Invited Speakers

  • Apostolos Giannopoulos, School of Applied Mathematical and Physical Sciences, National Technical University of Athens

    Τitle:    Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures.
    Abstract: We study the dimensional Brunn–Minkowski inequality for even log-concave probability measures $\mu$ on $\mathbb{R}^n$ via an analytic approach based on diffusion operators and gradient estimates. Our main result asserts that for every pair of symmetric convex sets $K,L$ in $\mathbb{R}^n$ and every $\lambda\in(0,1)$, $\mu(\lambda K+(1-\lambda)L)^{c_n} \geq \lambda \mu(K)^{c_n}+(1-\lambda)\mu(L)^{c_n}, $ where $c_n\geq c/n^3\ln n$ for some universal constant $c>0$. A key ingredient in our proof is the bound $\int_{\mathbb{R}^n} |\nabla\psi|\,d\mu \leq Cn$ that we establish  for isotropic log-concave probability measures $\mu$ on $\mathbb{R}^n$ with density $e^{-\psi}$, which is optimal in terms of the dimension. This estimate yields structural information on the size of sub-level sets of the gradient of $\psi$ and puts forth a geometric obstruction to further improvements of the Brunn–Minkowski exponent. We also present applications of this estimate to the weighted perimeter of level sets, projections, moment and surface area measures of isotropic log-concave functions, highlighting the central role of the gradient of the logarithmic potential in high-dimensional convexity.

    The talk is based on joint work with Alexandros Eskenazis and Natalia Tziotziou.

  • Dimitris Karlis, Dept. of Statistics, Athens University of Economics and Business (AUEB)


    Title:     Random Coefficient extensions for integer autoregressive models: a non-parametric approach.
    Abstract: In this talk, we use the class of integer autoregressive (INAR) time series models, widely used to model time series of counts. INAR models extend the idea of classical time series for continuous data in an admissible way to keep the discrete nature of the data. Random Coefficient INteger AutoRegressive (RCINAR) models constitute an important extension of the simple INAR model when the thinning parameters are considered to be random. In the present paper, we propose the case that the thinning parameter follows a discrete distribution with positive probability at a finite number of points. We do not specify any parametric family for the distribution.  We provide an EM algorithm to estimate the model while we link the model to the non-parametric Maximum Likelihood estimate of the mixing distribution. The ideas are then extended to the bivariate case where the thinning parameters are now a matrix of random variables. The finite mixture representation helps a lot to account for the extra variability but also extra correlation to the model.

platis
  • Ioannis Platis, Department of Mathematics, University of Patras


    Title:     Horizontal curvatures of surfaces in 3-dimensional, contact sub-Riemannian Lie groups.
    Abstract: In this talk we study horizontal curvatures for surfaces embedded in three-dimensional
    contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we are able to derive explicit formulas for horizontal Gauss curvature, horizontal mean curvature, and symplectic distortion for
    surfaces embedded in three dimensional Lie groups with a sub-Riemannian structure obtained by
    a contact form. We focus on two primary examples: the Heisenberg group and the affine-additive
    group. We classify surfaces of revolution within these groups that exhibit constant horizontal
    curvatures, often expressing their profiles through elementary or elliptic integrals.

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