Employment

• 2021 -- Associate Professor, University of California, Irvine, CA

• 2020 -- 2021 Assistant Professor, North Carolina State University, NC

• 2018 --2020 Assistant Professor, University of California, Irvine, CA

• 2017 -- 2018 Postdoctoral Researcher, Princeton, NJ

• 2017 - Postdoctoral Fellow, MSRI, Berkeley, CA

• 2015--2016 - Postdoctoral Researcher, Kent State University , Kent, OH

Visiting Positions

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

• 2011--2013 - Research Engineer, Chebyshev Laboratory at Saint Petersburg State University, Russia

Education

• 2015 - PhD, Mathematics, Michigan State University

• 2011 - BS, Mathematics, Saint Petersburg State University, Diploma with high distinctions

Awards

My research is currently supported by the NSF:

- 2021 - John Griggs Faculty Award, NC State
- 2021--2025  NSF CAREER DMS-2152401
- 2019--2022 NSF DMS-2152346 

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, 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)

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., Memoirs of the American Mathematical Society

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, Comptes Rendus Mathematique, Volume 357, Issue 4, (2019)

31. with A. Eskenazis, Dimension independent Bernstein--Markov inequalities in Gauss space, Journal of Approximation Theory, Volume 253, (2020).

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, The Journal of Geometric Analysis (2020)

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, Anal. PDE, Volume 13, Number 5 (2020)

35. with A. Eskenazis, Polynomial inequalities on the Hamming cube, Probab. Theory Relat. Fields 178, 235–287 (2020)

36. with F. Nazarov, On Weissler's conjecture on the Hamming cube I,  IMRN (2020)

37. with R. van Handel, A. Volberg, Rademacher type and Enflo type coincide, Annals of Mathematics,  Vol. 192, No. 2 (2020)

38. with A. Lindenberger, P. F. X. Müller, M. Schmuckenschläger, Hypercontractivity on the unit circle for ultraspherical measures: linear case, (2020). Revista Matematica Iberoamericana 

39. with R. Russell, Exponential integrability for log-concave measures, (2020) Analysis & PDE

40. with A. Eskenazis, Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces (2020),  Israel Journal of Mathematics

41. with R. L. Frank, Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere (2021), Journal of Functional Analysis

42. with A. Volberg, Banach space valued Pisier and Riesz type inequalities on discrete cube (2021)

43. with A. Eskenazis, Learning low-degree functions from a logarithmic number of random queries,  STOC 2022.

44. with J. de Dios Pont, R. Greenfeld, J. Madrid, Additive Energies on Discrete Cubes (2021). Discrete Analysis Journal. 

45. 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)

46. with A. Eskenazis, L. Streck,  Low-degree learning and the metric entropy of polynomials. Discrete Analysis Journal. 

47. with Y. Stone, The KKL inequality and Rademacher type 2. Discrete Analysis Journal

48. with D. Beltran, J. Madrid, On sharp isoperimetric inequalities on the hypercube (2023)

49. with D. Stolyarov, V. Vasyunin, P. Zatitskii, Bellman functions on simple non-convex domains in the plane (2023)

50. with O. Klein, R. Vershynin , Covering the hypercube, the uncertainty principle, and an interpolation formula (2023)

51. with L. Becker, D. Krachun, J. Madrid, Discrete Brunn-Minkowski Inequality for subsets of the cube (2024)

52. with Y. Stone, Sharpening the gap between L1 and L2 norms (2024)

Students at UCI

- 2023 -- present: Lekha Patil.
- 2023 -- present: Xinyuan Xie.
- 2022 -- present: Natanael Alpay.
- 2022 -- present: Yonathan Stone.
- 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

- 2022 -- 2023: Haonan Zhang. Now tenure-track assistant professor at University of South Carolina.
- 2023 -- 2025: Pavlos Kalantzopoulos. 

Conference organization

• Dual trimester program at HIM, Boolean Analysis in Computer Science, Fall 2024, Germany. 

•  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 beyond

• 2022: SQuaREs, San Jose, CA.

•  6/2022: 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.

Talks (last update 12/12/2022)

2022

1. Feb, IPAM, UCLA. [video]

2. Mar. Colloquium, University Of Hawaii

3. Mar. AGT&A Seminar. [video]

4. Jun. AIM workshop, San Jose. 

5. Sep. ICERM. Brown. [video]

6. Oct. ICERM. Brown. [video]

7. Dec. ICERM. Brown. [video]

2021

1. Jan. Functional Analysis Seminar, IMPAN, Poland [slides]

2. Feb. International Society of Georgian Scientists (ISGS)

3. Feb. Tbilisi Analysis & PDE Seminar. 

4. Mar. Colloquium, University of Massachusetts Lowell

5. Mar.  Probability/Statistics seminar at University of Southern California. [video], [slides]

6. Mar. Purdue analytic number theory and harmonic analysis (PANTHA).

7. Mar. Probability seminar at University of Illinois at Urbana-Champaign.

8. Mar. Analysis Seminar, University of Missouri. 

9. Oct. Combinatorics and Probability, UCI. 

10. Nov. Discrete Harmonic and Harmonic Analysis Seminar, University of Wuerzburg. 

11. Nov. Analysis Seminar, Chapman University. 

2020

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)

4. Aug. "Concentration Week at Texas A&M". 

5. Sep. Banach Spaces Webinar, "Sharpening the triangle inequality" [video]

6. Oct. Online Asymptotic Geometric Analysis Seminar, [slides]

7. Oct. Duke University.

8. Nov. Indiana University Bloomington [slides]

9. Nov. NC state

10. Nov. Corona Seminar, "Rademacher and Enflo type coincide" [video]

11. Dec. UCLA [slides]

2019

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 Florida, Gainesville;

14. Nov. Colloquium, Washington University in St. Louis, Missouri;

15. Dec. Workshop in convexity and geometric aspects of harmonic analysis, Georgia Tech;

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;