Events

Apr 9 - Apr 15, 2023

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  Reversal in the Stationary Prandtl Equations

  Prof. Nader Masmoudi

  Apr 13, 13:30 - 14:30

  B2 L5 R5220

  Reversal Stationary Prandtl Equations

  We investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by regions in which $u > 0$ and $u 0$. The classical point of view of regarding the Prandtl equations as an evolution equation in $x$ completely breaks down since $u$ changes sign. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. Joint work with Sameer Iyer.
• 

  High-order non-conforming finite elements for the Stokes equation

  Stefan Sauter, Professor, Institute of Mathematics, University of Zurich

  Apr 11, 16:00 - 17:00

  B2 L5 R5220

  High-order non-confirming Finite elements stokes equation

  We consider non-conforming discretizations of the stationary Stokes equation in two and three dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice.
• 

  Robust and efficient algorithms for phase equilibrium calculations of reservoir fluids at constant moles, volume and temperature

  Shuyu Sun, Professor of Earth Science and Engineering، KAUST

  Apr 10, 12:00 - 13:00

  B9 L3 R3128

  Reservoir simulation usually involves the fluid flow of partially miscible multi-component multi-phase mixture in porous media. Phase behavior of fluid mixture is a crucial component of many multi-phase flow framework. Accurate modeling and robust computation of the phase behavior is essential for optimal design and cost-effective operations in petroleum reservoirs as well as in a petroleum processing plant. A typical problem formulation in phase behavior is two-phase constant volume flash, i.e., the two-phase phase-split under the constant temperature, moles, and volume.

Apr 2 - Apr 8, 2023

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  Tides: Introduction and Modelling - Part 3

  Prof. Clodoaldo Grotta Ragazzo, Institute of Mathematics and Statistics of the University of Sao Paulo

  Apr 5, 10:00 - 12:00

  B1 L4 R4102

  "Force-deformation laws, Love numbers, and the Association Principle". This lecture contains a discussion about realistic force-deformation relations used for celestial bodies, their empirical description by means of Love numbers, and their mathematical modelling by means of the "Association Principle''.
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  Numerical Methods for Energy Minimisation: Application to Machine Learning Algorithms

  Prof. Charalambos Makridakis, Director of the Institute of Applied and Computational Mathematics of FORTH, Greece

  Apr 4, 16:00 - 17:00

  B2 L5 R5220

  numerical methods energy minimization Applied Machine Learning

  In this talk, we discuss problems and numerical methods arising in the calculus of variations and energy minimization. Among numerous applications, energy minimization is a core element of Machine Learning algorithms. Within the field of nonlinear PDEs, the calculus of variations has received a lot of attention from the analysis point of view. Although quite interesting and challenging, the numerical analysis of these problems is much less developed.
• 

  Tides: Introduction and Modelling - Part 2

  Prof. Clodoaldo Grotta Ragazzo, Institute of Mathematics and Statistics of the University of Sao Paulo

  Apr 4, 10:00 - 12:00

  B1 L4 R4102

  "Translation, rotation and Deformation". In this lecturer, we will present the simplest possible model for the motion of two extended rigid bodies interacting by gravity.
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  Using the smithy of computational science to enhance the robustness and efficiency of complex fluid flow simulations.

  Matteo Parsani, Associate Professor, Applied Mathematics and Computational Sciences

  Apr 3, 12:00 - 13:00

  B9 L3 R3128

  This talk will review the recent shift in the construction and modern analysis of a large class of spatially and temporally adaptive methods whose properties are very close to our current analytical knowledge about hyperbolic or mixed hyperbolic-parabolic partial differential equations (PDEs) in computational physics. Thus these algorithms can be regarded as the elite methods in the field. Next, we will show examples of how the robustness and efficiency of the fully-discrete representation of PDEs can be enhanced using computational science's smithy, i.e., "modern" numerical analysis. The talk will showcase complex flow problems in aeronautics, aerospace, and automotive sectors, provide preliminary results in other fields, and present an outlook for future research directions where data science can currently be the linesman.
• 

  Tides: Introduction and Modelling - Part 1

  Prof. Clodoaldo Grotta Ragazzo, Institute of Mathematics and Statistics of the University of Sao Paulo

