OverviewVisitors2023Professor Jose Carrillo, University of Oxford, UKJanuary 8th - January 19th Mathematics and Applications ColloquiumAMCSCEMSENonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applicationsProf. Jose Carrillo, Department of Mathematics, University of Oxford, UKTuesday, January 10, 2023, 15:30- 17:00Building 2, Level 5, Room 5209Fokker-Planck equationsCucker-Smale orientation dynamicsMcKean-Vlasov equationsKeller-Segel-type modelsContact PersonAthanasios TzavarasThis talk will be devoted to an overview of recent results in understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics, and financial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear diffusion Keller-Segel-type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under suitable assumptions on the Fourier modes of the interaction potential. 2022Professor Sir John Ball, Heriot-Watt University, Edinburgh, UKDecember Dean's Distinguished LectureAMCSCEMSELiquid crystals from a mathematical perspectiveProf. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UKMonday, December 12, 2022, 12:00- 13:00Building 1,Level 4, Room 4102Contact PersonAthanasios TzavarasLiquid crystals are materials whose properties are intermediate between normal fluids and solid crystals, and have widespread use as the working substance for computers, TV, and watch displays. The lecture will introduce these materials and what mathematics can say about them, and in particular, discuss how different theories of liquid crystals describe orientational defects in different ways. Professor Manoussos Grillakis, University of Maryland in College ParkNovember 15th - December 15th Mathematics and Applications ColloquiumAMCSCEMSEOn the role of pair correlations in the evolution of Bose-Einstein condensatesProf. Manoussos Grillakis, Department of Mathematics, University of Maryland in College Park.Wednesday, December 07, 2022, 15:30- 17:00Building 1, Level 3, Room 3119nonlinear Schr¨odinger equationContact PersonJinchao XuA Bose gas at zero temperature is described by a mean field which satisfies the cubic nonlinear Schr¨odinger equation (NLS) otherwise known as the Gross- Pitaevski equation. The mean field describes the evolution of the condensate in an average sense. I will describe a technique that introduces pair correlations in the evolution of the condensate. The resulting approximation tracks the evolu- tion of the condensate in norm provided that the pair wave-function satisfies an interesting system of coupled NLS equations. I will discuss the nonlinear struc- ture of the NLS system as well as a novel approach to the question of global existence of solutions of the system. Professor Hailiang Liu, Iowa State University, USAMay SeminarAMCSCEMSEMathematical Problems in Deep LearningProf. Hailiang Liu, Department of Mathematics, Iowa State University, USAWednesday, May 25, 2022, 15:00- 16:00B1, L4, R4102,Contact PersonAthanasios TzavarasI shall present some mathematical problems encountered in deep learning models. The results include optimal control of selection dynamics for deep neural networks, and gradient methods adaptive with energy. Some of the computational questions that will be addressed have a more general interest in engineering and sciences. 2020Professor Stefano Spirito, University of L'Aquila, ItalyFebruary 1st - February 15th SeminarAMCSCEMSEWeak solutions of the 2D Euler equationsStefano Spirito, Assistant Professor, Department of Mathematics, University of L’Aquila, ItalyTuesday, February 11, 2020, 15:00- 16:00Building 1, Level 3, Room 3119Cauchy problemEuler equationsContact PersonAthanasios TzavarasIn this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties. Professor Dimitrios Mitsotakis, Victoria University of Wellington, New ZealandJanuary 3rd - February 29th SeminarCEMSEA regularized shallow-water waves system with slip-wall boundary conditions: Theory and numerical analysisDimitrios Mitsotakis, Senior Lecturer, School of Mathematics and Statistic Victoria University of Wellington, New ZealandWednesday, February 05, 2020, 16:00- 17:00Building 1, Level 4, Room 4214Contact PersonAthanasios TzavarasIn this talk we present the derivation of a new Boussinesq-type system to describe the propagation of long waves of small amplitude in a basin with mildly varying bottom topography. We prove the existence and uniqueness of weak solutions for maximal times that do not depend on the amplitude of the waves. We then present the numerical solution of the new system using Galerkin finite element methods and prove the convergence of the semidiscrete solution to the exact solution. The system appears to describe well water waves even in benchmark experiments that involve also general bathymetries. 2019Professor Jan Giesselman, Technical University of Darmstadt, GermanyApril 1st - April 11th SeminarAMCSAPPLIEDPDECEMSEMini Course Part 1-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flowsProf. Jan Giesselmann, Technical University of Darmstadt, GermanyTuesday, April 02, 2019, 16:00- 17:00B1 L3 Room 3119Multi-face flowsnumerical methodsContact PersonAthanasios TzavarasIn this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation Dr. Suleyman Ulusoy, American University of Ras Al Khaimah, UAEMarch 17th - March 22nd SeminarAMCSAPPLIEDPDECEMSEOn Nonlocal Keller-Segel Type EquationsDr. Suleyman Ulusoy, American University of Ras Al Khaimah, UAEWednesday, March 20, 2019, 16:00- 17:00Building 1, Level 3, Room 3119Applied Partial Differential EquationsMathematical BiologyContact PersonAthanasios TzavarasIn the first part of the talk we investigate a Keller-Segel model with quorum sensing and a fractional diffusion operator. This model describes the collective cell movement due to chemical sensing with flux limitation for high cell densities and with anomalous media represented by a nonlinear, degenerate fractional diffusion operator. The purpose here is to introduce and prove the existence of a properly defined entropy solution. In the second part of the talk we will analyze an equation that is gradient flow of a functional related to Hardy-Littlewood-Sobolev inequality in whole Euclidean space of higher dimensions. Professor Dimitrios Mitsotakis, Victoria University of Wellington, New ZealandJanuary 26th - March 2nd Seminar AMCS Mini Course: Mathematical and numerical modelling of water wavesDimitrios Mitsotakis, Victoria Univ. Wellington New ZealandSunday, February 10, 2019, 16:00- 17:30Building 1, Level 3, Room 3119Water wave propagationmathematical modellingContact PersonAthanasios TzavarasAbstract : The mathematical modelling of water waves continues to attract great interest bo
