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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.org
Flatiron Institute: https://www.simonsfoundation.org/flatiron/
Simons Foundation Facebook: https://www.facebook.com/SimonsFoundation
Flatiron Institute Facebook: https://www.facebook.com/FlatironInstitute/
Simons Foundation Twitter: https://twitter.com/simonsfdn
Flatiron Institute Twitter: https://twitter.com/flatironinst

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  • 133 episodes
  • daily
  • Avg 59 min
  • English

Episodes 133

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  • Today · 45 min

    ICM 2026 Invited Section Lecture – Gabriel Navarro

    Character Correspondents in Finite Groups Two of the most important conjectures in the representation theory of finite groups have been recently proven: Richard Brauer’s Height Zero Conjecture (1955) and John McKay’s Degree Conjecture (1971). The proofs of both rely on the Classification of Finite Simple Groups. A key idea in their resolution has been to associate, to each irreducible character of a simple group, another character of a local subgroup that, remarkably, behaves in a corresponding way. This was proposed by M. Isaacs, G. Malle and this author in 2007.In the case of the McKay Conjecture, it took nearly 20 years to fully verify this correspondence, a milestone finally achieved by M. Cabanes and B. Späth. A similar strategy was applied to Brauer’s Height Zero Conjecture for the prime 2 by L. Ruhstorfer, after the so called Gluck--Wolf--Navarro--Tiep theorem was proved, and a reduction of B. Späth and this author. For odd primes, however, G. Malle, A. Schaeffer-Fry, P. H. Tiep, and the present author had to develop an entirely different approach to finally establish the result.This idea of character correspondents is now being extended to tackle other global/local conjectures, including Alperin’s Weight Conjecture, several refinements of the McKay Conjecture, and even Feit’s Conjecture on fields of values. The purpose of this talk is to explain these developments in greater detail. Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 59 min

    Salvatore Torquato: Hidden Order: The Geometry of Complex Patterns

    In this Presidential Lecture, Salvatore Torquato will discuss how the ‘hyperuniformity’ concept sheds light on these fascinating questions. In a hyperuniform point pattern, density fluctuations become small over large distances relative to those in garden-variety random systems. This single idea provides a unified framework for understanding the structure and geometry of periodic and quasiperiodic systems, as well as exotic disordered systems. Examples from physics, mathematics and biology will reveal surprising connections among optimization problems in discrete geometry, disordered ground states, sphere packings, quantum mechanics, number theory, the structure of the universe and avian photoreceptor mosaics. Torquato will also introduce ‘order metrics’ — mathematical measures that place periodic, quasiperiodic and correlated disordered patterns along a spectrum from greater order to greater disorder, for objective structural comparisons. Uploaded 05-10-26 For more information please visit: https://www.simonsfoundation.org/event/hidden-order-the-geometry-of-complex-patterns/ Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 43 min

    ICM 2026 Invited Section Lecture - Michael Stoll

    How many rational points can a curve have? I will give an overwiew of results and open problems related to the number of rational points on "nice" algebraic curves of genus at least 2 over the rational numbers (or, more generally, over algebraic number fields). Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 44 min

    ICM 2026 Invited Section Lecture - Xiaojun Chen

    Differential Stochastic Variational Inequalities and Optimization The variational inequality (VI) provides a broad unifying setting for the study of equilibrium problems and optimization. The differential variational inequality and stochastic variational inequality are generalizations of the VI and promising modeling paradigms when dynamics and uncertainties are involved in data analysis and decision making. We first discuss the mathematical formulations and recent results of the differential VI and stochastic VI. Next we introduce the differential stochastic VI with stochastic optimization (DSVIO), an ordinary differential equation whose right-hand side is defined by a stochastic VI and solutions of several stochastic optimization problems. The DSVIO provides a powerful modeling framework for various applications in data science and artificial intelligence. We provide sufficient conditions for the existence of a solution pair for the DSVIO in the space of absolutely continuous functions and the space of measurable functions. We discuss a convergent sample average approximation and time-stepping discretization scheme for numerical solutions of the DSVIO. Finally, we show applications of the DSVIO for optimizing multimodal large model-based embodied intelligence systems for the elderly mobility. Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 45 min

    ICM 2026 Invited Section Lecture - Richard Montgomery

    Recent progress in graph theory using expansion Graph expansion has long been recognised as an important and desirable property with applications in a wide range of areas in computer science and mathematics. A form of expansion known as `sublinear expansion' has been used particularly successfully in the last decade in extremal graph theory, playing a pivotal role in the progress on, and resolution of, a range of long-standing and notable problems. This talk will cover some of these advances, highlighting the role of sublinear expansion and the settings in which it is effective. Uploaded 05-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 47 min

