Simons Foundation Lectures

Simons Foundation

The Simons Foundation’s mission is to advance the frontiers of research in mathematics and the basic sciences.Co-founded in New York City by Jim and Marilyn Simons, the foundation exists to support basic — or discovery-driven — scientific research undertaken in the pursuit of understanding the phenomena of our world.The Simons Foundation’s support of science takes two forms: We support research by making grants to individual investigators and their projects through academic institutions, and, with the launch of the Flatiron Institute in 2016, we now conduct scientific research in-house, supporting teams of top computational scientists.Links:Simons Foundation: https://www.simonsfoundation.orgFlatiron Institute: https://www.simonsfoundation.org/flatiron/Simons Foundation Facebook: https://www.facebook.com/SimonsFoundationFlatiron Institute Facebook: https://www.facebook.com/FlatironInstitute/Simons Foundation Twitter: https://twitter.com/simonsfdnFlatiron Institute Twitter: https://twitter.com/flatironinst

  1. 5h ago

    ICM 2026 Invited Section Lecture - Michael Dumbser

    Compatible Numerical Schemes for Thermodynamically Compatible Systems of Hyperbolic Partial Differential EquationsUploaded 05-10-26In this contribution two recent types of compatible numerical discretizations for overdetermined, thermodynamically compatible systems of hyperbolic partial differential equations (PDE) are discussed. Overdetermined hyperbolic and thermodynamically compatible (HTC) systems satisfy an additional extra conservation law for the total energy density, which is a consequence of all the other equations and which corresponds to the first principle of thermodynamics. The second principle of thermodynamics is contained in the entropy inequality, if present in the governing PDE system under consideration. Very often, such systems are also endowed with stationary differential constraints (involutions), such as the divergence-free condition of the magnetic field in the Maxwell equations or the curl-free condition of the velocity field in the equations of linear acoustics. Preserving at least one of the two aforementioned additional structural properties of the governing PDE system exactly at the discrete level is the major objective of the present paper. The first type of numerical schemes achieves compatibility with the extra conservation law for the total energy for a very general class of nonlinear hyperbolic PDE systems, but does not satisfy additional stationary differential constraints. The second scheme is compatible with the extra conservation law and preserves involutions exactly at the discrete level, but only for a very particular class of problems. The design of compatible numerical schemes for general nonlinear hyperbolic systems which satisfy both structural properties at the same time is still the subject of ongoing and future research.

    ICM 2026 Invited Section Lecture - Michael Dumbser

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The Simons Foundation’s mission is to advance the frontiers of research in mathematics and the basic sciences.Co-founded in New York City by Jim and Marilyn Simons, the foundation exists to support basic — or discovery-driven — scientific research undertaken in the pursuit of understanding the phenomena of our world.The Simons Foundation’s support of science takes two forms: We support research by making grants to individual investigators and their projects through academic institutions, and, with the launch of the Flatiron Institute in 2016, we now conduct scientific research in-house, supporting teams of top computational scientists.Links:Simons Foundation: https://www.simonsfoundation.orgFlatiron Institute: https://www.simonsfoundation.org/flatiron/Simons Foundation Facebook: https://www.facebook.com/SimonsFoundationFlatiron Institute Facebook: https://www.facebook.com/FlatironInstitute/Simons Foundation Twitter: https://twitter.com/simonsfdnFlatiron Institute Twitter: https://twitter.com/flatironinst