Department of Mathematical Sciences

327 Mathematics and Computer Sciences Bldg

Kent State University Kent, OH, 44242 USA

Phone: (330)-672-3316

*e-mail:*zvavitch@math.kent.edu

*URL:*http://www.math.kent.edu/~zvavitch

- Citizenship
- Israel, Russia, USA.
- Born
- 06.09.1974, Moscow, Russia
- Marital Status
- married + 3.
- Wife: Tatiana Zvavitch
- Children: daughters Polina (born June 22, 1994), Maya (born August 5, 1999) and Anna (born April 1, 2011).

### Fields of interest:

- Convex Geometry
- Geometric Functional Analysis
- and applications of Probability and Harmonic Analysis to the above subjects.

### Education:

**1996-2001:**Ph.D. student of*Gideon Schechtman*, Weizmann Institute of Science, Department of Mathematics, (Rehovot, Israel).**1994-1996:**M.Sc. student of*Oded Schramm*, Weizmann Institute of Science, Department of Mathematics, (Rehovot, Israel).**1991-1994:**B.Sc. student, Moscow State University, Mechanics and Mathematics Department, (Moscow, Russia).**1991:**Graduated Moscow School # 67, (Moscow, USSR).

### Appointments:

**2014 - present:**Professor, Department of Mathematical Sciences, Kent State University.**2007-2014:**Associate Professor, Department of Mathematical Sciences, Kent State University.**2004-2007:**Assistant Professor, Department of Mathematical Sciences, Kent State University.**2001-2004:**Post Doctoral Fellow, Mathematics Department, University of Missouri-Columbia.

### Visiting Positions:

**May-June 2013**Visiting Professor, Universite Paris-Est Marne-la-Valle, France.**June-July 2012**Feinberg Foundation Visiting Faculty, Weizmann Institute of Science, Israel.**May-June 2011**Visiting Professor, Universite Paris-Est Marne-la-Valle, France.-
**Jan-Feb 2011**Visiting Fellow, Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K..

### Awards/Research Grants:

**2015**Oberwolfach Research in Pairs Grant. Awarded by Mathematisches Forschungsinstitut Oberwolfach. (with A. Koldobsky, D. Ryabogin and V. Yaskin).**2014-2015**National Science Foundation Grant: "CBMS Conference: Introduction to the theory of valuations on convex sets." Grant number DMS-1444411, Amount $35,000 (joint with B. Jaye, and D. Ryabogin).**2014-2015**National Science Foundation Grant: "Kent State Informal Analysis Seminar," Grant number DMS-1400019, Amount 45,000 (joint with Benjamin Jaye, Fedor Nazarov and Dmitry Ryabogin).**2011-2014**Harmonic Analysis in Convex Geometry. National Science Foundation Grant DMS-1101636, Amount 375,000 (joint with Dmitry Ryabogin).**2011**NSF/CBMS Regional Conference in the Mathematical Sciences- "Ergodic Methods in the Theory of Fractals", Amount 40,000 (joint with Dmitry Ryabogin).**2007-2010**FRG: Collaborative Research: Fourier analytic and probabilistic methods in geometric functional analysis and convexity. Grant number DMS-0652684, Amount 150,000.**2005-2008**Fourier Analytic Approach to the Geometric Tomography. National Science Foundation Grant DMS-0504049, Amount 79,626.**2006-2008**Supplement to the above NSF DMS-0504049 grant for graduate student support, Amount 13,000.**2006**NSF/CBMS Regional Conference in the Mathematical Sciences-"Probabilistic and combinatorial approach in analysis"-08/06/2006-08/13/2006, Amount 32,985 (joint with Per Enflo and Andrew Tonge).-
**2005**Summer Research and Creative Activity Appointment (Kent State). **1999-2000**Ben and Esther Rosenbloom Foundation Scholarship.**1996-2000**John F. Kennedy Memorial Fund Scholarship.

### Graduate Students:

- Matthew Alexander (Ph.d.) 2013- present
- Galyna Livshyts (Ph.d), 2011 - Spring 2015 (expected) (Assistant Professor, Georgia Institute of Technology starting Fall 2015).
- Jeffrey Schlaerth (Ph.d), 2005-present.
- Jaegil Kim (Ph.d), 2008 -2013 (currently PIMS postdoctoral fellow at the University of Alberta, Canada).
- Wei Bai (M.Sc), 2013-2014.
- Yuanyuan Peng (M.Sc), 2015- present.