  Apr 3, 10:00 - 12:00

  B1 L4 R4102

  "Qualitative theory of tides and their effects." It contains a qualitative explanation of tides and their effects: phase lags, forces that dissipate energy but do not dissipat angular momentum, circularization of orbits, spin-orbit synchronization and collision.
• 

  Non-Abelian Braiding with Sound and Light

  Guancong Ma, Associate Professor, Department of Physics, Hong Kong Baptist University

  Apr 3, 09:30 - 10:30

  B9 L2 R2131

  Abstract Non-Abelian-based theories are one of the foundations of modern physics. For example, non-Abelian braiding realized by the dynamic winding of anyons is widely considered an important candidate for quantum computers. Operations defined by non-Abelian groups are non-commutative in character, meaning that the outcomes of sequential operations depend on the order of execution. Non-Abelian processes can be mathematically captured by unitary matrices, which can manifest as a Berry-phase matrix that connects holonomic adiabatic evolutions of multiple states in parameter space. Because the

Mar 26 - Apr 1, 2023

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  On the rate of convergence of the Inviscid Limit for 2D Incompressible Fluid

  Associate Professor Stefano Spirito, Department of Mathematics, University of LAquila, Italy

  Mar 30, 12:00 - 13:00

  B1 L4 R4102

  This talk reviews recent results concerning the inviscid limit for the 2D Euler equations with unbounded vorticity. In particular, by using techniques from the theory of transport equation with no smooth vector fields, we show that the solutions obtained in the vanishing viscosity limit satisfy a representation formula in terms of the flow of the velocity and that the strong convergence of the vorticity holds and we give a rate of convergence.
• 

  Scalable parallel solvers for cardiac reaction-diffusion models and applications

  Luca F. Pavarino, Professor, Department of Mathematics, Università degli Studi di Pavia

  Mar 28, 16:00 - 17:00

  B2 L5 R5220

  Applied Partial Differential Equations parallel simulations

  After a brief introduction to the field of Computational Cardiology and cardiac reentry, we introduce and study some scalable domain decomposition preconditioners for cardiac reaction-diffusion models, discretized with splitting semi-implicit techniques in time and isoparametric finite elements in space.
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  From Contact to Fluid Structure Interavtion Information Transfer between Non-matching meshes for Coupled Simulations

  Prof. Rolf Krause, Università della Svizzera italiana

  Mar 27, 12:00 - 13:00

  B9 L3 R3128

  The transfer of information between non-matching meshes is an important ingredient for coupled multi-physics simulations. For most coupled problems information, such as displacements or stresses, has to be exchanged between, two different meshes. As an example consider fluid-structure interaction (FSI) problem, where information has to be transferred between a fluid and an elastic body (the "S"tructure in FSI).
• 

  Mathematics of Emergent Phenomena in Networks and Collective Motion

  Jan Haskovec, Senior Research Scientist, Applied Mathematics and Computational Sciences

  Mar 26, 12:00 - 13:00

  B9 L3 R3131

  Emergence of nontrivial patterns via collective actions of many individual entities is an ever-present phenomenon in physics, biology and social sciences. It has numerous applications in engineering, for instance, in swarm robotics. I shall demonstrate how tools from mathematical modeling and analysis help us gain understanding of fundamental principles and mechanisms of emergence. I will present my recent results in consensus formation and flocking models, taking into account their realistic aspects - noise, latency, finite speed of information propagation and anticipation. Moreover, I will introduce a continuum modeling framework for biological network formation, where emergence takes place through the interaction of structure and medium. The models are formulated in terms of ordinary, stochastic and partial differential equations. I shall explain how mathematical analysis of the respective models contributes to the understanding of how individual rules generate and influence the patterns observed on the global scale. Finally, I will explain how requirements on robustness of the network can be incorporated into the mathematical model.

Mar 19 - Mar 25, 2023

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  Proximal Algorithms for Large-Scale Convex Non-smooth Optimization

  Laurent Condat, Senior Research Scientist, Computer, Electrical and Mathematical Sciences and Engineering

  Mar 21, 16:00 - 17:00

  B2 L5 R5220

  algorithms stochastic algorithm

  Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of iterative fixed-point algorithms known as proximal splitting algorithms is particularly adequate: they consist of simple operations, handling the terms in the objective function separately. I will present a selection of recent primal-dual algorithms within a unified framework, which consists in solving monotone inclusions with well-chosen spaces and metrics.
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  On Fourier methods and machine learning techniques in Computational Finance.

