Professor of Mathematics

Paata Ivanisvili

pivanisv@uci.edu · x.com/PI010101

Department of Mathematics, University of California, Irvine

Papers

with S. V. Kislyakov, Correction up to a function with sparse spectrum and uniformly convergent Fourier series, Zap. Nauchn. Sem. POMI, Vol. 376, 25-47, (2010)
with N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Sur la fonction de Bellman pour des problèmes extrémaux sur lʼespace BMO, Comptes Rendus Mathematique, Volume 350, Issues 11-12, Pages 561-564, June (2012)
J-closed finite collections of Hardy-type subspaces, Zap. Nauchn. Sem. POMI, Vol. 401, 82-92 (2012)
with N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Bellman function for extremal problems in BMO, TAMS (2015) doi: dx.doi.org/10.1090/tran/6460
Inequality for Burkholder's martingale transform. Analysis & PDE 8-4 (2015), 765--806. DOI 10.2140/apde.2015.8.765
Bellman function approach to the sharp constants in uniform convexity. Advances in Calculus of Variations DOI: 10.1515/acv-2016-0008, August 2016
with D. M. Stolyarov, P. B. Zatitskiy Bellman VS Beurling: sharp estimates of uniform convexity for L^p spaces St. Petersburg Math. J. Vol. 27 (2016), No. 2, Pages 333-343
with A. Volberg, Hessian of Bellman functions and uniqueness of Brascamp--Lieb inequality, J. London Math. Soc. (2015), doi:10.1112/jlms/jdv040
with N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Sharp estimates of integral functionals on classes of functions with small mean oscillation. Comptes Rendus Mathematique, Vol. 353, Issue 2, (2015), pages 1081-1085
with A. Volberg, Bellman partial differential equation and the hill property for classical isoperimetric problems (2015)
with N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Bellman function for extremal problems in BMO II: evolution. Memoirs of the American Mathematical Society
with A. Volberg, Isoperimetric functional inequalities via the maximum principle: the exterior differential systems approach. (2015) V. P. Havin's volume
A bundling problem revisited. preprint, (2016)
with B. Jaye, F. Nazarov, Lower bounds for uncentered maximal functions in any dimension, International Mathematics Research Notices. Vol. 2016, Issue 00, 2016
Boundary value problem and the Ehrhard inequality, Studia Mathematica 246 (3) (2019)
with A. Volberg, Improving Beckner's bound via Hermite functions, Analysis & PDE, Vol. 10, No. 4 (2017), 929--942
with A. Volberg, F. Nazarov, On weak and strong sharp weighted estimates of square function, preprint (2016)
with A. Volberg, Poincare inequality 3/2 on the Hamming cube, Rev. Mat. Iberoam. (2019)
with K. Domelevo, S. Petermichl, S. Treil, A. Volberg, On the failure of lower square function estimates in the non-homogeneous weighted setting, Mathematische Annalen
Convolution estimates and number of disjoint partitions, The Electronic Journal of Combinatorics, Volume 24, Issue 2 (2017), Paper #P2.43
with F. Nazarov, A. Volberg, Square function and the Hamming cube: duality, Discrete Analysis 2018:1, 18 pp.
with A. Volberg, From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity, Journal of Functional Analysis
with I. Holmes, A. Volberg, The sharp constant in the weak (1,1) inequality for the square function: a new proof, Rev. Mat. Iberoam. (2019)
with F. Nazarov, A. Volberg, Hamming cube and martingales, Comptes Rendus Mathematique, Vol. 355, Iss. 10, (2017), pp. 1072--1076
with S. Treil, Superexponential estimates and weighted lower bounds for the square function, accepted to TAMS (2018)
with A. Volberg, Martingale transform and Square function: some end-point weak weighted estimates, (2017)
with F. Barthe, Bobkov's inequality via optimal control theory accepted to GAFA seminars
with P. Mozolyako, A. Volberg, Strong weighted and restricted weak weighted estimates of the square function, (2018)
with T. Tkocz, Comparison of moments of Rademacher chaoses, accepted to Arkiv for Matematik (2018)
with S. Zbarsky, Centered Hardy--Littlewood maximal operator on the real line: lower bounds, Comptes Rendus Mathematique, Volume 357, Issue 4, (2019)
with A. Eskenazis, Dimension independent Bernstein--Markov inequalities in Gauss space, Journal of Approximation Theory, Volume 253, (2020).
with E. A. Carlen, R. L. Frank, E. H. Lieb, Inequalities for Lp-norms that sharpen the triangle inequality and complement Hanner's inequality, The Journal of Geometric Analysis (2020)
with D. Li, R. van Handel, A. Volberg, Improving constant in end-point Poincare inequality on Hamming cube, (2018)
with C. Mooney, Sharpening the triangle inequality: envelopes between L2 and Lp spaces, Analysis & PDE, Volume 13, Number 5 (2020)
with A. Eskenazis, Polynomial inequalities on the Hamming cube, Probab. Theory Relat. Fields 178, 235–287 (2020)
