Paata Ivanisvili

Associate Professor, University of California, Irvine

Biography

Paata Ivanisvili is an Associate Professor in the Department of Mathematics at the University of California, Irvine. He obtained his Ph.D. in Mathematics from both Michigan State University and Saint Petersburg State University between 2011 and 2015. His professional journey includes positions as an Assistant Professor at North Carolina State University and a postdoctoral researcher at Princeton University and Kent State University. Ivanisvili joined UC Irvine as an Assistant Professor in 2018 and was promoted to Associate Professor in 2021.

Ivanisvili's research interests are concentrated in the areas of Analysis, Probability, Convex Geometry, and Discrete Approximation Theory. He has authored numerous peer-reviewed articles in reputable journals such as the Journal of Mathematical Sciences, Analysis & PDE, and the Journal of Functional Analysis. His work has received significant funding, including the NSF CAREER DMS grant for the period 2020-2025. Ivanisvili has also contributed to the organization of professional events, such as the upcoming dual trimester program on Boolean Analysis in Computer Science in Bonn, Germany, in Fall 2024.

At UC Irvine, Ivanisvili teaches a range of courses, including Functional Analysis and Probability. He has mentored several doctoral students and postdoctoral researchers, guiding them in their academic pursuits. Ivanisvili is actively involved in professional service, having served on various committees, such as the Analysis Qualifying Exam Committee and the Graduate Admissions & Advisory Committee. His contributions extend to the broader academic community through his participation in seminars and workshops worldwide.

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Degrees

PhD in Mathematics, Michigan State University, 2015
PhD in Mathematics, Saint Petersburg State University, 2015
BS, MS in Mathematics, Saint Petersburg State University, 2011

Distinctions

NSF CAREER DMS-2152401, 2020
NSF DMS-2152346, 2019

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Areas of Expertise

Mathematical Analysis
Probability Theory
Functional Analysis
Convex Geometry
Discrete Mathematics
Isoperimetric Inequalities
Hamming Cube
Bellman Functions
Hypercontractivity
Gaussian Measures

