Paata Ivanisvili (aka Ivanishvili)   Fine Hall, Room 102 Department of Mathematics Princeton University Princeton, NJ 08544 USA e-mail: paatai@math.princeton.edu

Employment

• 2017 -- Postdoctoral Researcher, Princeton University, Princeton, NJ
• 2017 (Spring and Fall) - Postdoctoral Fellow, MSRI; 1) Harmonic Analysis. 2) Geometric Functional Analysis and Applications. Berkeley, CA
• 2015--2016 (and Summer 2017) - Postdoctoral Researcher, Kent State University, Kent, OH
• 2011--2013 - Research Engineer, Stanislav Smirnov's Chebyshev Laboratory at Saint Petersburg State University, Russia

Visiting Positions

• Summer 2014 -- Visiting Scholar Position, Hausdorff Research Institute of Mathematics, Bonn, Germany

Education

• 2013--2015 - PhD, Mathematics, Michigan State University
• 2011--2015 - PhD, Mathematics, Saint Petersburg State University
• 2006--2011 - MS, Mathematics, Saint Petersburg State University, Diploma with high distinctions

Research Interests

Papers

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: dx.doi.org/10.1090/tran/6460
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., 148 pages, to appear in Memoirs of the AMS
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, (2016) accepted to Studia Math.
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, (2016)
19. with K. Domelevo, S. Petermichl, S. Treil, A. Volberg, On the failure of lower square function estimates in the non-homogeneous weighted setting, (2017)
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, accepted to Discrete Analysis (2017)
22. with A. Volberg, From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity, (2017)
23. with I. Holmes, A. Volberg, The sharp constant in the weak (1,1) inequality for the square function: a new proof, (2017)
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, (2017)
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, (2017)
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)
31. with A. Eskenazis, Dimension independent Bernstein--Markov inequalities in Gauss space, (2018)
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, (2018)

Talks

2019

1. Mar. AMS Sectional Meeting; Hawaii;
2. May. San Jose; AIM.
3. May. Florence; Italy.
4. Jul-Aug. Tel Aviv, Israel;

2018

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;

2017

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

2016

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;

2015

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;

2014

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;

2013

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

2013

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

2012

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