with F. Nazarov, On Weissler's conjecture on the Hamming cube I, International Mathematics Research Notices (2020)
with R. van Handel, A. Volberg, Rademacher type and Enflo type coincide, Annals of Mathematics, Vol. 192, No. 2 (2020)
with A. Lindenberger, P. F. X. Müller, M. Schmuckenschläger, Hypercontractivity on the unit circle for ultraspherical measures: linear case, (2020). Revista Matematica Iberoamericana
with R. Russell, Exponential integrability for log-concave measures, (2020) Analysis & PDE
with A. Eskenazis, Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces (2020), Israel Journal of Mathematics
with R. L. Frank, Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere (2021), Journal of Functional Analysis
with A. Volberg, Banach space valued Pisier and Riesz type inequalities on discrete cube (2021)
with A. Eskenazis, Learning low-degree functions from a logarithmic number of random queries, STOC 2022.
with J. de Dios Pont, R. Greenfeld, J. Madrid, Additive Energies on Discrete Cubes (2021). Discrete Analysis Journal.
with J. de Dios Pont, J. Madrid, A new proof of the description of the convex hull of space curves with totally positive torsion (2023). Accepted to MMJ.
with A. Eskenazis, L. Streck, Low-degree learning and the metric entropy of polynomials. Discrete Analysis Journal.
with Y. Stone, The KKL inequality and Rademacher type 2. Discrete Analysis Journal
with D. Beltran, J. Madrid, On sharp isoperimetric inequalities on the hypercube (2023). Accepted to TAMS
with D. Stolyarov, V. Vasyunin, P. Zatitskii, Bellman functions on simple non-convex domains in the plane (2023), accepted to MEMS
with O. Klein, R. Vershynin, Covering the hypercube, the uncertainty principle, and an interpolation formula accepted to Electronic Journal in Combinatorics
with L. Becker, D. Krachun, J. Madrid, Discrete Brunn-Minkowski Inequality for subsets of the cube. Combinatorica, Vol. 45, art. num. 48, (2025)
with Y. Stone, Sharpening the gap between L1 and L2 norms (2024)
with P. Durcik, J. Roos, Sharp isoperimetric inequalities on the Hamming cube near the critical exponent (2024). Accepted to Advances in Mathematics
with H. Zhang, On the Eldan-Gross inequality Accepted to Journal of Functional Analysis (2025)
with P. Kalantzopoulos, (P,Q) complex hypercontractivity (2024). Accepted Proc. Amer. Math. Soc (2025)
with R. Vershynin, X. Xie, Jackson's inequality on the hypercube (2024)
with N. Alpay, Lower Bounds for Dyadic Square Functions of indicator functions of sets (2025)
with P. Kalantzopoulos, Multiversion of the Hausdorff--Young inequality (2025)
with D. Beltran, J. Madrid, L. Patil, Optimal Young's convolutions inequality and its reverse form on the hypercube. Accepted to Journal d'Analyse Mathématique.
with X. Xie, Counterexample to majority optimality in NICD with erasures (2025)
with P. Durcik, J. Roos, X. Xie, Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent (2026)
with Z. Chen, J. de Dios Pont, J. Madrid, H. Wang, Almost-Orthogonality in Lp Spaces: A Case Study with Grok (2026)
with X. Xie, Grokability in five inequalities (2026)
with R. L. Frank, The sharp log Sobolev inequality on finite cycles. Accepted to Advances in Mathematics (2026)
with Z. Chen, J. Madrid, H. Wang, Carbery's inequality in the Schatten--von Neumann classes (2026)
with R. L. Frank, The sharp extension norm for a planar sector (2026)
with K. Domelevo, S. Petermichl, A. Volberg, Dimension-free bounds for Riesz transforms on the Hamming cube via a Bellman function (2026)
with R. L. Frank, C. Torres-Latorre, Minimizers for Coulomb gases constrained to a halfspace (2026)
with J. Hosle, Geometric Block Exponents and a Uniform Mixed-Alphabet Sumset Inequality (2026)
with R. L. Frank, The distance between homotopy classes of Sobolev maps on spheres (2026)
with X. Xie, H. Zhang, A Beckmann boundary form of Talagrand's conjecture on the discrete cube (2026)
with Yi C. Huang, The missing two-point inequality in Weissler's conjecture (2026)
with R. L. Frank, The Winding Number at the Critical Hölder Exponent 1/3: Failure of Universal Fourier Summation (2026)
with R. L. Frank, Counterexamples to the Landis conjecture in dimensions three and higher (2026)
with R. L. Frank, A counterexample to the Kato conjecture for positive commutators (2026)
The Hayman–Wu constant is π² (2026)
with S. Zhang, A proof of the Holmes–Holroyd–Ramírez cyclic-product conjecture (2026)
with R. L. Frank, Sharp comparison between the perimeter and its fractional analogue in two dimensions (2026)
Polynomial growth of Bohnenblust--Hille constants on the Hamming cube (2026). The original raw draft was circulated on X on August 27, 2026.
with R. L. Frank, The sharp constant in the Chang--Marshall inequality (2026)