It's me
Paata Ivanisvili (aka Ivanishvili)
Rowland Hall, Room 510K
Department of Mathematics
University of California, Irvine
Irvine, CA 92697
(949) 824-7121


Visiting Positions


Research Interests

Analysis, Probability, PDE, and Geometry


My new blog "Zeros and Ones"

New "Harmonic Analysis Seminar" at UC Irvine

Slides of my talks


My research is currently supported by the


- NSF DMS-1856486
- NSF CAREER DMS-1945102


  1. 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)
  2. with N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Bellman function for extremal problems on BMO, Comptes Rendus Mathematique, Volume 350, Issues 11-12, Pages 561-564, June (2012)
  3. J-closed finite collections of Hardy-type subspaces, Zap. Nauchn. Sem. POMI, Vol. 401, 82-92 (2012)
  4. with N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Bellman function for extremal problems in BMO, Trans. Amer. Math. Soc (2015) doi:
  5. Inequality for Burkholder's martingale transform. Analysis & PDE 8-4 (2015), 765--806. DOI 10.2140/apde.2015.8.765
  6. Bellman function approach to the sharp constants in uniform convexity. Advances in Calculus of Variations DOI: 10.1515/acv-2016-0008, August 2016
  7. 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
  8. with A. Volberg, Hessian of Bellman functions and uniqueness of Brascamp--Lieb inequality, J. London Math. Soc. (2015), doi:10.1112/jlms/jdv040
  9. 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
  10. with A. Volberg, Bellman partial differential equation and the hill property for classical isoperimetric problems (2015)
  11. 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 (138 pages)
  12. with A. Volberg, Isoperimetric functional inequalities via the maximum principle: the exterior differential systems approach. (2015) V. P. Havin's volume
  13. A bundling problem revisited. preprint, (2016)
  14. with B. Jaye F. Nazarov, Lower bounds for uncentered maximal functions in any dimension, Int. Math. Res. Notices Vol. 2016, Issue 00, 2016
  15. Boundary value problem and the Ehrhard inequality, Studia Mathematica 246 (3) (2019)
  16. with A. Volberg, Improving Beckner's bound via Hermite functions, Anal. PDE, Vol. 10, No. 4 (2017), 929--942
  17. with A. Volberg, F. Nazarov, On weak and strong sharp weighted estimates of square function , preprint (2016)
  18. with A. Volberg, Poincare inequality 3/2 on the Hamming cube, Rev. Mat. Iberoam. (2019)
  19. with K. Domelevo, S. Petermichl, S. Treil, A. Volberg, On the failure of lower square function estimates in the non-homogeneous weighted setting accepted to Mathematische Annalen
  20. Convolution estimates and number of disjoint partitions, The Electronic Journal of Combinatorics, Volume 24, Issue 2 (2017), Paper #P2.43
  21. with F. Nazarov, A. Volberg, Square function and the Hamming cube: duality, Discrete Analysis 2018:1, 18 pp.
  22. with A. Volberg, From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity, accepted to JFA
  23. 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)
  24. with F. Nazarov, A. Volberg, Hamming cube and martingales, Comptes Rendus Mathematique, Vol. 355, Iss. 10, (2017), pp. 1072--1076
  25. with S. Treil, Superexponential estimates and weighted lower bounds for the square function, accepted to Trans. Amer. Math. Soc. (2018)
  26. with A. Volberg, Martingale transform and Square function: some end-point weak weighted estimates, (2017)
  27. with F. Barthe, Bobkov's inequality via optimal control theory accepted to GAFA seminars
  28. with P. Mozolyako, A. Volberg, Strong weighted and restricted weak weighted estimates of the square function, (2018)
  29. with T. Tkocz, Comparison of moments of Rademacher chaoses, accepted to Arkiv for Matematik (2018)
  30. with S. Zbarsky, Centered Hardy--Littlewood maximal operator on the real line: lower bounds, (2018) accepted to Comt. Rend. Math.
  31. with A. Eskenazis, Dimension independent Bernstein--Markov inequalities in Gauss space, (2019) accepted to Journal of Approximation Theory.
  32. with E. A. Carlen, R. L. Frank, E. H. Lieb, Inequalities for Lp-norms that sharpen the triangle inequality and complement Hanner's inequality, accepted to Journal of Geometric Analysis
  33. with D. Li, R. van Handel, A. Volberg, Improving constant in end-point Poincare inequality on Hamming cube, (2018)
  34. with C. Mooney, Sharpening the triangle inequality: envelopes between L2 and Lp spaces, accepted to Analysis & PDE
  35. with A. Eskenazis, Polynomial inequalities on the Hamming cube, accepted to Probability Theory and Related Fields
  36. with F. Nazarov, On Weissler's conjecture on the Hamming cube I, (2019)
  37. with R. van Handel, A. Volberg, Rademacher type and Enflo type coincide, (2020)
  38. with A. Lindenberger, P. F. X. Müller, M. Schmuckenschläger, Hypercontractivity on the unit circle for ultraspherical measures: linear case, (2020)
  39. with R. Russell, Exponential integrability for log-concave measures, (2020)

