Period 1
9-11 July
Organizers: Philipp Grohs, Gitta Kutyniok, Roman Vershynin
Organizers: David Krieg, Klaus Ritter, Jan Vibyral
Information-based complexity (IBC) studies how many pieces of information are required to solve a (numerical) problem up to a prescribed error tolerance. The problems considered include function approximation and learning, numerical integration, optimization, or the solution of PDEs and SDEs. It is of particular interest how the complexity increases with the dimensionality of the problem (cf. curse of dimensionality versus tractability) and with the desired accuracy (cf. rate of convergence). The IBC workshop interacts naturally with several other workshops, including “Foundations of Data science and Machine Learning”, “Approximation Theory”, or “Stochastic Computation” as we study similar topics but from other perspectives. The two semi-plenary talks that we plan to include shall introduce the most important aspects of the field also to researchers from other communities.
Organizers: Paola Antonietti, Ralf Hiptmair, Markus Melenk
The Foundations of Numerical PDEs Workshop brings together researchers to discuss the latest advances in the numerical analysis of partial differential equations (PDEs). Focus topics of the workshop include
– Structure-preserving discretization of Hilbert complexes, including and generalizing FEEC (Finite Element Exterior Calculus) and offering a framework that unifies and extends traditional finite element methods, and forms the foundation of stable and robust numerical methods.
– Novel discretization techniques on polytopal meshes to improve flexibility, accuracy and efficiency of numerical methods for PDE-based multiphysics models in complex domains.
– Recent breakthroughs in the numerical modeling of wave propagation problems, including wave-number explicit analysis and wave-number robust numerical schemes.
The presentations at the workshop will address both theoretical developments, algorithmic challenges, and novel applications of numerical methods.
This workshop will have natural connections the the other FoCM workshops “Geometric Integration and Computational Mechanics” and “Geometric Integration and Computational Mechanics”.
Organizers: Ulrich Bauer, Michael Kerber, Xavier Pennec
Organizers: Saugata Basu, Greg Blekherman, Antonio Lerario
Organizers: Dan Huybrechs, Erik Koelink, Teresa Perez
Organizers: Lenaic Chizat, Young-Heon Kim, Jan Maas
Period 2
13-15 July
Organizers: Ben Adcock, Albert Cohen, Karlheinz Gröchenig
Organizers: Mireille Bossy, Nawaf Bou-Rabee, David Cohen
Organizers: Yussef Marzouk, Daniel Sanz-Alonso, Carola-Bibiane Schönlieb
Organizers: Melvin Leok, Sigrid Leyendecker, Ari Stern
Organizers: Türkü Özlüm Celik, Frank Sottile, Seth Sullivant
This workshop will highlight new results and recent developments in the theory and applications of computational algebraic geometry. Speakers will present results on a range of techniques in the field including symbolic and numerical methods. Tools from algebraic geometry have been applied to a broad range of fields including: biology, chemistry, economics, optimization, physics, robotics, and statistics.
Workshops with close interactions:
I.4: Computational Geometry and Topology
I.5: Real Number Complexity
II.7: Computational Number Theory
III.1: Continuous Optimization
III.5: Symbolic Analysis
Organizers: Folkmar Bornemann, Ioana Dumitriu, Joel Tropp
Organizers: Sabrina Kunzweiler, Elisa Lorenzo Garcia, Stefano Marseglia
Elliptic curves play a very important role in modern mathematics with applications ranging from the very theoretical to the very computational. For example, they are the backbone of Wiles proof of Fermat’s Last Theorem and of one of the most widely used cryptosystem.
More recently, isogenies of elliptic curves and abelian varieties gained attention as well.
They are used in different cryptographic schemes that are proposed in the context of post-quantum cryptography.
To make these schemes efficient, and to evaluate their security, it is important to understand the underlying mathematics.
Our workshop will gather experts working on the computational tools involving elliptic curves, abelian varieties and isogenies, as well as experts working on the cryptographic applications.
Period 3
16-18 July
Organizers: Radu Boţ, Nicolas Boumal, Katya Scheinberg
Organizers: Angela Capel Cuevas, Richard Kueng, Lin Lin
Organizers: Michael Feischl, Christian Kreuzer, Rob Stevenson
Organizers: Georg Gottwald, Eva Miranda, Cristobal Rojas
This workshop will bring together mathematicians working on computational dynamics, spanning a wide range from computability theory to data driven modelling. The workshop will ask questions when and how dynamical systems can be used to perform computation in the sense of Turing machines, including undecidability. Recent advances have shown that fluid flows can in principle be used to perform computations, implying that their future dynamics will be unpredictable. A probabilistic approach to dynamical systems which aims at understanding its statistical properties rather than the exact evolution of a single trajectory, offers an alternative to overcome the predictability barrier of certain dynamical systems. Set-oriented methods allow for the characterization of global statistical properties and detection of coherence in the flow, when the dynamical system is accessible only through some partial observations. The convergence properties of these methods have only recently been explored, giving rise to improved algorithms.
Organizers: Georg Regensburger, Sonia Rueda, Jacques-Arthur Weil
Organizers: Vanni Noferini, Elizaveta Rebova, Françoise Tisseur
Organizers: Kurusch Ebrahimi-Fard, Claudia Malvenuto, Christoph Spiegel