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Mathematics Webinar | Partial Differential Equations with Nonnegative Characteristic Form

20 Oct 2021, 09:30 (CEST)

Partial Differential Equations, Second-order, Geometric Structures, Boundary Value Problems
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Welcome from the Chair

1st Webinar on Mathematics

Partial Differential Equations with Nonnegative Characteristic Form

Second order Partial Differential Equations (PDEs) with non-negative characteristic form appear to be ubiquitous in Mathematics, e.g. in Differential Geometry, Stochastic Theory and in many applications of Mathematics, e.g. Kinetic Theory and Finance. Important special cases of such operators are those satisfying Hormander's condition. They enjoy regularity properties related to suitable geometric structure of the underlying space. The more we know about geometric structures, the better for regularity results, bounds and asymptotic estimates. The goal of the Webinar is to show recent results and advances in the field of PDEs. We believe that the mathematical community will benefit from the webinar.

Date: 20 October 2021

Time: 9:30 am CEST | 3:30 am EDT | 3:30 pm CST Asia

Webinar ID: 897 5522 0962

Webinar Secretariat: mathematics.webinar@mdpi.com

Chair

Department of Mathematics and Computer Sciences, University of Catania, Italy

DETAILS
Bio
Prof. Dr. Giuseppe Di Fazio has been Full Professor in Mathematical Analysis at University of Catania since 2007, and is also member of the "Unione Matematica Italiana (UMI)". He received his PhD in Mathematics in 1992. His research activity is about Partial Differential Equations (PDEs), especially regularity topics. He has delivered numerous seminars and talks at several universities. Temple University (Philadelphia USA), Tokyo Metropolitan University, University of Kyoto (Japan), Warsaw (Poland), ITB (Indonesia), American University of Beiruth – Arab University of Beiruth - Lebanese University (Lebanon), Beiruth (Lebanon), KAUST (KSA), Coimbra (Portugal). He is head of projects and Erasmus agreements. He is also the author of the books: Introduction and Applications to Integral Operators and PDE's, Voll I & II published by Taylor & Francis Group. He has also published 6 university textbooks.

Invited Speakers

Department of Mathematics, Polytechnic University of Milan, Italy

DETAILS
Bio
Prof. Dr. Marco Bramanti has been Full Professor in Mathematical Analysis at Polytechnic University of Milan since 2015. He obtained the title of PhD in Mathematics in 1993 at the University of Milan. He has been visiting professor at the University of Minnesota (USA), Universidad Autónoma de Madrid (Spain), Gent University (Belgium) and has been the research director of international students and researchers. He is the author of more than 40 scientific papers and monographs, and 15 university textbooks. Within the Department of Mathematics of Polytechnic of Milan, he also belongs to the Laboratory of Mathematics Education and Scientific Sperimentation, which organizes initiatives of training and scientific dissemination with Schools.

Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Italy

DETAILS
Bio
Prof. Dr. Sergio Polidoro has been Full Professor in Mathematical Analysis at University of Modena and Reggio Emilia, since 2007, and is member of the "Unione Matematica Italiana (UMI)" and "Istituto Nazionale di Alta Matematica" (National Institute of High Mathematics). He obtained the title of PhD in Mathematics in 1994. Research activity is mainly concerned with the regularity theory for second order linear partial differential equations with non-negative characteristic form, including Kolmogorov–Fokker–Planck equations and their applications to the kinetic theory and to financial problems. In this area, he is leading some Ph.D. students. He organized international conferences, gave seminars and talks in several universities and international conferences and has been visiting professor at Université Paris Diderot - Paris 7 (2011) and at Mittag-Leffler Institute - Stockholm (2013).

Webinar Content

On Wednesday, 20 October 2021, MDPI and the Journal Mathematics organized the 1st webinar on Mathematics, entitled " Partial Differential Equations with Nonnegative Characteristic Form".

The introduction was held by the Chair of the webinar, Prof. Dr. Giuseppe Di Fazio. He has been Full Professor in Mathematical Analysis at University of Catania since 2007, and is also member of the "Unione Matematica Italiana (UMI)". He received his PhD in Mathematics in 1992. His research activity is about Partial Differential Equations (PDEs), especially regularity topics. He has delivered numerous seminars and talks at several universities. He is also the author of several books.

The first speaker to quick off this webinar was Prof. Dr. Marco Bramanti, with his presentation "Heat Kernels for Sum of Squares of Homogeneous Hörmander Vector Fields". He has been Full Professor in Mathematical Analysis at Polytechnic University of Milan since 2015. He obtained the title of PhD in Mathematics in 1993 at the University of Milan. Within the Department of Mathematics of Polytechnic of Milan, he also belongs to the Laboratory of Mathematics Education and Scientific Sperimentation, which organizes initiatives of training and scientific dissemination with Schools.

The second presentation with the title "Asymptotic Estimates for Hörmander's Operators with Drift" was held by Prof. Dr. Sergio Polidoro. He has been Full Professor in Mathematical Analysis at University of Modena and Reggio Emilia, since 2007, and is member of the "Unione Matematica Italiana (UMI)" and "Istituto Nazionale di Alta Matematica" (National Institute of High Mathematics). He obtained the title of PhD in Mathematics in 1994. Research activity is mainly concerned with the regularity theory for second order linear partial differential equations with non-negative characteristic form, including Kolmogorov–Fokker–Planck equations and their applications to the kinetic theory and to financial problems.

The presentations were followed by a Q&A and a discussion, moderated by the Chair Prof. Dr. Giuseppe Di Fazio. The webinar was offered via Zoom and required registration to attend. The full recording can be found here on Sciforum website. In order to stay updated on the next webinars on Mathematics be sure to sign up for our newsletter by clicking on “Subscribe” at the top of the page.

Program

Speaker/Presentation

Time in CEST

Prof. Dr. Giuseppe Di Fazio

Heat Kernel Gaussian Estimates and Harnack Inequality in the Euclidean Setting

9:30 - 9:50 am

Prof. Dr. Marco Bramanti

Heat Kernels for Sum of Squares of Homogeneous Hörmander Vector Fields

9:50 - 10:35 am

Question Time

10:35 - 10:40 am

Prof. Dr. Sergio Polidoro

Asymptotic Estimates for Hörmander's Operators with Drift

10:40 - 11:25 am

Question Time

11:25 - 11:30 am

Closing of Webinar
Prof. Dr. Giuseppe Di Fazio

11:30 am

Relevant SIs

Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications
Guest Editor: Prof. Dr. Nikolai A. Kudryashov
Deadline for manuscript submissions: 30 November 2021

Partial Differential Equations and Applications
Guest Editor: Prof. Dr. Emma Previato
Deadline for manuscript submissions: 25 December 2021

Applications of Partial Differential Equations
Guest Editors: Prof. Dr. Patricia J. Y. Wong
Deadline for manuscript submissions: 31 March 2022

Partial Differential and Functional Differential Equations: Exact Solutions, Reductions, Symmetries, and Applications
Guest Editors: Prof. Dr. Andrei Dmitrievich Polyanin & Prof. Dr. Alexander V. Aksenov
Deadline for manuscript submissions: 31 March 2022

Advances in Differential and Difference Equations with Applications 2021
Guest Editor: Prof. Dr. Dumitru Baleanu
Deadline for manuscript submissions: 31 May 2022

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Organizers

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