2018 Int.Conf. on Applied Mathematics and Computational PhysicS, Budapest, Hungary, Jan 19-21, 2018

Plenary Speakers



Plenary Lecture I
Title: Geometric inequalities on Heisenberg-type groups
by: Prof Alexandru Kristály

Óbuda University, Budapest,
Hungary


 



Abstract: We establish a weighted pointwise Jacobian determinant inequality on corank 1 Carnot groups (e.g. Heisenberg groups) related to optimal mass transportation akin to the work of Cordero-Erausquin, McCann and Schmuckenschl\"ager. The weights appearing in our expression are distortion coefficients that reflect the delicate sub-Riemannian structure of our space including the presence of abnormal geodesics. Our inequality interpolates in some sense between Euclidean and sub-Riemannian structures, corresponding to the mass transportation along abnormal and strictly normal geodesics, respectively. As applications, entropy, Brunn-Minkowski and Borell-Brascamp-Lieb inequalities are established. These results refute a general point of view, according to which no geometric inequalities can be derived by optimal mass transportation on singular spaces. The talk is based on two joint papers with Z. Balogh (Bern) and K. Sipos (Bern).

Brief Biography: Prof Alexandru Kristály was born at 22 March 1975 and  is currently a Full Professor at the Óbuda University, Budapest, Hungary (since 2016) and a Full Professor in Mathematics Babes-Bolyai University, Cluj-Napoca, Romania (since 2013). His research interest is mainly focused to elliptic PDEs, Heisenberg groups, and Riemann/Finsler geometry as well as their applications to various real life problems. In 2004, he partially solved jointly with L. Kozma a fifty years old open problem of H.  Busemann in Finsler geometry (published in Journal of Geometry and Physics, 2006) concerning the characterization of Berwald spaces of non-positive curvature by means of synthetic properties (roughly, the validity of the curved Thales theorem). This result has been successfully applied to solve certain highly non-linear optimization problems on curved settings, described in the monograph by A. Kristály, V. Rădulescu and Cs. Varga, Variational Principles in Mathematical Physics, Geometry, and Economics, Encyclopedia of Mathematics and its Applications, No. 136, Cambridge University Press, Cambridge, UK. During the last ten years he published research articles in top journals as Mathematische Annalen (2013), Journal of Functional Analysis (2015), Calculus of Variations and Partial Differential Equations (2013, 2015, 2016), Journal de Mathématiques Pures et Appliquées (2010, 2014), Journal of Differential Equations (2006, 2007, 2008, 2010), Nonlinear Analysis: Real World Applications (2012, 2016), etc. His results have been presented in various international conferences all around the world (e.g., Switzerland, Brazil, Japan, France, Spain, Italy, Saudi-Arabia, Bulgaria, etc.) where Dr. Kristály was an invited speaker. He was invited to several prestigious institutions as Senior Research Fellow, e.g., to City University of Hong Kong, Hong Kong (2014, 2015), Institut des Hautes Etudes Scientifiques (IHES), Bures-sur- Yvette, France (2011, 2013), University of Kyoto, Kyoto, Japan (2012), Istituto Nazionale di Alta Matematica (INDAM), Universita di Catania, Catania, Italy (2005, 2009, 2011), Mathematisches Institute, Universitat Bern (2011, 2012, 2014, 2015). As a recognition of his scientific achievements, dr. Kristály was awarded by the Bolyai Plakett of the Hungarian Academy of Sciences, Budapest, Hungary (2013) and by the Spiru Haret Award of the Romanian Academy, Bucharest, Romania (2014). According to the Web of Science, his H-index is 14, and he has 317 citing articles without self- citations.