  Prof. Kees Oosterlee, Utrecht University

  Mar 20, 12:00 - 13:00

  B9 L3 R3128

  In this presentation we will explain how we can solve linear, semi-linear as well as nonlinear partial differential equations by the concept of backward stochastic differential equations and Fourier cosine expansions. We will discuss the highly efficient pricing of financial options in the Fourier context by means of the COS method. Particularly, we also present a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the effects of self-excitation and contagion of stock prices.
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  5th KAUST CEMSE MaS Workshop on Modelling and Simulation

  Speakers from KAUST, Melbourne, Utrecht, Karlsruhe, Erlangen, Brisbane, Langensteinbach, Lugano, Frankfurt, Italy

  Mar 20, 09:00 - Mar 25, 17:30

  B3 L5 R5209

  Applied Partial Differential Equations

  The workshop provides a forum for researchers to present and discuss recent progress in modelling and simulation research. Topics are Simulating unsteady CO 2 flow through brine-saturated cross-bedded sandstones: towards relative permeability curves for unstable displacement On Fourier methods and machine learning techniques in Computational Finance Pore-scale modelling of flow and transport in porous media Uncertainty Quantification of Density-Driven Groundwater Flow Simulation of unsaturated Density-Driven flow with a phreatic surface Modeling and Large-scale Simulation of Carbon Dioxide

Mar 12 - Mar 18, 2023

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  Gravitational Collapse of Self-similar stars

  Dr. Matthew Schrecker, Departments of Mathematics, University College London

  Mar 16, 16:00 - 17:00

  B1 L4 R4102

  Nonlinear Partial Differential Equation Gravitational collapse UCL

  The Euler-Poisson equations give the classical model of a self-gravitating star under Newtonian gravity. It is widely expected that, in certain regimes, initially smooth initial data may give rise to blow-up solutions, corresponding to the collapse of a star under its own gravity. In this talk, I will present recent work with Yan Guo, Mahir Hadzic and Juhi Jang that demonstrates the existence of smooth, radially symmetric, self-similar blow-up solutions for this problem. I will also comment on the stability of the obtained solution. At the heart of the analysis is the presence of a sonic point, a singularity in the self-similar model that poses serious analytical challenges in the search for a smooth solution.
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  Mathematical Analysis of Atmospheric and Oceanic Dynamics Models: Cloud Formation and Sea-ice Models

  Prof. Edriss S. Titi

  Mar 14, 16:00 - 17:00

  B3 L5 R5209

  atmosphere

  In this talk we will present rigorous analytical results concerning global regularity, in the viscous case, and finite-time singularity, in the inviscid case, for oceanic and atmospheric dynamics models. Moreover, we will also provide a rigorous justification of the derivation of the Primitive Equations of planetary scale oceanic dynamics from the three-dimensional Navier-Stokes equations as the vanishing limit of the small aspect ratio of the depth to horizontal width.
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  Algebraic Structures from beginning to Lie algebras-Part 2

  Associate Professor Amir Baklouti, Department of Mathematics, Umm Al-Qura University (KSA

  Mar 14, 14:00 - 16:00

  B1 L4 R4102

  This brief course will cover several algebraic structures, beginning with groups and culminating with algebras. Our primary the focus will be on Lie algebras, and we will introduce the essential properties and results necessary to comprehend the structure of Lie algebras and other related structures
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  Decision Trees for Fault Diagnosis in Circuits and Switching Networks - 2023-03-13

  Mikhail Moshkov, Professor, Applied Mathematics and Computational Sciences

  Mar 13, 12:00 - 13:00

  B9 L3 R3128

  We study theoretical problems of fault diagnosis in circuits and switching networks, which are among the most fundamental models for computing Boolean functions. We investigate two main cases: when the scheme (circuit or switching network) has the same mode of operation for both calculation and diagnostics, and when the scheme has two modes of operation -normal for calculation and special for diagnostics.
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  Algebraic Structures from beginning to Lie algebras- Part 1

  Associate Professor Amir Baklouti, Department of Mathematics, Umm Al-Qura University (KSA

  Mar 13, 10:00 - 12:00

  B1 L4 R4102

  This brief course will cover several algebraic structures, beginning with groups and culminating with algebras. Our primary the focus will be on Lie algebras, and we will introduce the essential properties and results necessary to comprehend the structure of Lie algebras and other related structures.