### Publications/Preprints:

- "Bezout Inequality for Mixed volumes," (with Ivan Soprunov),
**submitted.** - "On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalitiess," (with Galyna Livshyts,
Arnaud Marsiglietti and
Piotr Nayar),
**submitted.** - An isomorphic
version of the Busemann-Petty problem for arbitrary measures.
(with Alexander
Koldobsky),
**Geometriae Dedicata,**Volume 174, Issue 1 (2015), 261-277. - Stability of the
reverse Blaschke-Santalo inequality for unconditional convex
bodies. (with Jaegil Kim),
**Proceedings of the American Mathematical Society,**143 (2015), 1705-1717. - A Remark on the Extremal Non-Central Sections of
the Unit Cube. (with James Moody, Corey Stone and David Zach),
**"Asymptotic Geometric Analysis", Fields Institute Communications**221-229, 68, M. Ludwig et al. (eds.), Springer Science+Business Media, New York 2013. - An asymmetric convex body with maximal sections of constant volume. (with Fedor Nazarov
and Dmitry Ryabogin),
**Journal of American Mathematical Society,**27 (2014), no. 1, 43–68. - Non-uniqueness of convex bodies with prescribed volumes of sections and projections. (with Fedor Nazarov
and Dmitry Ryabogin),
**Mathematika,**59 (2013), 213-221. - An application of shadow systems to Mahler's conjecture. (with Matthieu Fradelizi, Mathieu Meyer).
**Discrete and Computational Geometry**, 48 (2012), no. 3, 721-734. - A problem of Klee on inner section functions of convex body. (with Richar J. Gardner, Dmitry Ryabogin, Vladyslav Yaskin),
**J. Differential Geometry**, 91, (2012), 261-279. - The geometry of p-convex intersection bodies.
(with Jaegil Kim and
Vladyslav Yaskin),
**Advances in Math.,**226, (2011), no 6, 5320-5337. - The unit ball is an attractor of the intersection body operator.
(with Alexander Fish,
Fedor Nazarov
and Dmitry Ryabogin),
**Advances in Math.,**226 (2011), no 3, 26290-2642. - A remark on the Mahler conjecture: local minimality of the unit cube. (with Fedor Nazarov, Fedor Petrov and Dmitry Ryabogin),
**Duke Mathematical Journal,**154, (2010), no 3, 419-430. - Gaussian Brunn-Minkowski-type inequalities. (with Richar J. Gardner),
**Trans. Amer. Math. Soc.**, 360. (2010), 10, 5333-5353. - "On the local equatorial characterization of zonoids and intersection bodies" (with Fedor Nazarov and Dmitry Ryabogin),
**Advances in Math.,**217 (2008), no. 3, 1368--1380. - "Gaussian measure of sections of dilates and shifts of convex bodies,"
**Advances in Applied Mathematics,**41/2 (2008), 247-254 - "The Busemann-Petty problem for arbitrary measures."
**Math. Ann.**331, (2005), 867-887. - "Reconstruction of convex bodies of
revolution from the areas of their shadows",
(with Dmitry Ryabogin),
**Archiv der Mathematik,**5 (2004), 450-460. - "An isomorphic version of the Busemann-Petty problem for Gaussian Measure"".ps",
**GAFA Seminar Notes 2002-2003**Lecture Notes in Math, Vol. 1850, (2004), 277-283. - "Gaussian Measure of Sections of convex bodies.
**Advances in Math.**188/1 (2004), 124-136. - "Fourier transform and Firey projections of convex bodies", (with Dmitry Ryabogin)
**Indiana Univ. Math. J.**53 (2004), 667-682. - "Projections of
convex bodies and the Fourier transform," (with Alexander Koldobsky and Dmitry Ryabogin),
**Israel J. Math.**139 (2004), 361-380. - "Supremum of process in terms of trees", (with Olivier Guedon),
**GAFA Seminar Notes 2001-200**, Lecture Notes in Math, Vol. 1807, (2003), 136-148. - "A remark on $p$-summing norms of operator", "Trends in Banach spaces and operator theory",
**Contemporary Mathematics 321**(Editor A. Kaminska), (2003). - "More on embedding subspaces of $L_p$ into $\ell^N_p$,
$0< p < 1$",
**GAFA Seminar Notes 1996-2000**, Lecture Notes in Math, Vol. 1745, pp.269-281. - "Isomorphic embedding of $\ell^n_p$ , $1< p < 2$, into
$\ell^{(1+\varepsilon)n}_1$", (with Assaf
Naor),
**Israel J. Math.**122 (2001), 371--380. - "Embedding subspaces of $L_p$ into $\ell^N_p$,
$0< p < 1$", (with Gideon
Schechtman),
**Math. Nachr.**227 (2001), 133--142.

