In this talk, we present a class of stochastic differential games that can incorporate the distribution of the variables of interest (e.g., the system states and/or decision-makers' actions) into the strategic-interaction problem. We motivate the use of this type of differential games in networked large-scale applications that cover a high variety of engineering systems. In particular, we focus on the crowd evacuation problem. First, we only consider local aggregated congestion terms that penalize the magnitude of the decision-makers’ strategies allowing us to avoid the formation of congestion. Second, we consider both local and global aggregated congestion terms to perform crowd aversion during the evacuation procedure. We present some numerical results and few future directions, e.g., the case where decision-makers do not have prior knowledge about the geometry of the structure to be evacuated neither the existing obstacles.

In the last decade, the networking research community has significantly fueled the network softwarization and virtualization trend. Network processing tasks, originally performed by dedicated hardware appliances, were converted into software components running on commodity hardware, and deployed in relevant cloud infrastructures (central and/or edge).

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.

In this wide-ranging conversation with Peter Rawlinson, Lucid Motors’ CEO and CTO, he will discuss why he believes the world is on the precipice of a global transition toward electric vehicles, and how Lucid’s revolutionary technology and design will be at the forefront of one of the most significant transformations of our time.

This scientific meeting will concentrate on stochastic algorithms and their rigorous numerical analysis for various problems, including statistical learning, optimization, and approximation. Stochastic algorithms are valuable tools when addressing challenging computational problems.

Real life multi-phase and multi-physics problems coupled across different scales present outstanding challenges, whose practical resolution often require unconventional numerical methods.

In this course, we introduce the Boltzmann equation, i.e. the equation that describes the behavior of rarefied gases at a mesoscopic scale. This scale can be considered as in between the microscopic scale (where the gas is described as a set of a large number of particles) and the macroscopic one (where the gas is described as a continuum fluid). Starting from the classical free transport equation, we will describe the crucial role of the collisional operator that can be deduced from physical assumptions. In particular, we will focus on the formal derivation of the Boltzmann equation and on the techniques used to cope with its particular, highly singular, collisional operator, in the study of the Cauchy problem. We will conclude with the study of the Boltzmann equation in the more physically relevant case of bounded domains, considering several different boundary conditions such as in flow, specular reflection, bounce-back reflection and diffuse boundary conditions.

In this course, we introduce the Boltzmann equation, i.e. the equation that describes the behavior of rarefied gases at a mesoscopic scale. This scale can be considered as in between the microscopic scale (where the gas is described as a set of a large number of particles) and the macroscopic one (where the gas is described as a continuum fluid). Starting from the classical free transport equation, we will describe the crucial role of the collisional operator that can be deduced from physical assumptions. In particular, we will focus on the formal derivation of the Boltzmann equation and on the techniques used to cope with its particular, highly singular, collisional operator, in the study of the Cauchy problem. We will conclude with the study of the Boltzmann equation in the more physically relevant case of bounded domains, considering several different boundary conditions such as in flow, specular reflection, bounce-back reflection and diffuse boundary conditions.

How to Use Mathematics to Predict Cancer Patient Responses to Immuno-therapy.

In this course, we introduce the Boltzmann equation, i.e. the equation that describes the behavior of rarefied gases at a mesoscopic scale. This scale can be considered as in between the microscopic scale (where the gas is described as a set of a large number of particles) and the macroscopic one (where the gas is described as a continuum fluid). Starting from the classical free transport equation, we will describe the crucial role of the collisional operator that can be deduced from physical assumptions. In particular, we will focus on the formal derivation of the Boltzmann equation and on the techniques used to cope with its particular, highly singular, collisional operator, in the study of the Cauchy problem. We will conclude with the study of the Boltzmann equation in the more physically relevant case of bounded domains, considering several different boundary conditions such as in flow, specular reflection, bounce-back reflection and diffuse boundary conditions.

Geometry plays an important role in the design and fabrication of so-called freeform shapes. This talk will illustrate the fruitful interplay between theory and applications in this area. The focus will be on discrete differential geometry and on applications in architecture and fabrication-aware design.

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify posterior inference.

This talk focus on advanced modeling and optimization techniques to solve complex problems in the scheduling and planning of processes, energy systems, and water systems. Modeling and optimization techniques integrated with other disciplines have a paramount role in supporting the energy transition planning and the water-energy nexus. Specifically, optimizing the integration of renewable energy sources and new energy carriers in the energy mix, increasing the efficiency of existing and novel systems (enterprise-wide, industry, buildings, supply chains), and supporting decarbonization in industry. First, we describe canonical optimization formulations and show their flexibility and capabilities to address complex optimization problems. Examples of applications include process synthesis, production scheduling, short-term hydro scheduling, unit commitment, and even the transfer of human resources within large organizations. Then we focus on applying stochastic optimization approaches to address a virtual power plant's self-scheduling and market involvement, and finally on applying advanced optimization strategies for trajectory planning of underwater vehicles in uncertain and transient flow fields.

Mixing is a key process in a wide variety of technological applications. Pharmaceuticals, consumer products, and oil & gas derivatives, among many other products, rely on an energy-efficient, robust and effective mixing process. We will formulate the mixing process as a PDE-constrained optimization problem using special norms that concentrate on the mixedness of a passive scalar transported by nonlinear governing equations.

A personal presentation describing current “data analysis / statistical” challenges in state-of-the art biomedical projects. First, I will provide an overview of the transition between a PhD in Mathematics to a postdoc in Computational Biology: How did it happen? What were the challenges? Secondly, I will briefly present several current case-studies where statistics and machine learning are core to understand novel biological data related to multi-omic data analysis, spatial profiling, gene therapy and more.

The aim of this course is to introduce some numerical methods to solve mean field games and related problems.

The aim of this course is to introduce some numerical methods to solve mean field games and related problems.

The aim of this course is to introduce some numerical methods to solve mean field games and related problems.

The aim of this course is to introduce some numerical methods to solve mean field games and related problems.

Two or multiple phases in fluid mixture commonly occur in petroleum industry, where oil, gas and water are often produced and transported together.  Petroleum reservoir engineers spent great efforts in drainage problems arising from the development and production of oil and gas reservoirs so as to obtain a high economic recovery, by developing, conducting, and interpolating the simulation of subsurface flows of reservoir fluids, including water, hydrocarbon, CO2, H2S for example in porous geological formation.

The aim of this course is to introduce some numerical methods to solve mean field games and related problems. Mean Field Games (MFGs) systems were introduced independently by [4] and [5] in order to model dynamic games with a large number of indistinguishable small players.

The aim of this course is to introduce some numerical methods to solve mean field games and related problems. Mean Field Games (MFGs) systems were introduced independently by [4] and [5] in order to model dynamic games with a large number of indistinguishable small players. In the model proposed in [5], the asymptotic equilibrium is described by means of a system of two Partial Diferential Equations (PDEs).

Finite element approximation of Stokes equations with non-smooth data

We introduce ProxSkip a surprisingly simple and provably efficient method for minimizing the sum of a smooth (ƒ) and an expensive nonsmooth proximable (ψ) function.

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology (PH) is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this talk we will discuss a random persistence diagram generation (RPDG) method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned by (i) a model based on pairwise interacting point processes for inference of persistence diagrams, and (ii) by a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm for generating samples of PDs. An example on a materials science problem will demonstrate the applicability of the RPDG method.