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Optimal Primal-Dual algorithms – APDO
We are interested in the minimization of a convex function under affine constraints. The goal of the project is to develop optimal primal-dual algorithms under the assumption of metric sub-regularity for the generalized gradient of the Lagrangian function. With an analogy to the unconstrained case,
Symmetries and moduli spaces in algebraic geometry and physics – SMAGP
The project "Symmetries and moduli spaces in algebraic geometry and physics" (SMAGP) is an interdisciplinary research project between algebraic geometry, theory of automorphic forms and theoretical physics. The main goal of the project is the description of geometric, algebraic and arithmetic proper
Free space Isomorphisms and Isometries – FRII
This project aims at substantially advancing the knowledge about Lipschitz-free spaces and their applications to metric geometry and to functional analysis. For a metric space (M,d) the free space F(M) is a Banach space that is built around the metric space M in such a way that M is isometr
Parabolic pluripotential theory – PARAPLUI
The goal of this project is to develop a parabolic pluripotential theory motivated by the Minimal Model Program (MMP), whose aim is the (birational) classification of projective manifolds. Inspired by the celebrated work of Birkar-Cascini-Hacon-Mckernan which showed the existence of minimal models f
Integro-Differential Equations from EVolutionary biology – DEEV
We propose to develop new approaches to solve unconventional mathematical questions inspired by the evolutionary dynamics of structured populations. The evolutionary dynamics of phenotypically structured populations are governed by stochastic and deterministic processes. These processes describe i
Schrödinger problem, optimal transport and stochastic calculus – SPOT
The goal of this project is to study the most probable trajectory followed by an interacting particle system when a spontaneous fluctuation is observed. In its most basic form, this is known as the Schrödinger problem. In their general form, the problems at the heart of this project are formulated
Quantum fields interacting with geometry – QFG
The main aim of the project is the application of techniques from partial differential equations, microlocal analysis and scattering theory to the study of quantum matter interacting with spacetime geometry. The last decade has witnessed spectacular progress in the mathematical description of phenom
new TRends in EXtremes, prediction and validation – T-REX
Forecast is a major task of statistics in many domains of application. It often takes the form of a probabilistic forecast where the so-called predictive istribution represents the uncertainty of the future outcome given the information available today. Of particular interest is the distributional
Quantum trajectories – QTraj
This project deals with Markov processes describing quantum experiments and technologies. This processes are quite singular and the study of their time asymptotic behavior requires the development of new tools for the analysis of Markov chains. Some members of this project recently obtained signific
From Fano to hyperKähler varieties: geometry and derived categories – FanoHK
In complex geometry, one distinguishes three classes of varieties, according to the sign of the canonical bundle. Among those with trivial canonical bundle, the hyperKaehler varieties are the least understood, notably because examples are missing. However, subtle links were observed with some Fano
SWItched DIffusions : Metastability and Stochastic algorithms – SWIDIMS
The SWIDIMS project is concerned with the study and use in stochastic algorithms of switched diffusion processes, which describe the evolution in time of a system that evolves according to a collection of stochastic differential equations, switching from one to the other at random times. The seminal
Design of spatio-temporal networks in stochastic and dynamic environment: new mathematical models and optimization approaches – DESIDE
The main objective of this proposal is to provide new mathematical models and optimization approaches for design of spatio-temporal networks in stochastic and dynamic environment . Optimization approaches and mathematical modelling will concern strategic, tactical and operational levels. More specif
Critical Regularity, Interfaces, Scale Interactions and Singularities in the dynamics of non-homogeneous fluids – CRISIS
The project CRISIS is conceived to to give rigorous mathematical grounds to the description of heterogeneity effects, singular behaviours and multi-scale processes which occur and interplay in several real world phenomena related to fluid mechanics, and improve their theoretical understanding. We ha
Randomness, dynamics and spectrum – ADYCT
