Prof. Ibrahim Hoteit, Professor, Dir. Nat. Climate Change Center Exc., Earth Science and Engineering, KAUST
Tuesday, January 31, 2023, 15:30
- 17:00
Building 1, Level 4, Room 4102
Contact Person
The talk will present our efforts to develop the next-generation operational system for the Red Sea, as part of Aramco’s resolution toward the fourth industrial revolution. This integrated system has been built around state-of-the-art ocean-atmosphere-wave general circulation models that have been specifically developed for the Red Sea region and nested within the global weather systems.
Prof. José Antonio Carrillo de la Plata, Mathematical Institute, University of Oxford
Sunday, January 15, 2023, 16:00
- 17:00
Building 1, Level 3, Room 3119
Contact Person
In this seminar, I will present a survey of micro, meso and macroscopic models where repulsion and attraction effects are included through pairwise potentials. I will discuss their interesting mathematical features and applications in mathematical biology and engineering. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. I will showcase the breadth of possible applications with three different phenomena in applications: segregation, phase transitions, and consensus.
Tuesday, January 10, 2023, 16:00
- 18:00
Building 1, Level 2, Room 2202; https://kaust.zoom.us/j/97190474480
Contact Person
This dissertation explores the uncertainty propagation in space fractional diffusion equations in one and multiple dimensions with variable diffusivity and order parameters.
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
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.
Prof. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UK
Tuesday, December 13, 2022, 15:30
- 17:00
Building 3,Level 5, Room 5220
Contact Person
For certain models of one-dimensional viscoelasticity, there are infinitely many equilibria representing phase mixtures. In order to prove convergence as time tends to infinity of solutions to a single equilibrium, it seems necessary to impose a nondegeneracy condition on the constitutive equation for the stress. The talk will explain this and show how in some cases, the nondegeneracy condition can be proved using the monodromy group of a holomorphic map. This is joint work with Inna Capdeboscq and Yasemin Şengül. John Ball is Professor of Mathematics at Heriot-Watt University, Edinburgh, and formerly Sedleian Professor of Natural Philosophy at Oxford. He is the current President of the Royal Society of Edinburgh, and a former President of the International Mathematical Union. He specializes in the applications of nonlinear analysis to problems of materials science, liquid crystals and computer vision. Among various awards he received the 2018 King Faisal Prize for Science, the 2018 Leonardo da Vinci Award of the European Academy of Sciences and the 2022 De Morgan Medal of the London Mathematical Society.
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
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.
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
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.
Prof. Patrick Farrell, University of Oxford
Tuesday, December 06, 2022, 15:30
- 17:00
Building 1, Level 3, Room 3119
Contact Person
In this work we present multigrid solvers for high-order finite element discretizations of these Riesz maps with optimal complexity in polynomial degree, i.e. With the same time and space complexity as sum-factorized operator application.
Tuesday, December 06, 2022, 12:00
- 13:00
Building 9, Level 2, Room 2322
Contact Person
Biological systems are distinguished by their enormous complexity and variability. That is why mathematical modelling and computational simulation of those systems is very difficult, in particular thinking of detailed models which are based on first principles. The difficulties start with geometric modelling which needs to extract basic structures from highly complex and variable phenotypes, on the other hand also has to take the statistic variability into account.
Professor Alessio Figalli, ETH Zurich
Tuesday, November 29, 2022, 16:00
- 17:00
https://kaust.zoom.us/j/94729398062
Contact Person
The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is smooth outside a set of singular points. Explicit examples show that the singular set could be, in general, as large as the regular set. In a recent paper with Ros-Oton and Serra we show that, generically, the singular set has codimension 3 inside the free boundary, solving a conjecture of Schaeffer in dimension n ≤ 4. The aim of this talk is to give an overview of these results.
Tuesday, November 29, 2022, 12:00
- 13:00
Building 9, Level 2, Room 2322
Contact Person
In this paper, we propose a new methodological framework for performing extreme quantile regression using artificial neural networks, which are able to capture complex non-linear relationships and scale well to high-dimensional data.
Prof. Manoussos Grillakis, Departments of Mathematics, University of Maryland
Sunday, November 27, 2022, 13:00
- 15:00
Building 1, Level 4, Room 4214
Contact Person
The Wave Map system describes the evolution of waves constrained on a (Riemannian)  manifold. For the 2 + 1 dimensional problem, when the target manifold is a sphere, the solution collapses in finite time. The Analysis is due to the pioneering work of Merle, Paphael and Rodnianski. Motivated by their work I will present a somewhat novel approach of the collapsing mechanism which is based on a view of the equations as a nonlinear gauge system. This is joint work with Dan Geba.