Mar 5 - Mar 11, 2023

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  Functional Differential Equations in Models of Collective Behavior - Colloquium

  Jan Haskovec, Senior Research Scientist, Applied Mathematics and Computational Sciences

  Mar 7, 16:00 - 17:00

  B4 L5 R5220

  Functional Differential Equation Models collective behavioral analysis

  I will give an overview of recent results for models of collective behavior governed by functional differential equations. The talk 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. I will explain that there are two main sources of delay - inter-agent communications and information processing
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  Bayesian Deep Learning

  Maurizio Filippone, Associate Professor, EURECOM, France

  Mar 6, 12:00 - 13:00

  B9 L3 R3128

  Bayesian computational statistics Deep learning

  The impressive success of Deep Learning (DL) in predictive performance tasks has fueled the hopes that this can help addressing societal challenges by supporting sound decision making. However, many open questions remain about their suitability to hold up to this promise. In this talk, I will discuss some of the current limitations of DL, which directly affect their wide adoption. I will focus in particular on the poor ability of DL models to quantify uncertainty in predictions, and I will present Bayesian DL as an attractive approach combining the flexibility of DL with probabilistic reasoning. I will then discuss the challenges associated with carrying out inference and specifying sensible priors for DL models. After presenting a few of my contributions to address these problems, I will conclude by presenting some interesting emerging research trends and open problems which define my current research agenda.

Feb 26 - Mar 4, 2023

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  A novel structure preserving scheme for Schrondiger-Poisson systems.

  Dr. Th. Katsaounis

  Feb 28, 16:00 - 17:00

  B2 L5 R5220

  Novel structure preserving Schrondiger Poisson Systems

  In this talk I will present a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrodinger-Poisson system. We use the Crank-Nicolson scheme as a time-stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system’s mass conservation and energy balance laws for constant discretization parameters.
• 

  Controlling acoustic wave propagation via rotational motion

  Ying Wu, Professor, Applied Mathematics and Computational Sciences

  Feb 27, 12:00 - 13:00

  B9 L2 H2 H2

  acoustic waves

  Propagation of acoustic waves in time-varying and/or moving media has attracted a lot of attentions and is expected to lead to many intriguing applications. In this talk, I will discuss our recent work on acoustic wave propagation in spinning media (air or water). I will start with a review of the theoretical foundation built upon the Mie scattering framework, in which both the wave equation and the boundary conditions will be specifically discussed. The study is limited in the linear regime and exhibit the peculiar scattering features.

Feb 12 - Feb 18, 2023

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  Asymptotic Analysis and Numerical Methods for Compressible Flows at Low Mach Numbers

  Prof. Dr. Andreas Meister, Professor, Department of Mathematics and Natural Sciences, University of Kassel

  Feb 14, 16:00 - 17:00

  B1 L4 R4102

  Asymptotic Performance Analysis numerical methods compressible flows Mach Numbers

  We will present a comprehensive study of a finite volume method for inviscid and viscous flow fields at high and low speeds. Thereby, the results of a formal asymptotic low Mach number analysis are used to extend the validity of the numerical method from the simulation of compressible flow fields at transonic as well as supersonic speed to the low Mach number regime.
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  An introduction to Patankar-type schemes

  Thomas Izgin, M.Sc., Department of Mathematics, University of Kassel

  Feb 14, 14:00 - 15:00

  B9 L3 R3229

  numerical analysis

  We present order conditions for various Patankar-type schemes as well as a new stability approach that examines the non-hyperbolic fixed points of the schemes for a general linear test problem. We formulate sufficient conditions for the stability of such non-hyperbolic fixed points and the local convergence of the numerical approximation towards the correct steady-state solution of the underlying test problem. To illustrate the theoretical results, we consider several members of the modified Patankar-type family within numerical experiments.
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  Research on Sound and Vibration @ Hong Kong PolyU

  Prof Li Cheng, Chair Professor and Director, The Hong Kong Polytechnic University

  Feb 13, 12:00 - 13:00

  B9 L3 R3128

  acoustic-elastic metamaterials

  As one of the founding departments in the Hong Kong Polytechnic University (PolyU) eighty-five years ago, the Department of Mechanical Engineering (ME) has been actively involved in both fundamental and applied research to advance the frontier of knowledge to serve Hong Kong, its surrounding region and beyond. The research foci of the department are in four major areas under three Research Centres and a Research Consortium under the University Niche Area scheme.