The last fifteen years have witnessed several significant progresses on the analytical understanding of chaotic dynamical systems, and in parallel on the study of models of random waves. Even if they took place in parallel, these new developments share many similarities in their objectives and metho
Higher Algebra, Geometry, and Topology – HighAGT
The present proposal is a program of fundamental research in Mathematics, more precisely in Algebra, Geometry, and Topology. Created over the past 50 years, the theory of higher structures (operads, homotopy algebras, infinity-categories) has given rise recently to powerful tools which lead to resol
New Trends in Control and Stabilization: Constraints and Non-local Terms – TRECOS
The goal of this project is to address new directions of research in control theory for partial differential equations, triggered by models from ecology and biology. In particular, our projet will deal with the development of new methods which will be applicable in many applications, from the tre
Space of Traffics and Asymptotics of Random Spectra – STARS
Random Matrix Theory developed during the last three decades in numerous fields of mathematics and physics. Free Probability Theory (FPT) is adapted for their analysis in large dimension. Operator-valued free probability and Traffic Probability Theory (TPT) are upgrades of FPT appropriate to describ
The aim of the project is to explore relations between combinatorial Hopf algebras (CHAs) and problems in physics (renormalization), algebra and topology (operads), control theory (Fliess operators) and probability (free probability, random walks). After the seminal work ofConnes and Kreimer the the
RarE and Typical fluctuation in non-Equilibrium classical and quaNtUm physics – RETENU
Ranging from nanosystems to macroscopic systems, classical or quantum, stochastic processes are essential to describe our world. The randomness may be inherent to the law of physics (quantum mechanics), to report on our ignorance of the complex interactions of these systems (noisy systems), or consc
Trisections and symplectic structures on smooth 4-manifolds & Higher dimensional generalizations – SyTriQ
This project concerns geometric topology, more precisely the study of smooth manifolds of dimension 4 and higher. Building on the recent theory of trisections of smooth 4--manifolds introduced by Gay and Kirby, the project investigates the relationship between this theory and symplectic geometry, an
Arithmetic of the j-invariant – JINVARIANT
The j-invariant is one of the most important and intriguing mathematical objects. In this project we will focus on studying arithmetical properties of the j-invariant, its generalizations, and adjacent objects (modular curves, modular forms, singular moduli, etc.). The members of the project are 6
Dynamic hyperbolic graphs – GrHyDy
In complex networks, it has been empirically observed that many networks typically are scale-free and exhibit a non-vanishing clustering coefficient. Models of complex networks that naturally exhibits these properties are random graph models in the hyperbolic plane, such as the random hyperbolic gra
Efficient Regularization of High-Dimensional Inverse Problems for Data Processing – EFFIREG
The need to efficiently process large amount of data has become ubiquitous in domains as wide as signal and image processing and machine learning. The objective of the EFFIREG project is to produce robust and computationally efficient data processing methods with theoretical performance guarantees
Non-local branching processes – NOLO
We are interested in the long-time behavior of infinite-dimensional branching processes and in the applications of these limiting results. Such stochastic processes are particle systems where particles move independently according to a Markov process. When a branching event occurs, a particle is rep
Methods for Low Dimensional Abelian Varieties – MELODIA
The main objective of the MELODIA project is to systematically study the algebraic structure of isogeny graphs of abelian varieties. Our investigations will be focused on low-dimensional abelian varieties defined over finite fields and directed towards attacking important open problems in number the
Random Schrödinger operators arising in the study of random walks – RAW
The aim of this project is to study random Schrödinger operators that have arised in recent years in connection with random walks in different settings, namely, random walks in random environments, random quantum walks, and random walks in highly connected networks. These settings all have in common
Arithmetic and geometry of discrete groups – AGDE
Arithmetic groups, and more generally groups of matrices with integral entries are an object of interest in geometric group theory, number theory and differential geometry and manifold topology. Our project integrates all these aspects. A central theme is the relation of the geometric structures ass