Assistant Professor Jonathan Siegel, Texas A and M University
Tuesday, November 22, 2022, 15:30
- 17:00
Building 1, Level 3, Room 3119
Contact Person
Sobolev spaces are centrally important objects in PDE theory. Consequently, to understand how deep neural networks can be used to numerically solve PDEs a necessary first step is to determine now efficiently they can approximate Sobolev functions. In this talk we consider this problem for deep ReLU neural networks, which are the most important class of neural networks in practical applications.
Tuesday, November 22, 2022, 12:00
- 13:00
Building 9, Level 2, Room 2322
Contact Person
Infinity-harmonic functions have recently found application in Semi-Supervised Learning, in the context of the so-called Lipschitz Learning. With this application in mind, we will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions and its several drawbacks, leading to the notion of AMLE (Absolutely Minimising Lipschitz Extension).
Monday, November 21, 2022, 12:00
- 13:00
Building 9, Level 2, Room 2322, Hall 1
Contact Person
In this talk, I will first give a convergence analysis of gradient descent (GD) method for training neural networks by relating them with finite element method. I will then present some acceleration techniques for GD method and also give some alternative training algorithms
Tuesday, November 15, 2022, 12:00
- 13:00
Building 9, Level 2, Room 2322
Contact Person
The talk will give an overview of recent results for models of collective behavior governed by functional differential equations. It will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role.
Prof. Simone Scacchi, Associate Professor of Numerical Analysis at the Department of Mathematics of the University of Milan
Tuesday, November 08, 2022, 15:30
- 17:00
Building 1, Level 3, Room 3119
Contact Person
In this seminar, we will present our work on Virtual Element Method (VEM) approximations. The Virtual Element Method is a recent numerical technique for solving partial differential equations on computational grids constituted by polygonal or polyhedral elements of very general shape. This work aims to develop effective linear solvers for general order VEM approximations of three-dimensional scalar elliptic equations in mixed form and Stokes equations. To this end, we consider block algebraic multigrid preconditioners and balancing domain decomposition by constraints (BDDC) preconditioners. The latter allows us to use conjugate gradient iterations, albeit the algebraic linear systems arising from the discretization of the differential problems are indefinite, ill-conditioned, and of saddle point nature.
Tuesday, November 08, 2022, 12:00
- 13:00
Building 9, Level 2, Room 2322
Contact Person
Surface water waves are a physically important phenomenon with which we all have some experience. They are also surprisingly complex and interesting from a mathematical perspective. I will discuss two recent projects in water wave modeling. The first deals with ocean waves, such as tsunamis, passing over the continental slope. It has long been known that the amplification of such waves is greater than what the traditional transmission coefficient would predict.
Prof. Michal Mankowski, Assistant Professor of Operations Research, Erasmus University Rotterdam, Netherlands
Tuesday, November 08, 2022, 10:00
- 11:30
Building 1, Level 3, Room 3119
Contact Person
The aim of this course is to familiarize the students with the usage of Computer Simulation tools for complex problems. The course will introduce the basic concepts of computation through modeling and simulation that are increasingly being used in industry and academia. The basic concepts of Discrete Event Simulation will be introduced along with the reliable methods of random variate generation and variance reduction. Later in the course, the concept of simulation-based optimization and output analysis will be discussed. The example of simulation (and optimization) applied to design an optimal organ allocation policy in the US will be discussed.
Monday, November 07, 2022, 14:00
- 16:00
Building 1, Level 2, Room 2202
Contact Person
In this thesis, we present three projects. First, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite-difference scheme for the approximation of the Hamiltonian. We show that the approximation scheme is stable under an appropriate condition on the discretization parameters and converges to the unique viscosity solution of the Hamilton-Jacobi equation.
Prof. Gonçalo dos Reis, School of Mathematics, University of Edinburgh
Tuesday, November 01, 2022, 15:30
- 17:00
Building 1, Level 3, Room 3119
Contact Person
We propose a novel approach of numerically approximate McKean-Vlasov SDEs that avoids the usual interacting particle approximation and Propagation of Chaos results altogether.