# Petros Valettas

Assistant Professor

**Contant Information**

**Contant Information**

University of Missouri

Mathematics Department

303 Mathematical Sciences Building

Columbia, MO 65211

E-mail: valettasp@missouri.edu

**Research Interests**

**Research Interests**

Asymptotic Convex Geometry

Geometric Functional Analysis

High-Dimensional Probability

Probabilistic Methods in Analysis and Geometry

**Teaching**

**Teaching**

Current Teaching at MU.

CMP_SC 7001/MATH 7960: Probability and Computing (Spring 2022)

MATH 1700: Calculus II (Spring 2022)

Past Teaching at MU.

CMP_SC 8001/MATH 8202: High-Dimensional Probability (Fall 2020)

CMP_SC 7001/MATH 7960: Probability and Computing (Fall 2019, Spring 2021)

MATH 4700/7700: Advanced Calculus I (Fall 2019, Spring 2021)

MATH 4140/7140: Matrix Theory (Summer 2018)

MATH 4100/7100: Differential Equations (Spring 2018)

MATH 2320: Discrete Mathematical Structures (Spring 2019, Fall 2019, 2020)

MATH 2300H: Calculus III (Fall 2021)

Past Teaching at Texas A&M.

Mathematical Probability

Topics in Applied Mathematics

Linear Algebra

Calculus I and III

Lecture Notes.

*Real Analysis: Metric Spaces*, University of Athens (2009). pdf

**Publications and Preprints**

**Publications and Preprints**

*On the existence of subgaussian directions for log-concave measures*(with A. Giannopoulos and G. Paouris), Contemporary Mathematics 545 (2011), 103-122.*Psi(α)-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.*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.*Distances between classical positions of centrally symmetric convex bodies*(with E. Markessinis), Houston Journal of Mathematics 41 (2015), 187-211.*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.*Neighborhoods on the Grassmannian of marginals with bounded isotropic constant*(with G. Paouris), Journal of Functional Analysis 267 (2014), 3427-3443.*Random version of Dvoretzky’s theorem in ell_p^n*(with G. Paouris and J. Zinn), Stochastic Processes and their Applications 127, Issue 10 (2017), 3187-3227.*On Dvoretzky’s theorem for subspaces of L_p*(with G. Paouris), Journal of Functional Analysis 275, Issue 8 (2018), 2225-2252.*Inequalities for the surface area of projections of convex bodies*(with A. Giannopoulos and A. Koldobsky), Canadian Journal of Mathematics 70 (2018), 804-823.*A Gaussian small deviation inequality for convex functions*(with G. Paouris), Annals of Probability 46, no. 3 (2018), 1441-1454.*On a quantitative reversal of Alexandrov’s inequality*(with G. Paouris and P. Pivovarov), Transactions of the American Mathematical Society 371, no. 5, (2019), 3309-3324.*Variance estimates and almost Euclidean structure*(with G. Paouris), Advances in Geometry 19, Issue 2, (2019), 165-189.*On the tightness of Gaussian concentration for convex functions*, Journal d' Analyse Mathématique 139, Issue 1 (2019), 341-367.*Dichotomies, structure, and concentration in normed spaces*(with G. Paouris), Advances in Mathematics 332 (2018), 438-464.*Gaussian convex bodies: a non-asymptotic approach*(with G. Paouris and P. Pivovarov), Zapiski Nauchnych Seminarov POMI 457 (2017), 286-316.*Hypercontractivity and lower deviation estimates in normed spaces*(with G. Paouris and K. Tikhomirov), Annals of Probability (to appear).*Concentration estimates for functions of finite high-dimensional random arrays*(with P. Dodos and K. Tyros), Preprint.*Decompositions of finite high-dimensional random arrays*(with P. Dodos and K. Tyros), Preprint.

**Book**

**Book**

*Geometry of isotropic convex bodies*