### Lecture notes and Surveys:

- Analytic methods in convex geometry. (with Dmitry Ryabogin ),
**Lectures given at the Polish Academy of Sciences 21 - 26, November 2011**, IM PAN Lecture Notes, Vol. 2, Warsaw 2014. - Harmonic Analysis and Uniqueness questions in Convex Geometry. (with Dmitry Ryabogin and Vladyslav Yaskin), to appear in
**Advances in Classic and Applied Analysis, on the occasion of Konstantin Oskolkov's 65th Birthday.** - Unified Fourier
analytic approach to the volume of projections and sections of
convex bodies; (with Alexander
Koldobsky and Dmitry
Ryabogin).
**Fourier Analysis and Convexity, (Editors: L. Brandolini, L. Cozani, A. Iosevich and G. Travaglini),**Birkhauser 2004, 119-131.

### Thesis:

- "The critical
probability for Voronoi percolation,"
M.Sc. thesis, Weizmann Institute of Science (1996).

- "Finite dimensional subspaces of $L_p$, $0 < p < \infty$" ".dvi," Ph.d. thesis, Weizmann Institute of Science (2001).

### Talks:

- "Convex Geometry and its Applications'', Oberwolfach, Germany 12/2015 (upcoming).
- "Convexity, Probability and Discrete Structures, a Geometric Viewpoint'', University Paris-Est Marne-La-Valle, France, 10/2015 (upcoming).
- "Affine Geometric Analysis", (BIRS), Casa Matematica Oaxaca (CMO), Mexico, 9/2015 (upcoming).
- Analysis Seminar, University of Akron, 11/2014.
- Analysis Seminar, University of Florence, Italy, 7/2014.
- Second Joint Meeting of AMS and the Israel Mathematical Union, Tel Aviv, Israel, 6/2014.
- Seminar, "High Dimensional After Noon", Weizmann Institute of Science, Israel, 6/2014.
- Colloquium, Polytechnic School of Engineering, NYU, New York, NY, 04/2014.
- AMS meeting, St. Louis, MO, 10/2013.
- PDE's and Applied math seminar, University of Akron.
- Colloquium, Bowling Green State University, 9/2013.
- "Convex Geometry" at the CIEM in Castro Urdiales, Spain, 9/2013.
- "Asymptotic Geometric Analysis II", Euler International Mathematical Institute, Saint-Petersburg, Russia, 6/2013.
- Analysis Seminar, Universite Paris-Est Marne La Vallee, 5/2013.
- "Southeast Geometry Seminar" (SGS) at University of Alabama at Birmingham, 5/2013.
- Colloquium, University of Missouri-Columbia, 4/2013.
- "Interplay of convex geometry and Banach space theory", BIRS, Canada, 3/2013.
- Analysis Seminar, University of Michigan, 2/2013.
- "Invariants in convex geometry and Banach space theory", Palo Alto, California, August, 2012.
- Geometric Functional Analysis and Probability Seminar, Weizmann Institute of Science, Israel, July, 2012.
- Colloquium, Ben Gurion University, Israle, June, 2012.
- Workshop on "Convexity and Asymptotic Geometric Analysis", The Centre de recherches mathematiques (CRM) of Montreal, Canada, April, 2012.
- Special lectures for PhD students, Polish Academy of Sciences, Warszawa, Poland, 21 - 26, November 2011.
- Conference "Convex Geometry, Analytic Aspects", Cortona, Italy, June 15, 2011.
- Conference "Integration, Vector Measures and Related Topics IV", Murcia, Spain, March 2, 2011.
- Discrete Analysis Program, Isaac Newton Institute for Mathematical Sciences, Cambridge UK, February 15, 2011.
- Workshop on Asymptotic Geometric Analysis and Convexity, Fields Institute, Toronto, ON, September 13 - 17, 2010.
- Probability and Geometry in High Dimensions, Universite Paris-Est Marne-la-Valle, France, May, 2010.
- Volume Inequalities, Banf, Banf International Research Station, Canada, March, 2010.
- Convex Geometry and its Applications, Oberwolfach, Germany, December 2009.
- Analysis Seminar, Technion - Israel Institute of Technology, 2009.
- Advances in Stochastic Inequalities and their Applications. Banf International Research Station, Canada June, 2009.
- Colloquium, The University of Akron, February, 2009
- Functional Analysis Seminar, University of Alberta, January, 2009.
- Affine Convex Geometric Analysis. Banf International Research Station, Canada, January, 2009.
- AMS meeting, Middletown, CT, October, 2008.
- AMS meeting, Vancouver, Canada. October, 2008.