Recent Publications

Y. Stone, “The KKL inequality and Rademacher type 2”, Discrete Analysis, 2024.
L. Becker, D. Krachun, J. Madrid, “Discrete Brunn-Minkowski Inequality for subsets of the cube”, 2024.
Y. Stone, “Sharpening the gap between L 1 and L 2 norms”, 2024.
P. Durcik, J. Roos, “Sharp isoperimetric inequalities on the Hamming cube near the critical exponent”, 2024.
H. Zhang, “On the Eldan–Gross inequality”, 2024.
P. Kalantzopoulos, “(P, Q) hypercontractivity”, 2024.
A. Eskenazis, L. Streck, “Low-degree learning and the metric entropy of polynomials”, Discrete Analysis, 2023.
R. Russell, “Exponential integrability in Gauss space”, Analysis & PDE, vol. 16, no. 5, 2023.
A. Eskenazis, “Sharp growth of the Ornstein-Yhlenbeck operator on Gaussian tail spaces”, Israel Journal of Mathematics, vol. 253, pp. 469–485, 2023.
J. De Dios, R. Greenfeld, J. Madrid, “Additive Energies on Discrete Cubes”, Discrete Analysis, 2023.
D. Beltran, J. Madrid, “On sharp isoperimetric inequalities on the hypercube”, 2023.
D. Stolyarov, V. Vasyunin, P. Zatitskii, “Bellman functions on simple non-convex domains in the plane”, 2023.
O. Klein, R. Vershynin, “Covering the hypercube, the uncertainty and an interpolation formula”, 2023.
F. Nazarov, “On Weissler’s conjecture on the Hamming cube I”, IMRN, no. 9, pp. 6991-7020, 2022.
J. de Dios Pont, J. Madrid, “A new proof of the description of the convex hull of space curves with totally positive torsion”, 2022.
R. L. Frank, “Hypercontractivity of the semigroup of the fractional laplacian on the n- sphere”, Journal of Functional Analysis, vol. 281, no. 8, 2021.
A. Lindenberger, P. Muller, M. Schmuckenschlager, “Hypercontractivity on the unit circle for ultraspherical measures: linear case”, Revista Matematica Iberomareicana, vol. 38, no. 4, pp. 1335–1348, 2021.
A. Volberg, “Banach space valued Pisier and Riesz type inequalities on discrete cube”, 2021.
I. Holmes, A. Volberg, “The sharp constant in the weak (1,1) inequality for the square function: a new proof”, Revista Matematica Iberoamericana, vol. 36, no. 3, pp. 741–770, 2020.
E. A. Carlen, R. L. Frank, E. H. Lieb, “Inequalities in L p -norms that sharpen the triangle inequality and complement Hanner’s inequality”, J. Geom. Anal, 2020.
A. Eskenazis, “Dimension independent Bernstein–Markov inequalities in Gauss space”, Journal of Approximation Theory, vol. 253, 2020.
C. Mooney, “Sharpening the triangle inequality: envelopes between L2 and Lp spaces”, Anal. & PDE, vol. 13, no. 5, pp. 1591–1603, 2020.
F. Barthe, “Bobkov’s inequality via optimal control theory”, Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2256, Springer, 2020.
A. Volberg, “Poincaré inequality 3/2 on the Hamming cube”, Revista Mathematica Iberoamericana, 2019.
A. Volberg, “From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity”, Journal of Functional Analysis, vol. 276, no. 9, pp. 2716–2730, 2019.
S. Treil, “Superexponential estimates and weighted lower bounds for the square function”, Trans. Amer. Math. Soc., vol. 372, pp. 1139–1157, 2019.
S. Zbarsky, “Centered Hardy–Littlewood maximal operator on the real line: lower bounds”, Comptes Rendus Mathematique, vol. 357, no. 4, 2019.
“Boundary value problem and the Ehrhard inequality”, Studia Math., vol. 246, no. 3, pp. 257–293, 2019.
A. Volberg, “Isoperimetric functional inequalities via the maximum principle: the exterior differential systems approach”, 50 years with Hardy spaces, Birkhauser/Springer, Cham, pp. 281-305, 2018.
F. Nazarov, A. Volberg, “Square function and the Hamming cube: duality”, Discrete Analysis, vol. 1, pp. 18pp, 2018.
“Bellman function approach to the sharp constants in uniform convexity”, Adv. Calc. Var., vol. 11, no. 1, 2018.
P. Mozolyako, A. Volberg, “Strong weighted and restricted weak weighted estimates of the square function”, 2018.
D. Li, R. van Handel, A. Volberg, “Improving constant in end-point Poincare inequality on Hamming cube”, 2018.
A. Volberg, “Improving Beckner’s bound via Hermite functions”, Analysis & PDE, vol. 10, no. 4, pp. 929–942, 2017.
B. Jaye, F. Nazarov, “Lower bounds for uncentered maximal function in any dimensions”, Int. Math. Res. Notices, vol. 8, pp. 2464–2479, 2017.
F. Nazarov, A. Volberg, “Hamming cube and martingales”, Comptes Rendus Mathematique, vol. 355, no. 10, pp. 1072–1076, 2017.
“Convolution estimates and number of disjoint partitions”, The Electronic Journal of Combinatorics, vol. 24, no. 2, pp. Paper #P2.43, 2017.
A. Volberg, “Martingale transform and Square function: some end-point weak weighted estimates”, 2017.
P. B. Zatitskiy, D. M. Stolyarov, “Bellman VS Beurling: sharp estimates of uniform convexity for Lp spaces”, St. Petersburg Math. J., vol. 27, pp. 333–343, 2016.
“A bundling problem revisited”, 2016.
“Inequality for Burkholder’s martingale transform”, Analysis & PDE, vol. 8, no. 4, pp. 765–806, 2015.
F. Nazarov, A. Volberg, “On weak and strong sharp weighted estimates of square function”, 2015.
A. Volberg, “Bellman partial differential equation and the hill property for classical isoperimetric problems”, 2015.
“J-closed finite collections of Hardy-type subspaces”, Journal of Mathematical Sciences, vol. 194, no. 6, pp. 645–650, 2013.
N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, “Sur la fonction de Bellman pour des problèmes extémaux sur l’espace BMO”, Comptes Rendus Mathematique, vol. 350, no. 11-12, pp. 561–564, 2012.
S. Kislyakov, “Correction up to a function with sparse spectrum and uniformly convergent Fourier series”, Journal of Mathematical Sciences, vol. 172, no. 2, pp. 195–206, 2011.

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Most Cited Publications

N. N. Osipov, D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, “Bellman function for extremal problems in BMO”, Trans. Amer. Math. Soc., vol. 368, pp. 3415–3468, 2016.
Ivanishvili P., Osipov N.N., Stolyarov D.M., Vasyunin V.I., Zatitskiy P.B., “On Bellman function for extremal problems in BMO”, Comptes Rendus Mathematique, vol. 350, pp. 561-564, 2012.
A. Eskenazis, “Learning low-degree functions from a logarithmic number of random queries”, pp. 203–207, 2022. Presented at 54th Annual ACM SIGACT Symposium on Theory of Computing, June 2022.
R. van Handel, S. Volberg, “Rademacher type and Enﬂo type coincide”, Annals of Math, vol. 192, no. 2, pp. 665–678, 2020.
D. Stolyarov, V. Vasyunin, P. Zatitskiy, “Bellman function for extremal problems in BMO II: evolution”, Mem. Amer. Math. Soc., vol. 255, no. 1220, pp. 0–133, 2018.
A. Eskenazis, “Polynomial inequalities on the Hamming cube”, Probability Theory and Related Fields, vol. 178, pp. 235-287, 2020.
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, no. 12, pp. 1081–1085, 2015.
A. Volberg, “Hessian of Bellman functions and uniqueness of Brascamp–Lieb inequality”, J. London Math. Soc., vol. 92, no. 3, pp. 657–674, 2015.
K. Domelevo, S. Petermichl, S. Treil, A. Volberg, “On the failure of lower square function estimates in the non-homogeneous weighted setting”, Math. Ann., vol. 374, pp. 1923–1952, 2019.
T. Tkocz, “Comparison of moments of Rademacher chaoses”, Arkiv för Matematik, vol. 5, no. 1, 2019.

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Contact Information

Website: https://sites.google.com/view/paata

Email: pivanisv@uci.edu

Address: Department of Mathematics, University of California, Irvine

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This profile was last updated on 2/14/2025.

This profile was created with the help of AI.