
Learning, geometry and PDEs, a promising interaction?
— Emmanuel Franck
20 janvier 2022  09:00Salle de conférences IRMA
In this talk, we want to introduce different examples or problems of interaction between deep learning, geometry, PDEs and numerical methods. We will start by illustrating the ability of deep learning to deal with physical problems starting from a classical problem in fluid mechanics: the closure. In a second step, we will introduce recent works mixing learning and differential geometry which allow to tackle unstructured data. We will illustrate this with simple examples from PDEs. Finally, we will show how ideas from analytical mechanics (and symplectic geometry) can interact with machine learning and numerical simulations of PDEs.
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Emmanuel Franck did his Ph.D. thesis from 2009 to 2012 at the CEA on the numerical approximation of the radiative transfer equation. After that he did a 2 year postdoc at the Max Planck Institute for Plasma Physics in Munich on numerical methods for MHD in nuclear fusion. He is an INRIA young researcher since 2014 and his work focuses on the numerical approximation of PDEs in fluid mechanics and plasma physics. He is a member of the Modelling and Control (MOCO) research group at IRMA, Strasbourg.

The physical processes driving galaxy formation and evolution span a vast range of scales, from the large scale structures of the universe to the turbulent interstellar medium and the interactions between light and matter. In this talk, I will present some of the empirical scaling relations that guide our understanding of these complex physical processes, focussing notably on the fate of gas within galaxies, star formation, and the relation between galaxies and their surrounding dark matter haloes.
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Jonathan Freundlich did his Ph.D. between 2012 and 2015 at the Paris Observatory, probing star formation across cosmic time and modelling the influence of baryons on dark matter haloes. He was afterwards a postdoc at the Hebrew University of Jerusalem, where he gained experience in analysing cosmological simulations. He became Maître de Conférences at the Strasbourg Observatory in 2021, within the Galaxies, High Energy, Cosmology, Compact Objects & Stars (GALHECOS) research group.

The MLIR compiler framework is a novel compiler infrastructure that eases the process of developing new interacting compiler passes, built on top of the LLVM compiler. According to mlir.llvm.org, it "significantly reduces the cost of building domain specific compilers". I will shortly introduce MLIR and explain how to generate optimized compiled code using this framework.
Then, I will present our experience in the MICROCARD European project (https://microcard.eu/), in collaboration with INRIA Bordeaux and KIT among other partners. Our aim is to write software to simulate cardiac electrophysiology using wholeheart models with subcellular resolution, on future exascale supercomputers. It builds on the existing open source openCARP project (opencarp.org), a cardiac electrophysiology simulator for insilico experiments. OpenCARP includes a solver and the ionic model component describing ionic transmembrane currents, as ordinary differential equations (ODEs). They are provided using a DSL (domain specific language) for ODEs named easyML. The easyML input is analyzed and transformed into code by a python parser, which we modified to plug it to MLIR and generate OpenMP and vectorized efficient code. MLIR can also be used to generate GPU code, and we plan to experiment with this in the near future.
BBB link: https://bbb.unistra.fr/b/hum51dsufmzq
About the speaker: Vincent Loechner is assistant professor at University of Strasbourg in the computer science department, and the ICube Laboratory in the parallelism team (ICPS). He is also part of the INRIA CAMUS team. He is in charge of the compilation and code optimization workpackage of the MICROCARD European project.

Stronglycorrelated quantum systems are often extremely fragile and notoriously hard to control, which poses challenges for possible technological applications. That is why a certain subclass of quantum states, the socalled topological phases of matter, recently attracted much attention. These are characterised by a certain degree of stability and robustness under perturbations, rooted in their special mathematical properties. A priori, it is not always clear whether a given quantum state of matter is topological or not. We propose a mathematical criterion, which we call “the geometric test", to tell whether a state of matter is in a topological phase. We then apply our test to stronglyinteracting states of matter in Quantum Hall effect, observed in certain 2d materials (Galliumarsenide, graphene, ...) at low temperatures and in strong magnetic fields. I will explain the idea of the test (which works pretty well) and the results, based on recent work with Dimitri Zvonkine (CNRS, Versailles Mathematics Laboratory, ParisSaclay University, France).
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Semyon Klevtsov obtained his PhD in 2009 at Rutgers University (USA), working on mathematical aspects of string theory. After postdoctoral stays in Brussels and Cologne, he joined the Institute for Advanced Mathematical Research (IRMA) at the University of Strasbourg, as professor of mathematical physics. His most recent research is focused on mathematical aspects of the strongly correlated electron systems in condensed matter physics.

