Institut de recherche mathématique avancée

Résumé : Abstract: Despite the massive adoption of parallel architectures in modern electronic devices, parallel programming is still an expert's job. (SemAutomatic parallelization techniques are amongst the main hopes to bridge the gap between low parallel programming expertise and high and ubiquitous parallel architecture complexity. The polyhedral model has been at the root of many advances in the automatic parallelization and optimization field during the last decade. It is an algebraic representation of some classes of compute-intensive loops which allows us to analyze them in depth and to manipulate them aggressively. In this talk, I will present an introduction to the polyhedral model and how this formal representation complements the art of parallel programming with a science of loop transformation. I will review some ongoing academic and industrial work to rely on this model to integrate parallel programmer expertise to compilers and to design new tools to ease efficient parallel programming.

Speaker: Cedric Bastoul is full professor at the university of Strasbourg, associated with the Parallel Computing team at ICube laboratory and Inria. His research interests are in compiler technologies for optimization and parallelization with a strong emphasis on code restructuring using the polyhedral model. He created or maintains several well known tools in the high-level compilation community as the code generator CLooG and the parametric integer programming solver PIP. Recently, he served as Chief Scientist of Distributed and Parallel Software and director of Central Software Institute Paris at Huawei, and as Director at Qualcomm's Compiler Labs, heading R&D programs and working on generative AI software optimization.

Résumé : In our talk, we will present an extension of arithmetic intersection theory of adelic divisors on quasi-projective varieties introduced by Yuan–Zhang to the case where these divisors are not necessarily arithmetically nef. The key tool to realize this extension is the concept of relative finite energy established by T. Darvas et al.. In particular, our theory will allow to compute heights on mixed Shimura varieties, e. g., the arithmetic self-intersection number of the line bundle of Siegel–Jacobi forms on the universal abelian variety. This is joint work with José Burgos Gil.

Résumé : The aim of this talk is to explore several historical optimization problems together, namely Dido’s problem and the brachistochrone problem, by adopting an optimal control perspective. We start by introducing optimal control theory. This mathematical discipline consists in determining the best way to influence a dynamical system through a control or input so as to steer it toward a target state [control], while minimizing or maximizing a given cost functional [optimal]. Optimal control theory is used in a wide range of fields, including aerospace engineering (rocket trajectory optimization), finance (optimal portfolio management), and biology (population management). We focus on the case where a dynamical system is described by ordinary differential equations and we present Pontryagin’s Maximum Principle. An outline of the proof, aimed at providing insight into this principle, will also be given. Finally, we apply this framework to the historical problems mentioned above.

Résumé : Résumé : I will give a leisurely, elementary introduction to these two subjects, and then describe some recent progress on the so-called enumerative P=W conjecture, which provides a surprising link between the moduli spaces of Higgs bundles and integrable systems.