# Leonid Slavin

## Associate Professor

## Associate Professor

### French Hall

5428E

A&S Mathematical Sciences - 0025

## Education

Ph.D.: Michigan State University East Lansing, MI, 2004 (Mathematics)

M. Sc.: St.-Petersburg State Technical University St.-Petersburg, Russia, 1996 (Engineering)

## Research and Practice Interests

Euclidean harmonic analyss: singular integral operators, maximal functions, square functions, Hardy spaces, and BMO. The main focus has been on Bellman functions and the related questions of transference between results for martingales and their continuous analogs. Most recent interests are in Monge-Ampere equations arising in Bellman contexts and connections between the geometry of developable surfaces and optimizers in sharp inequalities; geometric measure theory (Erdos--Falconer conjecture); quasi-conformal and quasi-regular mappings (Beurling--Ahlfors transform); dimension-free action of Fourier multipliers on BMO and sharp interpolation using BMO; exponential estimates on trees; and two-weight Bellman treatment of classical dyadic operators.

## Positions and Work Experience

2016 -To Present Associate Professor, University of Cincinnati, Cincinnati, OH

2009 -2016 Assistant Professor, University of Cincinnati, Cincinnati, OH

2008 -2008 Member, Fields Institute, University of Toronto, Toronto, Canada

2007 -2009 Postdoctoral fellow, University of Missouri, Columbia, MO

2004 -2007 Postdoctoral fellow, University of Connecticut, Storrs, CT

## Research Support

Grant: #317925 Investigators:Slavin, Leonid 09-01-2014 -08-31-2019 Simons Foundation Bellman functions, Monge-Ampere equations, and sharp integral estimates Role:PI $35,000.00 Active Type:Grant Level:National

Grant: #DMS-1001567 Investigators:Leonid Slavin 07-01-2010 -08-31-2014 NSF, Division of Mathematical Sciences Weighted, non-local, and product-type Bellman estimates in Harmonic Analysis Role:PI $144,000 Completed Type:Grant Level:National

Grant: #DMS-1041763 Investigators:Leonid Slavin (PI), Wolodymyr Madych (co-PI) 07-01-2007 -06-30-2011 NSF, Division of Mathematical Sciences Topics in pure and applied harmonic analysis Role:PI $120,000 Completed Type:Grant Level:National

Grant: #DMS-1412170 Investigators:Goldberg, Michael; Slavin, Leonid 02-01-2014 -01-31-2017 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2014-2016 Role:co-PI $15,408.00 Active Type:Grant Level:Regional

Grant: #DMS-1305523 Investigators:M. Goldberg, L. Slavin 02-01-2013 -01-31-2014 NSF, Division of Mathematical Sciences The 2013 Ohio River Analysis Meeting Role:co-PI $10,000 Completed Type:Grant Level:Regional

Investigators:L. Slavin 06-2014 -08-2014 Taft Research Center Taft Summer Research fellowship "Bellman functions in harmonic analysis: new frontiers" $8,500 Completed Type:Fellowship Level:University

Investigators:Leonid Slavin, Vasily Vasyunin 01-01-2011 -03-31-2011 Taft Foundation Taft Research Seminar "Bellman function method in harmonic analysis" Role:convener $16,000 Completed Type:Grant Level:University

Grant: #DMS-1700077 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 02-01-2017 -01-31-2020 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2017-2019 Role:Collaborator $14,000.00 Active Level:Federal

Grant: #DMS-2000161 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 02-01-2020 -01-31-2023 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2020-2022 Role:PI $16,000.00 Awarded Level:Federal

Grant: #711643 Investigators:Slavin, Leonid 09-01-2020 -08-31-2025 Simons Foundation Sharp integral estimates and dimensional analysis using Bellman functions Role:PI $42,000.00 Awarded Level:Private Non-Profit

## Abbreviated Publications

### Peer Reviewed Publications

**Best constants for a family of Carleson sequences**, *Adv. Math.*, **289** (2016), pp. 685-724

**The John--Nirenberg constant of BMO^p, p>2 **(with V. Vasyunin), *Alegbra i Analiz*, **28** (2016), no. 2, pp. 72-96 (Russian). Translation to appear in *St. Petersburg Math. J. *

**Inequalities for BMO on alpha-trees** (with V. Vasyunin), *Int. Math. Res. Notices, *(2016) , no. 13, pp. 4708-4102

**Weak integral conditions for BMO** (with A. Logunov, D. Stolyarov, V. Vasyunin, and P. Zatitskiy). *Proc. Amer. Math. Soc.*, **143**(7) (2015), pp. 2913-2926

**Sharp L^p estimates on BMO** (with V. Vasyunin), *Indiana U. Math. J.,* **61**(3) (2012), pp. 1051-1110

**Sharp results in the integral-form John--Nirenberg inequality** (with V. Vasyunin), *Trans. Amer. Math. Soc.*, **363**(8) (2011), pp. 4135-4169

**New estimates for the Beurling--Ahlfors operator on differential forms** (with S. Petermichl and B. Wick), *J. of Operator Theory*, **65**(2) (2011), pp. 307-324

**Monge--Ampere equations and Bellman functions: the dyadic maximal operator**, (with A. Stokolos and V. Vasyunin), *C. R. Acad. Sci. Paris, Ser. I* **346** (2008), pp. 585-588

**The s-function and the exponential integral*** (*with A. Volberg*)*, *Contemporary Mathematics*, **444** (2007), pp. 215-228

**Bellman function and the H^1--BMO duality*** *(with A. Volberg), *Contemporary Mathematics* **428** (2007), pp. 113-126

### Other Publication

Cincinnati Lectures on Bellman Functions, by V. Vasyunin, edited by L. Slavin

The John--Nirenberg constant of BMO^p, 1<= p<= 2, pp. 1-27. Submitted.

## Courses Taught

15-MATH-226 APPLIED CALC I Level:Undergraduate

15-MATH-251 CALCULUS I Level:Undergraduate

15-MATH-252 CALCULUS II Level:Undergraduate

15-MATH-264 CALC & AN GEOM IV Level:Undergraduate

15-MATH-273 DIFFERENTIAL EQNS Level:Undergraduate

ADV. TECH. CALCULUS Level:Undergraduate

15-MATH-351 LINEAR ALGEBRA I Level:Undergraduate

15-MATH-408 INTRO ANALYSIS I Level:Undergraduate

15-MATH-7002 REAL ANALYSIS Level:Graduate