2023
Professor Jose Carrillo, University of Oxford, UK
January 8th - January 19th
Mathematics and Applications Colloquium
Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications
Prof. Jose Carrillo, Department of Mathematics, University of Oxford, UK
Tuesday, January 10, 2023, 15:30
- 17:00
Building 2, Level 5, Room 5209
Contact Person
Athanasios Tzavaras
This 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.
2022
Professor Sir John Ball, Heriot-Watt University, Edinburgh, UK
December
Dean's Distinguished Lecture
Liquid crystals from a mathematical perspective
Prof. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UK
Monday, December 12, 2022, 12:00
- 13:00
Building 1,Level 4, Room 4102
Contact Person
Athanasios Tzavaras
Liquid 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 Park
November 15th - December 15th
Mathematics and Applications Colloquium
On the role of pair correlations in the evolution of Bose-Einstein condensates
Prof. Manoussos Grillakis, Department of Mathematics, University of Maryland in College Park.
Wednesday, December 07, 2022, 15:30
- 17:00
Building 1, Level 3, Room 3119
Contact Person
Jinchao Xu
A 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, USA
May
Seminar
Mathematical Problems in Deep Learning
Prof. Hailiang Liu, Department of Mathematics, Iowa State University, USA
Wednesday, May 25, 2022, 15:00
- 16:00
B1, L4, R4102,
Contact Person
Athanasios Tzavaras
I 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.
2020
Professor Stefano Spirito, University of L'Aquila, Italy
February 1st - February 15th
Seminar
Weak solutions of the 2D Euler equations
Stefano Spirito, Assistant Professor, Department of Mathematics, University of L’Aquila, Italy
Tuesday, February 11, 2020, 15:00
- 16:00
Building 1, Level 3, Room 3119
Contact Person
Athanasios Tzavaras
In 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 Zealand
January 3rd - February 29th
Seminar
A regularized shallow-water waves system with slip-wall boundary conditions: Theory and numerical analysis
Dimitrios Mitsotakis, Senior Lecturer, School of Mathematics and Statistic Victoria University of Wellington, New Zealand
Wednesday, February 05, 2020, 16:00
- 17:00
Building 1, Level 4, Room 4214
Contact Person
Athanasios Tzavaras
In 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.
2019
Professor Jan Giesselman, Technical University of Darmstadt, Germany
April 1st - April 11th
Seminar
Mini Course Part 1-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows
Prof. Jan Giesselmann, Technical University of Darmstadt, Germany
Tuesday, April 02, 2019, 16:00
- 17:00
B1 L3 Room 3119
Contact Person
Athanasios Tzavaras
In 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, UAE
March 17th - March 22nd
Seminar
On Nonlocal Keller-Segel Type Equations
Dr. Suleyman Ulusoy, American University of Ras Al Khaimah, UAE
Wednesday, March 20, 2019, 16:00
- 17:00
Building 1, Level 3, Room 3119
Contact Person
Athanasios Tzavaras
In 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 Zealand
January 26th - March 2nd
Seminar
AMCS Mini Course: Mathematical and numerical modelling of water waves
Dimitrios Mitsotakis, Victoria Univ. Wellington New Zealand
Sunday, February 10, 2019, 16:00
- 17:30
Building 1, Level 3, Room 3119
Contact Person
Athanasios Tzavaras
Abstract : The mathematical modelling of water waves continues to attract great interest bo