- Analysis Seminar, University of Valencia, Spain. July, 2008
- Analysis Seminar, Univeridad Complutense Madrid, Madrid, Spain, June, 2008.
- Colloquium, Univeridad Complutense Madrid, Madrid, Spain, June 2008.
- Karcher Colloquium, University of Oklahoma, April, 2008.
- PME Colloquium, Youngstown University, April, 2008.
- Miniconference on Classical Convex Geometry, University of Missouri-Columbia, March, 2008.
- Analysis Seminar, University of Wisconsin-Madison, February, 2008.
- Analysis Seminar, Georgia State University, December, 2007.
- Concentration Week on "probability Inequalities with Applications to High Dimensional Phenomena", College Station, Texas, August, 2007.
- Workshop in Analysis and Probability, College Station, Texas, August, 2007.
- Colloquium, University of Pittsburgh. February 2007.
- Colloquium, University of Oregon. January 2007.
- Colloquium, University of South Carolina. January 2007.
- Workshop on Harmonic and Geometric Analysis, The Louisiana State University, Baton Rouge, 1/2007,
- Konvexgeometrie, Oberwolfach, December 2006.
- Colloquium, University of Alabama at Birmingham, 12/2006.
- Analysis Seminar, Michigan State University, Ocober 2006.
- Colloquium, Univeridad Complutense Madrid, Madrid, Spain 2006.
- Banach spaces and their applications in Analysis a conference in honor of Nigel Kalton's 60th birthday, Miami University, Ohio, May 2006 (upcoming).
- Colloquium, Polytechnic University, Brooklyn, NY, April, 2006.
- AMS Special Session on Recent Trends in Convex and Discrete Geometry, San Antonio, TX, January 2006
- Conference on "Contemporary Ramifications of Banach Space Theory", Institute for Advanced Studies of the Hebrew University of Jerusalem. June 2005.
- Colloquium, Polytechnic University, Brooklyn, NY, April 2005.
- Colloquium, University of Missouri-Columbia, March 2005.
- Southeast Geometry Conference, University of South Carolina, March 2005.
- Analysis Seminar, McGill University, January 2005.
- AMS Special Special Session on Trends in Operator Theory and Banach Spaces, Pittsburgh, PA, November, 2004.
- Invited lecture, Workshop on "Geometric Tomography", Alicante, Spain, October, 2004.
- Conference on Gaussian Measure and Geometric Convexity, Snowbird, Utah, July, 2004.
- AMS Special Session on Analytic Convex Geometry, Lawrenceville, NJ, April 2004.
- Colloquium, Kent State University, March 2004.
- Colloquium, Western Washington University, February 2004.
- Colloquium, University of Maine, February 2004.
- Colloquium, University of Alberta, January 2004.
- Functional Analysis Seminar, University of Alberta, January 2004.
- Colloquium, Case Western Reserve University, November 2003.
- Karcher Colloquium, University of Oklahoma, October 2003.
- Prairie Analysis Seminar, Kansas State University, October 2003.
- SUMIRFAS 2003, College Station, Texas, August, 2003.
- Workshop in Linear Analysis and Probability, College Station, Texas, July, 2003.
- Colloquium, University of South Florida, Tampa, March, 2003.
- AMS Special Session on Banach Space Theory and Convex Geometry, Baltimore, January 2003.
- AMS Meeting, Northeastern University, Boston, October, 2002.
- Conference on Convexity and Asymptotic Theory of Normed Spaces, PIMS at the University of British Columbia, July 2002.
- Trends in Banach Space, The University of Memphis, November 2001.
- Banach Space Seminar, University of Missouri-Columbia, October 2001.
- Functional Analysis Seminar, University Paris 6, December 14, 2000.
- Functional Analysis Seminar, University de Marne-La-Valle, Paris, December 5, 2000.
- SUMIRFAS 2000, College Station, Texas, August 12, 2000.
- Workshop in Linear Analysis and Probability, College Station, Texas, July 19, 2000.
- International Workshop on Geometric Convex Analysis, Technion, Israel, March 19, 2000.
- Functional Analysis Seminar, Technion, Israel, December 16, 1999.
- Israel Mathematical Union meeting, University of Haifa, Israel May, 1999.

