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** Petros Valettas**

Postdoctoral Fellow

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** Contact Information**

University of Missouri

Mathematics Department

202 Mathematical Sciences Building

Columbia, MO 65211

E-mail: valettasp@missouri.edu

**Research Interests**

- Asymptotic Convex Geometry
- Geometric Functional Analysis
- High-dimensional Probability
- Concentration of measure
- Probabilistic Methods in Analysis and Geometry

My work is supported in part by the National Science Foundation Grant DMS - 1612936

**Teaching**

- Current teaching at MU.
- Math 8208: Topics in Functional Analysis (graduate, Spring 2017)
- Math 4100/7100: Differential Equations (Fall 2016)
- Math 2320: Discrete Math Structures (Spring 2016, Spring 2017)
- Math 2300: Calculus III (Spring 2016, Fall 2017)
- Math 1700: Calculus II (Fall 2015)
- Past teaching at Texas A&M.
- Math 151: Calculus I (Spring 2014, Fall 2014)
- Math 251: Calculus III (Fall 2012, Fall 2013, Spring 2015)
- Math 304: Linear Algebra (Spring 2013)
- Math 311: Topics in Applied Mathematics I (Summer 2014)
- Math 411: Mathematical Probability (Summer 2015)
- Lecture Notes.
*Real Analysis: Metric Spaces*, University of Athens (2009). pdf

** Seminars**

**Publications and preprints**

*On the existence of subgaussian directions for log-concave measures***545**(2011), 103-122. pdf*Psi(a)-estimates for marginals of log-concave probability measures*(with A. Giannopoulos and G. Paouris), Proceedings of the American Mathematical Society**140**, no. 4 (2012), 1297-1308. pdf*On the distribution of Psi(2)-norm of linear functionals on isotropic convex bodies*(with A. Giannopoulos and G. Paouris), Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics**2050**(2012), 227-253. pdf*Distances between classical positions of centrally symmetric convex bodies*(with E. Markessinis), Houston Journal of Mathematics**41**(2015), 187-211. pdf*On the geometry of log-concave probability measures with bounded log-Sobolev constant*(with P. Stavrakakis), Proceedings of the Asymptotic Geometric Analysis Programme, Fields Institute Communications**68**(2013), 359-380. pdf*Neighborhoods on the Grassmannian of marginals with bounded isotropic constant*(with G. Paouris), Journal of Functional Analysis**267**(2014), 3427-3443. pdf*Random version of Dvoretzky’s theorem in ell_p^n*(with G. Paouris and J. Zinn), Stochastic Processes and their Applications**127**(2017), 3187-3227. pdf*On Dvoretzky’s theorem for subspaces of L_p*(with G. Paouris), preprint. pdf*Inequalities for the surface area of projections of convex bodies*(with A. Giannopoulos and A. Koldobsky), Canadian Journal of Mathematics (to appear). pdf*A Gaussian small deviation inequality for convex functions*(with G. Paouris), Annals of Probability (to appear). pdf*On a quantitative reversal of Alexandrov’s inequality*(with G. Paouris and P. Pivovarov), Transactions of the American Mathematical Society (to appear). pdf*Variance estimates and almost Euclidean structure*(with G. Paouris), Advances in Geometry (to appear). pdf*On the tightness of Gaussian concentration for convex functions*, Journal d’Analyse Mathématique (to appear). pdf*Dichotomies, structure, and concentration results*(with G. Paouris), preprint.*Gaussian convex bodies: a non-asymptotic approach*(with G. Paouris and P. Pivovarov), Zapiski Nauchnych Seminarov POMI**457**(2017), 286-316.

**Research Monograph**

*Geometry of isotropic convex bodies *(with S. Brazitikos, A. Giannopoulos and B-H. Vritsiou) Mathematical Surveys and Monographs **196**, Amer. Math. Soc. (2014) AMS