Synergistic activities

    - 2021--2025: Yearly Summer School API (Analysis and Probability in Irvine) funded through my NSF CAREER award.
    - 6/2021: Co-organizing AIM workshop, San Jose, CA.
    - 5/2020: Grand Awards Judge ISEF 2020 in Anaheim, CA. (Cancelled COVID-19)
    - 2019--present: Co-organizing Harmonic Analysis Seminar at UC Irvine, CA.
    - 5/2019: curriculum for Math CEO at UCI: Pentominoes Game.
    - 9/2018: Co-organized workshop Discrete Structures: Harmonic Analysis and Probability at Clay Math. Institute, UK.



  1. July. Real Analysis, Harmonic Analysis and Applications. Oberwolfach, Germany; (Cancelled COVID-19)
  2. July. Contemporary Analysis and Its Applications. Slovenia; (Cancelled COVID-19)
  3. May. France; (Cancelled COVID-19)


  1. Feb. Kent State University, Colloquium Talk and Analysis seminar talk
  2. March. AMS sectional meeting Hawaii, Honolulu;
  3. April. Caltech, joint UCLA/Analysis seminar;
  4. May. HIM, Trimester program, Harmonic analysis, Bonn, Germany;
  5. May. AIM, San Jose;
  6. May. Geometric and Functional inequalities in Convexity and Probability, Florence, Italy
  7. June. CMS meeting, Probabilistic Methods in Geometric Functional Analysis and Convexity, Regina, Canada;
  8. June. Operators, Functions, and Systems of Mathematical Physics Conference, Baku, Azerbaijan;
  9. June. St. Petersburg Summer Meeting in Analysis, Russia;
  10. Sep. Conference, Batumi, Georgia;
  11. Sep. Aristotle University of Thessaloniki, Analysis Seminar, Greece;
  12. Sep. AMS Sectional meeting, Wisconsin--Madison;
  13. Nov. AMS Sectional meeting, University of Flroida, Gainesville;
  14. Dec. Workshop in convexity and geometric aspects of harmonic analysis, Georgia Tech;


  1. Feb. Princeton University; Analysis Seminar;
  2. Feb. Princeton University; Probability Seminar;
  3. Feb. Simons Collaboration on Algorithms & Geometry;
  4. Feb. Georgia Tech.; Analysis Seminar;
  5. Mar. Carnegie Mellon University; Combinatorics Seminar;
  6. May. International conference dedicated to the memory of Sergey Mergelyan, Armenia;
  7. May. Aristotle University of Thessaloniki, Analysis Seminar, Greece;
  8. Jul. PCMI, Harmonic Analysis;
  9. Sep. IX International Conference of the Georgian Mathematical Union, Batumi, Georgia;
  10. Sep. Clay Math. Institute, Discrete Structures: Harmonic Analysis and Probability;


  1. Apr. MSRI, HA Postdoc Seminar;
  2. Sep. MSRI, GFA Postdoc Seminar;
  3. Sep. MSRI, GFA Young Researchers Seminar;


  1. Feb. University of Wisconsin-Madison, Analysis Seminar;
  2. Mar. AMS sectional meeting, Athens, GA;
  3. Jul. Texas A&M University, Workshop in Analysis and Probability;
  4. Sep. Michigan State University, Analysis and PDE Seminar;
  5. Sep. University of Missouri (2 talks); Analysis Seminar; Convex Geometry Seminar;
  6. Oct. The University of Akron, PDE and Applied mathematics seminar;


  1. Jan. University of Helsinki, Analysis Seminar;
  2. Feb. Cincinnati, the 5th Ohio River Analysis Meeting;
  3. Apr. Chebyshev Laboratory at St. Petersburg State University, Russia;
  4. Sep. Kent State University, Measure Theory Seminar;
  5. Nov. Kent State University, Measure Theory Seminar;


  1. Jun. Hausdorff institute of mathematics, Trimester program in harmonic analysis and PDE, Germany;
  2. Jun. XXIII St.Petersburg Summer Meeting in Mathematical Analysis, Russia;
  3. Nov. Kent State University, Measure Theory Seminar;


  1. Oct. Summer School; Optimal Transport and Applications, UCLA;
  2. Dec. Michigan State University, Analysis and PDE seminar;


  1. Mar. Harmonic and Complex Analysis and its Applications, Tenerife, Canary Islands;


  1. Jun. XX St.Petersburg Summer Meeting in Mathematical Analysis, Russia;