### Conference Organized

- CBMS Regional Conference in the Mathematical Sciences-"Introduction to the Theory of Valuations and Convex Sets,'' featuring Semen Alesker, August 10-15, 2015 (with B. Jaye and D. Ryabogin.).
- Informal Analysis Seminar, March 14-15, 2015 (with Kent State Analysis Group).
- Informal Analysis Seminar, March 1-2, 2014 (with Kent State Analysis Group).
- "Geometric Tomography and Harmonic Analysis", BIRS, Banff, Canada, 3/2014 (with A. Koldobsky, D. Ryabogin and V. Yaskin).
- "Sections of convex bodies ", American Institute of Mathematics, August 2013 (with A. Koldobsky, D. Ryabogin and V. Yaskin).
- Informal Analysis Seminar, November 16-18, 2012 (with Kent State Analysis Group).
- AMS Special Session on Harmonic Analysis and Convexity, University of Akron, OH, October 20-21, 2012 (with B. Jaye, D. Ryabogin).
- Informal Analysis Seminar, October 18-19, 2012 (with Kent State Analysis Group).
- CBMS Regional Conference in the Mathematical Sciences-"Ergodic Methods in the Theory of Fractals" 6/2012 (with D. Ryabogin).
- Informal Analysis Seminar, March 30th - April 1st, 2012 (with Kent State Analysis Group).
- "Harmonic Analysis in Convex Geometry", BIRS, Banff, Canada, May 2011 (with A. Koldobsky, D. Ryabogin and V. Yaskin).
- "Mahler's conjecture and duality in convex geometry", American Institute of Mathematics, August 2010 (with A. Koldobsky, D. Ryabogin and V. Yaskin).
- "Informal Analysis Seminar Dedicated to the Work of Joe Diestel", March, 2010, (with Analysis group at Kent State).
- "Summer school on Fourier analytic and probabilistic methods in geometric functional analysis and convexity", with FRG group, August 2008.
- Informal Analysis Seminar, October, 2007, (with Analysis group at Kent State).
- "Fourier analytic methods in convex geometry", American Institute of Mathematics, August 2007 (with A. Koldobsky, D. Ryabogin).
- AMS Special Session on Affine Invariants, Randomness and Approximation in Convex Geometry, Stevens Institute of Technology, Hoboken, NJ 4/2007. (with E. Werner).
- Informal Analysis Seminar, , December, 2006, (with Analysis group at Kent State).
- NSF/CBMS Conference -"Probabilistic and combinatorial approach in analysis", 8/2006 (with P. Enflo and A. Tonge).
- "Conference to Celebrate the Life and Work of Vladimir Gurariy." (with R. Aron, J. Diestel, P. Enflo, V. Lomonosov and A. Tonge).

