedagogical committee, Sorbonne Université; academic selection committees.

Contact

omer.friedland [at] sorbonne-universite.fr

IMJ-PRG · Campus Pierre et Marie Curie · Office 16-26 416
4 place Jussieu, 75252 Paris, France