In 2019, diabetes caused 1.5 million global deaths, with 48% occurring before age 70. While Type 1 diabetes strongly depends on genetic components and is usually diagnosed in childhood, Type 2 diabetes is primarily caused by long term consumption of high calories foods. Lifestyle choices significantly influence the risk of Type 2 diabetes and obesity, including energy intake, diet composition, physical activity, and smoking.

When pressure acoustic waves interact with rotating scatterers, they undergo peculiar and intriguing characteristics. In this talk, I will discuss our recent findings on the physics of acoustic scattering and propagation in spinning fluids.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Until very recently, distribution-led local flexibility markets were exclusively an academic endeavor, with few practical applications, mostly limited to small-scale innovation projects. However, with European regulation finally catching up with the realities of modern distribution networks, local flexibility markets are slowly becoming a reality - new ones popping up across the continent, or some even becoming a BAU option in the most advanced countries.

The Pauli-Poisswell equation models fast-moving charges in semiclassical semi-relativistic quantum dynamics. It is at the center of a hierarchy of models from the Dirac-Maxwell equation to the Euler-Poisson equation that is linked by asymptotic analysis of small parameters such as the Planck constant or inverse speed of light. We discuss the models and their application in plasma and accelerator physics as well as the many mathematical problems they pose

We consider the widely used continuous $Q_{k+1}-Q_k$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

A subtle difference in a diffusion model can lead to an opposite conclusion. We need to understand how each component involved in the diffusion phenomenon contributes to the diffusion model. In this talk, we will discuss how nonconstant persistence and permeability play a role in the diffusion phenomenon.

The term doubly nonlinear refers to the fact that the diffusion part depends nonlinearly both on the gradient and the solution itself. Such equations describe several physical phenomena and were introduced by Lions and Kalashnikov. These equations have an intrinsic mathematical interest because they represent a natural bridge between the more natural generalizations of the heat equation: the p-Laplacian and the porous medium equation.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

Coffee time: 15:30–16:00. We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and allow us to design adaptive finite element methods for solving curved geometric singularities.

In the last decade reinforcement learning has demonstrated tremendous progress in terms of being a model-free control paradigm for decision making in complex systems with uncertainty and partial observability, thus making it a candidate technology for demand response with a promise of true scalability.

In this talk, we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus on the case of neuroscience.

Over the past decades, Jeff has been lucky enough to follow some of these developments from a front-row seat. He will share selected perspectives on current and past research including the various pendulum swings over the years between extremes, such as expertise-based knowledge engineering vs. data-centric machine learning, autonomous vs. mixed-initiative systems, publicly available chatbot capabilities vs. personalized, policy-governed multi-agent systems. In this talk, I will show what past research in AI has to teach us about the future.

Coffee Time: 15:30 - 16:00. The phase-field model, a powerful modeling tool for dealing with interface problems, has been widely used in various fields such as computational physics, computational biology, materials engineering, and even image processing. The dissipation of free energy is an important and fundamental property of the phase-field model.

We provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity. This is a joint work with A. Biswas and J. Tian.

Let us consider an elliptic equation of second order in variational form i.e. div(A(x)∇u) = divf in a bounded domain Ω ⊂ Rn where the function f belongs to some suitable function space.

Splitting methods have been shown to a useful tool in solving phase field equations. However, rigorous nonlinear stability analysis has not been available. In this short course, we will discuss some recent development in this direction.

Coffee Time: 15:30 - 16:00. Splitting methods are a well-established tool for numerically integrating time-dependent partial differential equations. These methods split the vector field into disjoint components, which are integrated separately using an appropriate time step. The individual flows are then combined to obtain the desired numerical approximation.

Many problems in applied geometry amount to the solution of a typically nonlinear partial differential equation. We will discuss why it may not be a good idea to discretize the equation, but to take the viewpoint of discrete differential geometry and discretize the theory.

A fascination with symmetric forms seems to be an innate feature of human perception and for millennia it has influenced art and natural philosophy. The concept of symmetry is one of the very few on which mathematicians and physicists agree, namely that Symmetry ≡ Groups. We describe some special symmetries and related problems including symmetric polynomials and monstrous moonshine.

We will give an overview of the development of Abstract Algebra from Galois to our time. The talk will be accessible to general audience with basic mathematical background.

The studies in numerical approximation of partial differential equations are characterized by the necessity of managing complex geometries and their discretization. We focus our attention on two different fields where complex geometries are very common: the mathematical modeling of fluid-structure interaction problems and the family of virtual element methods.

Clinical research often requires the simultaneous study of longitudinal repeated measurements and time-to-event (i.e., survival) data. Joint models, which can combine these two types of data, are invaluable tools in this context.