### Referee/Rewier work:

- Natural Sciences and Engineering Research Council of Canada.
- Israel Science Foundation.
- National Science Foundation.
- Advances in Applied Mathematics.
- Advances in Mathematics.
- Annals of Probability.
- Bulletin of the Korean Mathematical Society.
- Canadian Mathematical Bulletin.
- Discrete & Computational Geometry.
- GAFA Seminar Notes.
- Geometriae Dedicata.
- Glasgow Mathematical Journal.
- Houston Journal of Mathematics
- Electronic Communications in Probability.
- Indagationes Mathematicae.
- International Mathematics Research Notices.
- Israel Journal in Mathematics.
- Journal of Approximation Theory.
- Journal of Geometric Analysis.
- Journal of Functional Analysis.
- Journal of Inequalities and Applications.
- Journal of Mathematical Analysis and Applications.
- Journal of Online Mathematics and its Applications.
- Mathematika.
- Mathematische Annalen.
- Monatshefte fur Mathematik.
- Proceedings of the American Mathematical Society.
- Publicationes Mathematicae Debrecen.
- Science in China, Series A: Mathematics.
- The Annals of Probability.
- Zentralblatt Math.

### Teaching experience:

- Basic Mathematical Concepts II, Summer 2015.
- Theory of Numbers (4/57011), Spring 2015.
- Differential Geometry (4/55011), Fall 2013.
- Graph Theory and Combinatorics (4/52021), Fall 2013.
- Probability and Statistics for High-School Teachers (57091), Fall 2012; Fall 2014.
- Introduction to Partial Differential Equations, Winter 2010.
- Asymptotic Theory of Finite Dimensional Normed Spaces, Fall 2010.
- Introduction to Topology I and II. Fall 2008, Winter 2009.
- Topics in Probability Theory and Stochastic Processes, Fall 2008.
- Discrete Geometry. Fall 2006. Summer 2015.
- Calculus with Precalculus. Fall 2006, Winter 2007.
- Functions of Real Variables. Winter 2006.
- Introduction to Analysis I and II (42001/52001 and 42002/52002), Fall/Spring Semesters 2005/2006; 2009/2010; 2011/2012; 2014/2015.
- Analytic Geometry and Calculus III (22005). Fall 2005.
- Linear Algebra and Applications (21001). Fall 2004, Winter 2005, Fall 2007, Winter 2010.
- Measure Theory Seminar (72095). Fall 2004- PRESENT.
- Developmental mathematics (11004). Summer Semester 2004.
- College Algebra (11011). Summer Semester 2004.
**University of Missouri-Columbia**

- Elementary Differential Equations (math 304). Winter Semester 2003.
- Calculus III (math 201). Winter Semester 2004, Fall Semester 2003, Fall Semester 2002.
- Probability Models (math 315). Winter Semester 2004, Fall Semester 2003, Winter Semester 2002.
- Finite Mathematics (math 60). Winter Semester 2002.
- Mathematical Modeling 1 (Digital Signal Processing) (math 314). Fall Semester 2001.
- Finite Mathematics (math 60). Fall Semester 2001.
**Weizmann Institute of Science**

- Teaching Assistant for the course ``Combinatorial Games'' (Prof. A. Fraenkel, WIS), 1999-2000
- Teaching Assistant for the course "Mathematical Modeling in Biology" (Prof. L. Segel, WIS), 1999-2000, 2000-2001
- Mentor, Israeli Summer Science Youth Workshop, Weizmann Institute of Science, August 1999.
- Taught mathematics for gifted Russian high-school students, The Youth Activities Section at the Weizmann Institute of Science.
- Mentor, Summer Science Institute, Weizmann Institute of Science,
International Camp, 1998, 1997.
**Moscow, Russia**

- Teacher at Moscow School 67, 1991-1994.

**Kent State University**

### University/Departmental Service:

- College Advisory Committee 2012-2013.
- Coordinator of Graduate Studies 2007 - present.
- Chair Review Committee 2012.
- University Advisory Committee on Academic Assessment 2011- present.
- Graduate Studies committee 2006-2007.
- Faculty Advisory committee 2005-2006, 2011-2012, 2012-2013, 2014-2015.
- Hiring committee member 2005, 2007.
- Developed departmental web-page.
- Colloquium Chair 2004-2007, 2011-2013.