Speaker: Themis Sapsis (MIT)Title: Optimal sampling and extreme-event aware learning for probabilistic modeling of extremes in complex systemsAbstract: Analysis of real-world physical and engineering systems is characterized by unique computational challenges associated with high dimensionality of parameter spaces, large cost of simulations or experiments, as well as existence of uncertainty. For a wide range of these problems the goal is to either quantify uncertainty and compute risk for critical events, optimize parameters or control strategies, and/or making decisions. In this talk we will discuss two aspects related to the modeling of extreme events: i) optimal sampling of data for the characterization of extreme events, and ii) extreme-event aware learning, i.e. learning methods that do not necessarily assume the existence of extreme events in the training data.In the first part of the talk, we will discuss how Bayesian active learning provides a flexible framework for i) identifying the most informative data for extremes, which is relevant for engineering problems where optimal experimental design is feasible, or ii) quantify the value of data in a prescribed dataset, e.g. relevant for climate modeling. Despite its attractive properties, the Bayesian framework is often prohibitively expensive in terms of the required simulations or experiments, even in the active learning setting. We introduce a new class of acquisition functions that utilize a likelihood-weighted ratio that accounts for the importance of the output relative to the input. This ratio acts essentially as a probabilistic sampling weight and guides the sampling algorithm towards regions of the input space where the objective function assumes abnormal values, resulting in significant savings of computational or experimental resources needed for convergence. We show that the adopted acquisition functions can be rigorously derived as the asymptotic limit of an optimal acquisition function that has a minimax form over a functional space. Subsequently, we demonstrate their favorable properties compared to standard methods on benchmark functions commonly used in the optimization community as well as real world applications involving turbulence, fluid-structure interaction problems and optimal sensor placement.In the second part of the talk, we examine the problem of learning for extremes without the assumption of extreme events in the training data. We introduce the framework of Extreme Event Aware (e2a or eta) or η-learning which does not assume the existence of extreme events in the available data. η-learning reduces the uncertainty even in `unchartered' extreme event regions, by enforcing the extreme event statistics of a few observables during training, which can be available or assumed through qualitative arguments or other forms of analysis. This type of statistical regularization results in models that fit the observed data, but also enforces consistency with the prescribed or assumed statistics of some observables, enabling the generation of unprecedented extreme events even when the training data lack extremes therein. A series of theoretical results based on optimal transport theory offers a rigorous justification and highlights the optimality of the introduced method. The favorable properties η-learning are demonstrated in synthetic examples as well as a real world example involving modeling extreme precipitation events.

Speaker: Vyjayanthi Chari (UC Riverside)Title: Representations of quantum affine sl(n) and connections with affine Hecke algebras and the category O(gl(r))Abstract:The study of finite dimensional representations of quantum affine algebras goes back several decades. Many important results have been proved and deep techniques have been developed over the years; but many interesting natural questions remain unanswered. More recently the work of Hernandez and Leclerc on monoidal categorification has led to a renewed interest in the subject. The influential work of Kashiwara and his collaborators have led to further substantial developments in the subject. In this talk, we will be guided by another remarkable connection, via affine Hecke algebras, with the category of smooth representations of GLn(F) where F is a non–Archimedan field. We will discuss this connection, especially with the work of Lapid–Minguez. Motivated in part by their work, we introduce a family of modules for the quantum affine algebra and give an explicit determinantal formula for its character. As an application of our results we explain how to compute certain Kazhdan–Lusztig coefficients in the Bernstein-Gelfand–Gelfand category O.*Pre-colloquium reception at 4:00 pm in 553 Lake Hall.

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Thursday, April 3rd at 5pm Lewis Music Library, MIT Light reception to followBut Does It Still Smell Like Teen Spirit?: Sound, Identity, Expectation, and the Dialogue of the Cover SongIn this talk, music analyst, ethnomusicologist, and MIT Associate Professor of Music Leslie A. Tilley presents her work-in-progress on the analysis of cover songs. Examining the genres, styles, identities, and contexts of Nirvana’s grunge hit “Smells Like Teen Spirit” and two important covers by women artists—the bare acoustic piano cover by alternative confessional singer-songwriter Tori Amos and the epic orchestral version by Malia J and Think Up Anger, featured in Marvel's 2021 blockbuster movie Black Widow—Tilley explores the spaces that popular music recordings leave open for radical reimaginings, the diverse and contradictory responses such invitations evoke in both artists and listeners, and the multiple analytical lenses needed unpack these complex musical and social dialogues.About the SpeakerLeslie A. Tilley is an Associate Professor of Music at the Massachusetts Institute of Technology. She is a music analyst and ethnomusicologist with research interests in musical transformation and alternative approaches to music theory, analysis, and pedagogy. Her book Making it up Together: The Art of Collective Improvisation in Balinese Music and Beyond (University of Chicago Press, 2019) presents close analyses of the Balinese improvised forms reyong norot and kendang arja while offering broad-reaching analytical frameworks for examining improvisation and collective creativity across genres and cultures. The book won the prestigious Emerging Scholar Book Award from the Society for Music Theory in 2022. Tilley's current work expands the purview of her forays into musical transformation, proposing analytical models for a comparative and multi-modal approach to the analysis of cover songs.About the Music Forum SeriesThe MIT Music & Theater Arts Music Forum is a series of public presentations by music scholars from inside and outside of MIT. Hosted in the Lewis Music Library and presented in partnership with MIT Libraries, the MTA Music Forum Series gives the MIT Community an opportunity to engage with leading voices in every field of music scholarship. Past presenters include John Harbison, Julia Wolfe, Terry Riley, Don Byron, and others.

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Speaker: Xinyu Fang (Harvard)Title: Outline of the argument for Mordell's conjectureAbstract:I will present an outline of the argument for the proof of Mordell's conjecture, following Section 5 of Lawrence-Venkatesh. Specifically, I will explain how to reduce Mordell's conjecture to two key inputs: the existence of a good abelian-by-finite family (the Kodaira-Parshin family) and the finiteness of rational points whose fiber along the finite map has large Galois orbits (proven using p-adic Hodge theory).Reference:$\bullet$ Lawrence and Venkatesh, Diophantine problems and $p$-adic period mappings, Section 5.