Embedded Files
Papers
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. 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 Matheamtics 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)
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 (2023)
with L. Becker, D. Krachun, J. Madrid, Discrete Brunn-Minkowski Inequality for subsets of the cube. Accepted to Combinatorica (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)
with H. Zhang, On the Eldan-Gross inequality (2024)
with P. Kalantzopoulos, (P,Q) complex hypercontractivity (2024)
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 (2025)
Awards
Awards
- 2019--2022 NSF DMS-2152346
- 2021 - John Griggs Faculty Award, NC State
- 2020--2026 NSF CAREER DMS-2152401
- 2025-2026 Simons Fellows in Mathematics.
Students at UCI
Students at UCI
- 2024 -- present: Nika Areshidze.
- 2023 -- present: Lekha Patil. [1]
- 2023 -- present: Xinyuan Xie. [1]
- 2022 -- present: Natanael Alpay. [1]
- 2022 -- 2025: PhD Yonathan Stone. [1], [2], Current job at Epic.
- 2018--2022: Erya Yang. PhD. Since 2022 she is an assistant professor at business school of Sun Yat-sen University, China.
Visiting Assistant Professors at UCI
Visiting Assistant Professors at UCI
- 2022 -- 2023: Haonan Zhang. [1] Now tenure-track assistant professor at University of South Carolina.
- 2023 -- 2025: Pavlos Kalantzopoulos.[1], [2], Now postdoc at University of Waterloo.
Conference organization
Conference organization
Dual trimester program at HIM, Boolean Analysis in Computer Science, Fall 2024, Germany.
School: PAC Learning and Boolean Harmonic Analysis, HIM , Bonn (September 2024)
Workshop: Analysis and Geometry on Discrete Spaces, HIM, Bonn (October 2024).
Workshop: Analysis in TCS: testing, learning, and complexity, HIM, Bonn (November 2024)
Workshop: Information theory, Boolean functions, and lattice problems, HIM Bonn (November 2024)
2021--2025: yearly Summer/Fall School.
- 10/2021: Discrete Analysis and Complexity of Quantum Algorithms
- 10/2022: Computational Learning Theory and Fourier Analysis
- 10/2023: Heat flow, two-point inequalities and beyond2022: SQuaREs, San Jose, CA.
6/2022: Analysis on the hypercube with applications to quantum computing, AIM workshop, [Photo] San Jose, CA.
2019--present: Harmonic Analysis Seminar at UC Irvine, CA.
5/2019: Curriculum for Math CEO at UCI: Pentominoes Game.
9/2018: Workshop Discrete Structures: Harmonic Analysis and Probability at Clay Math. Institute, UK.
2025
2025
Jan. USC Probability and Statistics Seminar.
Feb. Online Analysis Research Seminar (OARS)
Feb. MPS Workshop on Computation in Mathematic, Simons Foundation.
Feb. Colloquium, Virginia Tech
Feb. Colloquium, Fullerton
Mar. Colloquium, University of Cincinnati
Mar. Colloquium, University of Hawaii
Jun. Invited panel judge at EPOCH AI’s 2025 Frontier Mathematics Symposium on mathematics and AI.
Jul. Real Analysis, Harmonic Analysis, and Applications, Workshop, Oberwolfach, Germany
2024
2024
no traveling due to childbirth.
2023
2023
Feb. Probability and Combinatorics Seminar, UCI
Oct. Colloquium, University of Houston.
Nov. LA probability forum
Nov. Ergodic Theory and Analsyis seminar, Rutgers
2022
2022
Feb, IPAM, UCLA. [video]
Mar. Colloquium, University Of Hawaii
Mar. AGT&A Seminar. [video]
Jun. AIM workshop, San Jose.
Sep. ICERM. Brown. [video]
Oct. ICERM. Brown. [video]
Dec. ICERM. Brown. [video]
2021
2021
Jan. Functional Analysis Seminar, IMPAN, Poland [slides]
Feb. International Society of Georgian Scientists (ISGS)
Feb. Tbilisi Analysis & PDE Seminar.
Mar. Colloquium, University of Massachusetts Lowell
Mar. Probability/Statistics seminar at University of Southern California. [video], [slides]
Mar. Purdue analytic number theory and harmonic analysis (PANTHA).
Mar. Probability seminar at University of Illinois at Urbana-Champaign.