Feb 5 - Feb 11, 2023

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  Point processes and their application to modeling drug seizure and overdose interactions

  Prof. George Mohler, Computer Science, Boston College

  Feb 8, 17:00 - 18:00

  KAUST

  point processes stochastic models

  In this talk we first provide an introduction to point processes, which are stochastic models for the occurrence of events in space and time. We then discuss the application of point processes to investigate the relationship between law enforcement drug seizures and accidental overdoses in Indianapolis. We will also discuss results from a field-experiment in Indianapolis where point process based harm indices were used to inform the distribution of addiction treatment information.
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  Theoretical understanding of learning dynamics in modern deep learning

  Dr. Zhanxing Zhu, Senior Research Professor. Changping National lab, Beijing

  Feb 7, 16:00 - 17:00

  B2 L5 R5209

  Coffee Time: 15:30-16:00. It has been a long-standing debate that “Is deep learning alchemy or science? ”, since the success of deep learning mainly relies on various engineering design and tricks, and lack of theoretical foundation. Unfortunately, the underlying mechanism of deep learning is still mysterious, severely limiting its further development from both theoretical and application aspects.
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  On the Mathematics of Turbulent flows

  Luigi C. Berselli, Visiting Faculty, University of Pisa

  Feb 6, 12:00 - 13:00

  B9 L3 R3128

  Mathematical modeling Turbulent

  The understanding and description of turbulent flows poses several different problems in which theory, modeling, and (numerical) experiments interact in a multidisciplinary way. In this talk we present some of the basic tools, focusing on the mathematical foundation of the models used to describe the larger scales of the incompressible motions at high Reynolds number. Recent perspectives and open problems are also discussed.
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  Waves Functional Materials - 2023-02-05

  Ying Wu, Professor, Applied Mathematics and Computational Sciences

  Feb 5, 12:00 - 13:00

  B9 L2 H2

  Waves Functional Materials

  Wave functional materials are artificial materials that can control wave propagation as wish. In this talk, I will give a brief review on the progress of wave functional materials and reveal the secret behind the engineering of these materials to achieve desired properties. In particular, I will focus on our contributions on metamaterials and metasurfaces.

Jan 29 - Feb 4, 2023

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  Forward and Backward Tracking of Oil Spills Under Ensemble DA Uncertainties with Real World Applications in the Red Sea

  Ibrahim Hoteit, Professor, Earth Science and Engineering

  Jan 31, 15:30 - 17:00

  B1 L4 R4102

  Oil Spills

  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.
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  Applied Nonlinear Partial Differential Equations (PDEs)

  Peter Markowich, Al-Khawarzmi Distinguished Professor, Applied Mathematics and Computational Sciences

  Jan 30, 14:30 - Jan 31, 17:15

  KAUST

  Most phenomena in Nature are nonlinear, and their modeling requires nonlinear partial differential equations (PDE). These are elusive objects, and solving them explicitly is almost always out of reach. We are then left to prove that solutions exist, are unique, satisfy specific properties that somehow characterize them, and then implement numerical methods to approximate those solutions. Existence shows we are modeling a real problem and uniqueness that it is meaningful. However, for the model to be useful and the numerical methods to converge, we need to understand the behavior of the
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  Driving Innovation by Simulation

  Dr. Emad Dlala, Vice President Powertrain, Lucid Motors Co.

  Jan 30, 12:00 - 13:00

  B9 L3 R3128

  Driving innovation aerodynamic simulations

  Dr. Emad Dlala is Vice President of Powertrain at Lucid. He is responsible for powertrain development and engineering, including batteries, drive units, and power electronics. He also leads Lucid’s systems efficiency strategy. Emad previously served as Senior Director of Efficiency and Energy Technology. Emad has been with Lucid in various technical roles since 2015 where he’s led efforts to develop breakthrough technologies that achieved unmatched range and performance in the Lucid Air. Emad brings more than two decades of engineering experience to his current leadership role. Prior to Lucid, he worked as a Senior Application Engineer at ANSYS Inc. developing cutting-edge, computer-based engineering simulation technologies. Emad holds a Ph.D. and M.Sc. in Electrical Engineering from Aalto University, Finland, and a B.Sc. in Electrical Engineering from Al-Zawiya University, Libya.

