ICM 2026 Invited Section Lecture – Franc Forstneric

Kaustuv Manna: Discovery of multifold fermions and observation of quantized Photocurrents in topological chiral crystalsMore details: https://www.simonsfoundation.org/event/young-research-leaders-in-topological-materials-and-beyond/Uploaded 14-10-19 Learn more about your ad choices. Visit megaphone.fm/adchoices

On Complexity of Deterministic Model Based Derivative Free Optimization MethodsIn many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches in practice are model-based trust-region methods, such as those pioneered by M.J.D Powell. While relatively complex to implement, these methods are now available in standard scientific computing platforms, including MATLAB and SciPy. However, theoretical analysis of their computational complexity lags behind practice. In particular, it is important to bound the number of function evaluations required to achieve a desired level of accuracy. In this lecture we will discuss a variety of derivative free optimization methods and their worst case complexity bounds. We will then show how to systematically derive complexity bounds for classical model based trust region methods and their modern variations. We establish, for the first time, that these methods can have the same worst case complexity than any other known DFO method. We will conclude with some of the open problems and future directions in this domain.Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

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Berthold Jaeck: Observation of a Majorana zero mode in a topologically protected edge channelMore details: https://www.simonsfoundation.org/event/young-research-leaders-in-topological-materials-and-beyond/Uploaded 14-10-19 Learn more about your ad choices. Visit megaphone.fm/adchoices

Fernando de Juan: Intrinsic circular photocurrents in topological semimetalsMore details: https://www.simonsfoundation.org/event/young-research-leaders-in-topological-materials-and-beyond/Uploaded 14-10-19 Learn more about your ad choices. Visit megaphone.fm/adchoices

From Stein Manifolds to Oka Manifolds: The H-Principle in Complex AnalysisIn this talk, I will describe the main developments in the theory of the h-principle in complex analysis and geometry, better known as the Oka principle. I will present the key notions of Oka manifolds and Oka maps, which developed from the Oka-Grauert principle and Gromov's theory of elliptic complex manifolds and elliptic holomorphic submersions, and their characterization by simpler approximation and ellipticity conditions. I will discuss recent and ongoing developments, open problems, and mention applications to the classical theory of minimal surfaces.Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices

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This session invites contributions that examine how mathematical knowledge has been established, communicated, and accepted across historical contexts, with particular attention to the interrelated roles of proof, demonstration, and persuasion. Rather than treating proof as a fixed or universal standard, the session foregrounds the historically contingent practices, norms, and epistemic values that have shaped what has counted as an adequate or convincing demonstration in different mathematical cultures.Uploaded 09-09-26Topics may include the historical evolution of standards of demonstration; the diagrammatic, procedural, and rhetorical means by which mathematical arguments have been made persuasive; and the roles of individuals, texts, instruments, and institutions in legitimizing mathematical claims. Contributions may range from ancient and medieval cultures of inquiry to early modern and modern mathematical practice and may engage with diverse epistemic traditions and contexts.The session also welcomes work that reflects on the relationship between formal proof and other modes of mathematical reasoning, including explanation, visualization, approximation, and heuristic argument. By attending to how demonstration and persuasion have functioned within historical communities, this session aims to illuminate the dynamic interplay between mathematical rigor, communicative practice, and epistemic authority. Session InformationDavid Dunning, Erica Meszaros, Jacqueline Feke, Caroline Ehrhardt, Adrian Rice Learn more about your ad choices. Visit megaphone.fm/adchoices

More details: https://www.simonsfoundation.org/event/ccb-colloquium-chao-tang/Uploaded 14-10-19 Learn more about your ad choices. Visit megaphone.fm/adchoices

Holomorphic Foliations with Numerically Trivial Canonical BundleThe lecture will survey what is currently known about the structure of holomorphic foliations with canonical singularlities and numerically trivial canonical bundle on projective manifolds.Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices