Petros Valettas
Assistant Professor
Contant Information
University of Missouri
Mathematics Department
303 Mathematical Sciences Building
Columbia, MO 65211
E-mail: valettasp@missouri.edu
Research Interests
Asymptotic Convex Geometry
Geometric Functional Analysis
High-Dimensional Probability
Probabilistic Methods in Analysis and Geometry
Teaching
Current Teaching at MU.
MATH 8480: Advanced Probability (Spring 2024)
Past Teaching at MU.
CMP_SC 8001/MATH 8202: High-Dimensional Probability (Fall 2020, 2022)
CMP_SC 7001/MATH 7960: Probability and Computing (Fall 2019, Spring 2021, 2022)
MATH 8480: Advanced Probability (Spring 2023)
MATH 4700/7700: Advanced Calculus I (Fall 2019, Spring 2021)
MATH 4140/7140: Matrix Theory (Summer 2018)
MATH 4100/7100: Differential Equations (Spring 2018, Fall 2023)
MATH 2320: Discrete Mathematical Structures (Spring 2019, Fall 2019, 2020)
MATH 2300H: Honors Calculus III (Fall 2021)
MATH 1700: Calculus II (Spring 2022, 2023)
MATH 1500H: Honors Calculus I (Fall 2022)
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
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 50, no. 2 (2022), 688-734. pdf
Concentration estimates for functions of finite high-dimensional random arrays (with P. Dodos and K. Tyros), Random Structures & Algorithms 63, Issue 4 (2023), 997-1053. pdf
Decompositions of finite high-dimensional random arrays (with P. Dodos and K. Tyros), Preprint. pdf
Approximate Real Symmetric Tensor Rank (with A. Ergür and J. Rebollo-Bueno), Arnold Mathematical Journal 9 (2023), 455-480. 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