Mar. Analysis Seminar, University of Missouri.
Oct. Combinatorics and Probability, UCI.
Nov. Discrete Harmonic and Harmonic Analysis Seminar, University of Wuerzburg.
Nov. Analysis Seminar, Chapman University.
2020
2020
July. Real Analysis, Harmonic Analysis and Applications. Oberwolfach, Germany; (Cancelled COVID-19)
July. Contemporary Analysis and Its Applications. Slovenia; (Cancelled COVID-19)
May. France; (Cancelled COVID-19)
Aug. "Concentration Week at Texas A&M".
Sep. Banach Spaces Webinar, "Sharpening the triangle inequality" [video]
Oct. Online Asymptotic Geometric Analysis Seminar, [slides]
Oct. Duke University.
Nov. Indiana University Bloomington [slides]
Nov. NC state
Nov. Corona Seminar, "Rademacher and Enflo type coincide" [video]
Dec. UCLA [slides]
2019
2019
Feb. Kent State University, Colloquium Talk and Analysis seminar talk
March. AMS sectional meeting Hawaii, Honolulu;
April. Caltech, joint UCLA/Analysis seminar;
May. HIM, Trimester program, Harmonic analysis, Bonn, Germany;
May. AIM, San Jose;
May. Geometric and Functional inequalities in Convexity and Probability, Florence, Italy
June. CMS meeting, Probabilistic Methods in Geometric Functional Analysis and Convexity, Regina, Canada;
June. Operators, Functions, and Systems of Mathematical Physics Conference, Baku, Azerbaijan;
June. St. Petersburg Summer Meeting in Analysis, Russia;
Sep. Conference, Batumi, Georgia;
Sep. Aristotle University of Thessaloniki, Analysis Seminar, Greece;
Sep. AMS Sectional meeting, Wisconsin--Madison;
Nov. AMS Sectional meeting, University of Florida, Gainesville;
Nov. Colloquium, Washington University in St. Louis, Missouri;
Dec. Workshop in convexity and geometric aspects of harmonic analysis, Georgia Tech;
2018
2018
Feb. Princeton University; Analysis Seminar;
Feb. Princeton University; Probability Seminar;
Feb. Simons Collaboration on Algorithms & Geometry;
Feb. Georgia Tech.; Analysis Seminar;
Mar. Carnegie Mellon University; Combinatorics Seminar;
May. International conference dedicated to the memory of Sergey Mergelyan, Armenia;
May. Aristotle University of Thessaloniki, Analysis Seminar, Greece;
Jul. PCMI, Harmonic Analysis;
Sep. IX International Conference of the Georgian Mathematical Union, Batumi, Georgia;
Sep. Clay Math. Institute, Discrete Structures: Harmonic Analysis and Probability;
2017
2017
Apr. MSRI, HA Postdoc Seminar;
Sep. MSRI, GFA Postdoc Seminar;
Sep. MSRI, GFA Young Researchers Seminar;
2016
2016
Feb. University of Wisconsin-Madison, Analysis Seminar;
Mar. AMS sectional meeting, Athens, GA;
Jul. Texas A&M University, Workshop in Analysis and Probability;
Sep. Michigan State University, Analysis and PDE Seminar;
Sep. University of Missouri (2 talks); Analysis Seminar; Convex Geometry Seminar;
Oct. The University of Akron, PDE and Applied mathematics seminar;
2015
2015
Jan. University of Helsinki, Analysis Seminar;
Feb. Cincinnati, the 5th Ohio River Analysis Meeting;
Apr. Chebyshev Laboratory at St. Petersburg State University, Russia;
Sep. Kent State University, Measure Theory Seminar;
Nov. Kent State University, Measure Theory Seminar;
2014
2014
Jun. Hausdorff institute of mathematics, Trimester program in harmonic analysis and PDE, Germany;
Jun. XXIII St.Petersburg Summer Meeting in Mathematical Analysis, Russia;
Nov. Kent State University, Measure Theory Seminar;
2013
2013
Oct. Summer School; Optimal Transport and Applications, UCLA;
Dec. Michigan State University, Analysis and PDE seminar;
2013
2013
Mar. Harmonic and Complex Analysis and its Applications, Tenerife, Canary Islands;
2012
2012
Jun. XX St.Petersburg Summer Meeting in Mathematical Analysis, Russia;
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