Jan 15 - Jan 21, 2023

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  Aggregation-Diffusion and Kinetic PDEs for collective behavior: applications in the sciences

  Prof. José Antonio Carrillo de la Plata, Mathematical Institute, University of Oxford

  Jan 15, 16:00 - 17:00

  B1 L3 R3119

  Partial Differential Equations University of Oxford

  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.

Jan 8 - Jan 14, 2023

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  Simulation and Calibration of Uncertain Space Fractional Diffusion Equations

  Hasnaa Alzahrani, Ph.D. Student, Applied Mathematics and Computational Sciences

  Jan 10, 16:00 - 18:00

  B1 L2 R2202

  This dissertation explores the uncertainty propagation in space fractional diffusion equations in one and multiple dimensions with variable diffusivity and order parameters.
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  Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications

  Prof. Jose Carrillo, Department of Mathematics, University of Oxford, UK

  Jan 10, 15:30 - 17:00

  B2 L5 R5209

  Fokker-Planck equations Cucker-Smale orientation dynamics McKean-Vlasov equations Keller-Segel-type models

  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.

Dec 11 - Dec 17, 2022

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  Monodromy and approach to equilibrium for viscoelastic models allowing microstructure

  Prof. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UK

  Dec 13, 15:30 - 17:00

  B3 L5 R5220

  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.
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  Liquid crystals from a mathematical perspective

  Prof. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UK

  Dec 12, 12:00 - 13:00

  B1 L4 R4102

  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.

Dec 4 - Dec 10, 2022

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  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.

  Dec 7, 15:30 - 17:00

  B1 L3 R3119

  nonlinear Schr¨odinger equation

  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.
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  Optimal-complexity Multigrid Solvers for High-order FEM in the de Rham Complex

  Prof. Patrick Farrell, University of Oxford

  Dec 6, 15:30 - 17:00

  B1 L3 R3119

  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.
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  Modelling and Simulation of Biological Systems - 2022-12-06

  Gabriel Wittum, Professor, Applied Mathematics and Computational Sciences

  Dec 6, 12:00 - 13:00

  B9 L2 R2322

  Biological systems

  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.

Nov 27 - Dec 3, 2022

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  Generic Regularity in Obstacle Problems

  Professor Alessio Figalli, ETH Zurich

  Nov 29, 16:00 - 17:00

  KAUST

  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.
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  A unifying partially-interpretable framework for neural network-based extreme quantile regression

  Raphaël Huser, Associate Professor, Statistics

  Nov 29, 12:00 - 13:00

  B9 L2 R2322

  Artificial Neural Network quantile regression

  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.
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  On the collapse mechanism of Wave Maps

  Prof. Manoussos Grillakis, Departments of Mathematics, University of Maryland

  Nov 27, 13:00 - 15:00

  B1 L4 R4214

  Partial Differential Equations

  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.

Nov 20 - Nov 26, 2022

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  Sharp Approximation Rates for Deep ReLU Neural Networks on Sobolev Spaces

  Assistant Professor Jonathan Siegel, Texas A and M University

  Nov 22, 15:30 - 17:00

  B1 L3 R3119

  ReLU Neural Network Sobolev Spaces

  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.
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  Lipschitz learning and the infinity-Laplacian

  Miguel Urbano, Professor, Applied Mathematics and Computational Sciences

  Nov 22, 12:00 - 13:00

  B9 L2 R2322

  Lipschitz additive nonlinear uncertainty infinity Laplacian

  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).
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  On training algorithms for neural networks

  Jinchao Xu, Professor, Applied Mathematics and Computational Sciences

  Nov 21, 12:00 - 13:00

  B9 L2 R2322 H1

  Deep learning deep neural networks

  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

Nov 13 - Nov 19, 2022

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  Functional Differential Equations in Models of Collective Behavior - Graduate Seminar

  Jan Haskovec, Senior Research Scientist, Applied Mathematics and Computational Sciences

  Nov 15, 12:00 - 13:00

  B9 L2 R2322

  Functional Differential Equation

  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.