Conférences - Mathématiques numériques - États-Unis

Institute for Pure & Applied Mathematics (IPAM), Los Angeles

Due to their high complexity, our understanding of strongly correlated quantum many-body systems is still limited. This concerns, for example, both static and dynamical equilibrium properties of fermionic systems and quantum magnets in condensed matter physics, as well as complex molecules with strong entanglement in quantum chemistry. Other big challenges are the analysis of non-equilibrium dynamics of closed systems, systems interacting with an environment, and transport problems. Tensor network states such as MPS, TTN, PEPS, and MERA are designed to capture the structure of entanglement in quantum systems in compressed representations. They are also particularly well-suited for the study of topological ordered phases of matter which cannot be described within the framework of spontaneous symmetry breaking. A better mathematical understanding of approximate tensor network representations is emerging for cycle-free networks like MPS and TTN. Current interesting questions concern, for example, the algorithmic stability and complexity, error accumulation, and the optimal choice of single-particle orbitals. Much less is known about the mathematical properties of formats like PEPS which allow cycles and are very natural physically for (D>1)-dimensional systems. The cycles can lead to mathematically intricate situations where, for example, the set of tensor network states is not closed. A major long-term challenge is to identify formats and algorithms that combine key physical properties of PEPS with the algorithmic robustness of MPS and TTN. In this workshop, we will focus on the interplay between specific applications and theoretical developments. In particular, we will discuss specific challenging applications, new algorithms, and mathematical properties of tensor network state methods for the study of ground states, systems at nonzero temperatures, dynamical response, and non-equilibrium phenomena.

tensor network states, tensor decompositions, quantum many-body physics, quantum chemistry

Physique numérique,    Physique de la matière condensée et des matériaux

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to the use of computational mathematics in computer assisted proofs. There are an increasing number of famous conjectures and theorems that have recently been proven using computer assisted proofs. A highly incomplete list in alphabetical order includes the Dirac-Schwinger conjecture, the double bubble conjecture, Kepler's conjecture (Hilbert's 18th problem), Smale's 14th problem, the 290-theorem, the weak Goldbach conjecture etc. In many of these cases the proofs are based on using numerical computations with approximations, a technique that belongs to the field of computational mathematics and scientific computing rather than computer science.

Michigan Technological University, Houghton, Michigan

The primary focus of the proposed parallel-in-time workshop is to educate and inspire researchers and students in new and innovative numerical techniques for the parallel-in-time solution of large-scale evolution problems on modern supercomputing architectures, and to stimulate further studies in their analysis and applications.

The Computational Geometry Week (CG Week 2021) is the premier international forum for advances in computational geometry and its many applications.

ICERM

Rough path theory emerged as a branch of stochastic analysis to give an improved approach to dealing with the interactions of complex random systems. In that context, it continues to resolve important questions, but its broader theoretical footprint has been substantial. Most notable is its contribution to Hairer’s Fields-Medal-winning work on regularity structures. At the core of rough path theory is the so-called signature transform which, while being simple to define, has rich mathematical properties bringing in aspects of analysis, geometry, and algebra. Hambly and Lyons (Annals of Math, 2010) built upon earlier work of Chen, showing how the signature represents the path uniquely up to generalized reparameterizations. This turns out to have practical implications allowing one to summarise the space of functions on unparameterized paths and data streams in a very economical way.

Over the past five years, a significant strand of applied work has been undertaken to exploit the mathematical richness of this object in diverse data science challenges from healthcare, to computer vision to gesture recognition. The log signature is becoming a powerful way to summarise the fine structure of a data stream in a neural net. The emergence of neural differential equations as an important tool in data science further deepens the connections with rough paths.

Program Coordinator;     Tél.: [4018635030];     Email.: info@icerm.brown.edu

Society for Industrial and Applied Mathematics (SIAM)

This Conference is an outgrowth of the new SIAM Activity Group on ACDA, founded last year, which aims to create a professional home for the broad, dispersed community of researchers working on applications of discrete mathematics. In particular, we want to foster a rich interplay between concrete applications and theoretical advancement/algorithm development for combinatorial problems. As such, we would like the ACDA conference to be an attractive meeting for researchers working on applied discrete math within many communities – including combinatorial scientific computing, discrete computational biology, theoretical computer science, network science, combinatorial optimization, algorithm engineering, parallel algorithms and more.

Mathématiques appliquées (en général),    Algorithmes et structures de données

Society for Industrial and Applied Mathematics (SIAM)

The purpose of this conference is to highlight the major theoretical advances in the field, the development of new tools for discrete mathematics, and the most significant of the new applications of discrete mathematics to problems arising in industry and business. The conference also seeks to bring together participants from the many different environments where discrete mathematics is developed and applied.

This is the meeting of the SIAM Activity Group on Discrete Mathematics.

Mathématiques appliquées (en général),    Algorithmes et structures de données

Society for Industrial and Applied Mathematics (SIAM)

Algèbre,    Calcul infinitésimal, équations différentielles et intégrales

ICERM

The workshop aims to spur a holistic approach to the design of time-dependent PDE discretizations, particularly in terms of developing time integration techniques that are intertwined with spatial discretization techniques, focusing on: generalized ImEx methods, asymptotic-preserving and structure-preserving methods, methods that exploit low-rank dynamics, analysis of order reduction, parallel in time methods, and performant, maintainable, extensible software implementations.

Program Coordinator;     Tél.: [4018635030];     Email.: info@icerm.brown.edu

integrationtechniques, spatialdiscretizationtechniques, ImExmethods, orderreduction, software