Numerical simulations inevitably requires the use of modern visualization methods at different stages to analyze datasets, extract information from them, to guide phenomenon modeling, to validate or invalidate models or as a tool for evaluating experimental results. The access to increasingly powerful computing machines enables scientists to simulate ever larger and more complex phenomena. Largescale simulations generally output timevarying multivariate volumetric data, modeled by volume meshes of increasingly complex size, topology, geometry, composition, ... Direct volume rendering (DVR) is a well known method for visualizing volume data and its implementation on graphics processors (GPU), based on volume raycasting algorithm, offers good rendering quality combined to good performance. However, such an implementation on simulated data presenting abovementioned characteristics is a difficult problem that remains open. A key challenge of research is to make visualization techniques follow up with this drastically increasing complexity.
After an introduction to volume rendering on GPU and its adaptation to large datasets, I will address the challenges of insitu visualization of large and complex unstructured meshes from numerical simulation through the presentation of the ANR LUMVis project.
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Jonathan Sarton is an associate professor at the University of Strasbourg in the computer science department, and the ICube Laboratory in the Computer Graphics and Geometry team (IGG). His research focuses on high performance scientific visualization, volume rendering on GPU, parallel rendering, and insitu visualization in HPC environment. He is the scientific leader of the LUMVis ANR project.

I will present the state of the art on theoretical/numerical modelling of the magnetic reconnection process that is believed to be the central mechanism at work to explain magnetic eruptions in many astrophysical plasmas. In particular, I will highlight the main limitations when using standard numerical schemes to integrate the relevant set of partial differential equations in the magnetohydrodynamic framework. Finally, I will present hope for future numerical strategy based on machine/deep learning trough physicsinformed neural networks.
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
About the speaker: Hubert Baty is Maître de Conférences at the University of Strasbourg, and pursues his research at the Observatoire astronomique de Strasbourg. His research focuses on instabilities and magnetic reconnection in magneticallydominated plasmas with applications to solar/stellar corona and astrophysical jets.

Morse theory and finiteness properties of groups and spaces
— Pierre Py
22 septembre 2022  09:00Salle de conférences IRMA
We will start the talk by recalling classical facts from Morse theory. In other words we will discuss the following classical question: what do the critical points of a function on a manifold tell us about the topology of the manifold? After that we will discuss the following question. Given a manifold M and a smooth map f from M to the circle, can we deform f to a map which has no critical points? Or a minimal number of critical points?
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Pierre Py is a CNRS junior researcher at IRMA. He graduated from ENS Lyon with a Ph.D. degree in 2008. After a postdoctoral stay at the University of Chicago, he joined IRMA as a CNRS researcher in 2011. His research interests evolved over time from the study of symplectic diffeomorphism groups towards Kähler geometry and its interactions with topology and geometric group theory.

The first part of the talk will consist in a short introduction to the field of computer verified proofs. Why verify proofs with a computer? What can be verified? What are the challenges? In a second part, I will give an overview of our formalizations concerning the foundations of geometry based on the axiom systems of Hilbert, Tarski and Euclid. In particular, I will present a joint work with Michael Beeson and Freek Wiedijk which consisted in mechanically verifying the proofs of the first book of Euclid's Elements while trying to stay as close as possible to the original proofs. I will discuss the classification of 34 versions of the axioms of parallels (joint work with Pierre Boutry). We will finish by presenting a syntactic proof of the independence of the axiom of parallels (joint work with Michael Beeson and Pierre Boutry).
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Julien Narboux is Maître de Conférences at the Université de Strasbourg, and pursues his research at ICube (IGG team). His research interests include formal proofs and formalisation of foundations of geometry and applications. He is especially interested in automated reasoning (in particular in geometry) and using proof assistants for teaching.

A large observational effort is currently underway to better probe and understand the first billion years of the Universe, an epoch from which we know very little, because of the enormous distances involved, making its observation very difficult. The new observational means involve giant radio telescopes on the ground, as well as new facilities in space (e.g., the JWST), focusing on the intergalactic medium and forming galaxies, respectively, to give us a new, complementary view of the early universe. To prepare and interpret these upcoming data, numerical simulations of the early Universe are required, involving a wide range of physics and requiring a variety of numerical approaches. I will showcase the recent works of our group in this field, including the largest simulation of the Epoch of Reionization ever made, Cosmic Dawn III (https://codasimulation.github.io/), performed on Summit at Oak Ridge Leadership Computing Facility, the challenges it presented, and some of the challenges ahead.
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum51dsufmzq
Pierre Ocvirk is Astronome Adjoint at Observatoire de Strasbourg and member of the CDS (Centre de Données de Strasbourg). His research focuses on the modelling of the epoch of reionization using giant simulations, and galaxy formation with an emphasis on hydroradiative processes.