**Petros Valettas**

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**Department of Electrical Engineering & Computer Science**

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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

**Teaching**

- Current teaching at MU.
- MATH 8208: Topics in Functional Analysis (graduate, Spring 2017)
- MATH 7700: Advanced Calculus I (graduate, Fall 2019)
- MATH 4140/7140: Matrix Theory (Summer 2018)
- MATH 4100/7100: Differential Equations (Fall 2016, 2018, Spring 2018)
- MATH 4060/7060: Connecting Geometry to Middle and Secondary Schools (Fall 2018)
- MATH 2320: Discrete Mathematical Structures (Spring 2016, 2017, 2019, Fall 2019)
- MATH 2300: Calculus III (Spring 2016, Fall 2017)
- MATH 1700: Calculus II (Fall 2015)
- CMP_SC 4001/7001: Topics in Computer Science: Probability & Computing (Fall 2019)
- Past teaching at Texas A&M.
- Math 151: Calculus I (Spring 2014, Fall 2014)
- Math 251: Calculus III (Fall 2012, 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**, Issue 10 (2017), 3187-3227. pdf*On Dvoretzky’s theorem for subspaces of L_p*(with G. Paouris), Journal of Functional Analysis**275**, Issue 8 (2018), 2225-2252. pdf*Inequalities for the surface area of projections of convex bodies*(with A. Giannopoulos and A. Koldobsky), Canadian Journal of Mathematics**70**(2018), 804-823. pdf*A Gaussian small deviation inequality for convex functions*(with G. Paouris), Annals of Probability**46**, no. 3 (2018), 1441-1454. pdf*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. pdf*Variance estimates and almost Euclidean structure*(with G. Paouris), Advances in Geometry**19**, Issue 2, (2019), 165-189. pdf*On the tightness of Gaussian concentration for convex functions*, Journal d’Analyse Mathématique**139**, Issue 1 (2019), 341-367. pdf*Dichotomies, structure, and concentration in normed spaces*(with G. Paouris), Advances in Mathematics**332**(2018), 438-464. pdf*Gaussian convex bodies: a non-asymptotic approach*(with G. Paouris and P. Pivovarov), Zapiski Nauchnych Seminarov POMI**457**(2017), 286-316. pdf*Hypercontractivity, and lower deviation estimates in normed spaces*(with G. Paouris and K. Tikhomirov), Preprint. pdf

**Book**

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