People in the Department

< Back to list

Leonid Slavin

Title: Associate Professor
Office: 5428E French Hall
Tel: 513-556-4125
Email: leonid.slavin@uc.edu
Web: http://homepages.uc.edu/~slavinld

Education

  • Ph.D., Michigan State University, East Lansing, MI, 2004 (Mathematics).
  • M. Sc., St.-Petersburg State Technical University, St.-Petersburg, Russia, 1996 (Engineering).

Research Information

Research 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.

Research Support

  • (PI), Slavin, Leonid, Bellman functions, Monge-Ampere equations, and sharp integral estimates , Simons Foundation. (317925), $35,000.00. 09/01/2014 to 08/31/2019. Status: Active.
  • (PI), Leonid Slavin, Weighted, non-local, and product-type Bellman estimates in Harmonic Analysis, NSF, Division of Mathematical Sciences. (DMS-1001567), $144,000. 07/01/2010 to 08/31/2014. Status: Completed.
  • (PI), Leonid Slavin (PI), Wolodymyr Madych (co-PI), Topics in pure and applied harmonic analysis, NSF, Division of Mathematical Sciences. (DMS-1041763), $120,000. 07/01/2007 to 06/30/2011. Status: Completed.
  • (co-PI), Goldberg, Michael; Slavin, Leonid, Collaborative Research: Ohio River Analysis Meetings 2014-2016, National Science Foundation. (DMS-1412170), $15,408.00. 02/01/2014 to 01/31/2017. Status: Active.
  • (co-PI), M. Goldberg, L. Slavin, The 2013 Ohio River Analysis Meeting, NSF, Division of Mathematical Sciences. (DMS-1305523), $10,000. 02/01/2013 to 01/31/2014. Status: Completed.
  • L. Slavin, Taft Summer Research fellowship "Bellman functions in harmonic analysis: new frontiers", Taft Research Center. $8,500. 06-2014 to 08-2014. Status: Completed.
  • (convener), Leonid Slavin, Vasily Vasyunin, Taft Research Seminar "Bellman function method in harmonic analysis", Taft Foundation. $16,000. 01/01/2011 to 03/31/2011. Status: Completed.
  • (Collaborator), Goldberg, Michael; Slavin, Leonid; Speight, Gareth, Collaborative Research: Ohio River Analysis Meetings 2017-2019, National Science Foundation. (DMS-1700077), $14,000.00. 02/01/2017 to 01/31/2020. Status: Active.
  • (Collaborator), Goldberg, Michael; Slavin, Leonid; Speight, Gareth, Collaborative Research: Ohio River Analysis Meetings 2017-2019, National Science Foundation. (DMS-1700077), $14,000.00. 02/01/2017 to 01/31/2020. Status: Active.
  • (Collaborator), Goldberg, Michael; Slavin, Leonid; Speight, Gareth, Collaborative Research: Ohio River Analysis Meetings 2017-2019, National Science Foundation. (DMS-1700077), $14,000.00. 02/01/2017 to 01/31/2020. Status: Active.
  • (Collaborator), Goldberg, Michael; Slavin, Leonid; Speight, Gareth, Collaborative Research: Ohio River Analysis Meetings 2017-2019, National Science Foundation. (DMS-1700077), $14,000.00. 02/01/2017 to 01/31/2020. Status: Active.

Publications

Peer Reviewed Publications

  • Best constants for a family of Carleson sequences, Adv. Math., 289 (2016), pp. 685-724[Link]
  • 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. [Link]
  • Inequalities for BMO on alpha-trees (with V. Vasyunin), Int. Math. Res. Notices, (2016) , no. 13, pp. 4708-4102[Link]
  • 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 Publications

  • Cincinnati Lectures on Bellman Functions, by V. Vasyunin, edited by L. Slavin[Link]
  • The John--Nirenberg constant of BMO^p, 1<= p<= 2, pp. 1-27. Submitted.[Link]

Experience & Service

Work Experience

  • 2016 to Present, Associate Professor, University of Cincinnati, Cincinnati, OH.
  • 2009 to 2016, Assistant Professor, University of Cincinnati, Cincinnati, OH.
  • 2008 to 2008, Member, Fields Institute, University of Toronto, Toronto, Canada.
  • 2007 to 2009, Postdoctoral fellow, University of Missouri, Columbia, MO.
  • 2004 to 2007, Postdoctoral fellow, University of Connecticut, Storrs, CT.

Events Organized

  • Conference. Ohio River Analysis Meeting 2011-2017 (2011 to 2017) , University of Cincinnati, Cincinnati, OH (odd years), University of Kentucky, Lexington, KY (even years).
  • AMS Special Session "Sharp inequalities and Bellman functions in Harmonic Analysis", Spring Southeastern sectional meeting (03/05/2016 to 03/06/2016) , University of Georgia, Athens, GA.
  • Workshop. Taft Research Seminar "Bellman function method in harmonic analysis" (01/05/2011 to 03/20/2011) , University of Cincinnati.
  • Workshop. Bellman function satellite conference (01/31/2011 to 01/31/2011) , University of Cincinnati.

Courses Taught

  • 15-MATH-226 APPLIED CALC I
    Level: Undergraduate
    Term: 09A

  • 15-MATH-251 CALCULUS I
    Level: Undergraduate
    Term: 09A

  • 15-MATH-252 CALCULUS II
    Level: Undergraduate
    Term: 10W

  • 15-MATH-264 CALC & AN GEOM IV
    Level: Undergraduate
    Term: 10A

  • 15-MATH-273 DIFFERENTIAL EQNS
    Level: Undergraduate
    Term: 11A

  • ADV. TECH. CALCULUS
    ADV. TECH. CALCULUS
    Level: Undergraduate
    Term: 11A

  • 15-MATH-351 LINEAR ALGEBRA I
    Level: Undergraduate
    Term: 12W

  • 15-MATH-408 INTRO ANALYSIS I
    Level: Undergraduate
    Term: 12W

  • 15-MATH-7002 REAL ANALYSIS
    Level: Graduate
    Term: 12FS

Open Positions
View Opportunities
Update Personal Profile
eProfessional