    ICM 2026 Invited Section Lecture - Benjamin Bakker

    Mixed Non-Abelian Hodge Theory and the Linear Shafarevich Conjecture For a complex algebraic variety X, classical Hodge theory imposes extra structure on the singular cohomology Hk(X,C) of X using the theory of harmonic forms. Non-abelian Hodge theory similarly enriches the geometry of the algebraic variety of representations of the fundamental group (which is thought of as H1(X,GLr(C))) by using harmonic metrics on local systems. The theory in the "pure" case of smooth projective X was largely worked out in the 1990s beginning with the seminal work of Simpson and has seen many applications, for example the proof of Eyssidieux--Katzarkov--Pantev--Ramachandran of the linear Shafarevich conjecture for such X. In this talk, I will survey recent advances in the "mixed" case of arbitrary complex algebraic varieties X, and show how these tools can be used to prove a number of important results about the topology of algebraic varieties, as well as a general version of the linear Shafarevich conjecture. This is based on joint work with Y. Brunebarbe and J. Tsimerman. Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 41 min

    ICM 2026 Invited Section Lecture - Otis Chodosh

    Minimal Surfaces and Comparison Geometry We discuss applications of area-minimization to the study of curvature in Riemannian geometry. Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Today · 59 min

    Li Ye: Energetics of Integrating the Brain and Body (October 7, 2027)

    In this Presidential Lecture, Li Ye will discuss his research program, which seeks to understand the brain by investigating how neural circuits monitor, allocate, and utilize energy throughout the body. By combining innovative imaging technologies, chemical biology and neural circuit mapping, he and his colleagues have uncovered previously unknown pathways linking metabolism, behavior and brain activity. These discoveries reveal fundamental principles of brain-body communication and may ultimately provide new opportunities to understand and treat obesity, diabetes, neurodegenerative disorders and other diseases shaped by metabolic dysfunction. Uploaded 26-10-26 For more information please visit: https://www.simonsfoundation.org/events/energetics-of-integrating-the-brain-and-body/ Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Yesterday · 49 min

    ICM 2026 Invited Section Lecture - Frédéric Faure

    Can Quantum Dynamics Emerge from Classical Chaos? Abstract Anosov geodesic flows are among the simplest mathematical models of deterministic chaos. We explain how, quite unexpectedly, quantum dynamics emerges from purely classical correlation functions. The underlying mechanism is the discrete Pollicott–Ruelle spectrum of the geodesic flow, revealed through microlocal analysis. This spectrum naturally arranges into vertical bands; when the rightmost band is separated from the rest by a gap, it governs an effective dynamics that mirrors quantum evolution. Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Yesterday · 13 min

    Mathematical Impressions: Regular Polylinks

    A video illustrating the beautiful geometry behind symmetrical linkages of regular polygons. Uploaded 22-05-14 http://www.simonsfoundation.org/multimedia/regular-polylinks/ Learn more about your ad choices. Visit megaphone.fm/adchoices

  • Yesterday · 1 hr 6 min

    Antoine Browaeys - Exploring Many-Body Problems With Arrays of Individual Atoms (October 11, 2023)

    Over the last twenty years, physicists have learned to manipulate individual quantum objects, such as atoms, ions, molecules, quantum circuits and electronic spins. Scientists can now build a synthetic quantum computer “atom by atom.” By controlling the interactions between atoms, scientists can study the properties of these elementary many-body systems, including quantum magnetism, transport of excitations and superconductivity, and thus gain a deeper understanding of the N-body problem. More recently, scientists realized that these quantum machines may find applications in industry, such as finding the solution of combinatorial optimization problems. Uploaded 08-11-23 In this lecture, Antoine Browaeys will present an example of a synthetic quantum system based on laser-cooled ensembles of individual atoms trapped in microscopic optical tweezer arrays. By exciting the atoms to Rydberg states, he and his colleagues can make the atoms interact even at distances of more than 10 micrometers. In this way, they can study the magnetic properties of an ensemble of more than a hundred interacting one-half spins in a regime in which simulations by usual numerical methods are already very challenging. Some aspects of this research led to the creation of a startup called Pasqal. More details: https://www.simonsfoundation.org/event/exploring-many-body-problems-with-arrays-of-individual-atoms/ Learn more about your ad choices. Visit megaphone.fm/adchoices

Showing 1–20 of 133 episodes