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Abstract: Quaternionic modular forms on G_2 carry a surprisingly rich arithmetic structure. For example, they have a theory of Fourier expansions where the Fourier coefficients are indexed by totally real cubic rings. For quaternionic modular forms on G_2 associated via functoriality with certain modular forms on PGL_2, Gross conjectured in 2000 that their Fourier coefficients encode L-values of cubic twists of the modular form (echoing Waldspurger's work on Fourier coefficients of half-integral weight modular forms). This talk will report on recent work proving Gross's conjecture when the modular forms are dihedral, giving the first examples for which it is known. Everything in the talk is joint work with Petar Bakic, Alex Horawa, and Siyan Daniel Li-Huerta.

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Abstract: Advanced manufacturing enables rapid fabrication of complex materials and structures, allowing exploration of large design spaces in materials composition, microstructure, and processing conditions. However, the high dimensionality of these spaces, together with manufacturing uncertainties and defects, poses major challenges for traditional computational science and engineering methods. Addressing these challenges requires new approaches that integrate multi-modal data with physics-based modeling and artificial intelligence to accelerate scientific discovery and materials innovation. This seminar introduces Scientific Artificial Intelligence (Sci-AI) approaches for discovering materials constitutive laws, modeling complex materials behavior, and designing new materials with targeted properties. The central theme is the tight coupling of physical principles, data-driven learning, and interpretability, enabling AI models to move beyond black-box prediction toward reliable scientific inference. The talk is organized around three interconnected themes. First, a hierarchical symbolic AI framework is presented for the automated discovery of physically interpretable constitutive laws directly from data, allowing the model to identify governing mechanisms, enforce dimensional consistency and physical constraints, and balance accuracy with model complexity. Second, a physics-informed, image-based encoder–decoder architecture is introduced to accelerate materials behavior modeling by learning compact latent representations of complex microstructural and field data, while seamlessly fusing high-fidelity simulations, in-situ imaging, and external sensing information across multiple length and time scales. Third, a generative AI framework is developed for inverse materials design, enabling the synthesis of physically plausible microstructures conditioned on nonlinear material properties, processing constraints, and performance targets, thereby closing the loop from data and modeling to design and manufacturing. Overall, this seminar highlights recent advances in Sci-AI for computational science and engineering and demonstrates how physics-guided machine learning can bridge data and models to enable advanced materials modeling and design.

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Abstract: I will discuss results and ideas at the interface of stochastic processes, statistical modeling, and the movement ecology of wild animals. Recently published results demonstrate broad differences in the tendency for carnivores to utilize heavily traveled routeways within their home ranges and ways in which range-residency can be incorporated in dynamic models of population growth. New ideas focus on opportunities for investigating learning from animal movement data and the potential influences of vision on correlated movement.

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Abstract: Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce Synchronized Optimal Transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. With given correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.

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Abstract: This workshop will bring together several leading world experts in the field of operator algebras, which has seen sustained interest over the last century. The primary focus will be on recent important developments surrounding the theory of C*-algebras and finitary approximations. There will also be a spotlight on key standing problems in the area, particularly on structure and classification of operator algebras associated to groups and dynamical systems, and qualitative and quantitative approximation properties.

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Abstract: TBA

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Abstract: Nonparametric tests for functional data are a challenging class of tests to work with because of the potentially high dimensional nature of the data. One of the main challenges for considering rank-based tests, like the Mann-Whitney or Wilcoxon Rank Sum tests (MWW), is that the unit of observation is typically a curve. Thus any rank-based test must consider ways of ranking curves. While several procedures, including depth-based methods, have recently been used to create scores for rank-based tests, these scores are not constructed under the null and often introduce additional, uncontrolled for variability. We therefore reconsider the problem of rank-based tests for functional data and develop an alternative approach that incorporates the null hypothesis throughout. Our approach first ranks realizations from the curves at each measurement occurrence, then calculates a summary statistic for the ranks of each subject, and finally re-ranks the summary statistic in a procedure we refer to as a doubly ranked test. We propose two summaries for the middle step: a sufficient statistic and the average rank. As we demonstrate, doubly rank tests are more powerful while maintaining ideal type I error in the two sample, MWW setting. We also extend our framework to more than two samples, developing a Kruskal-Wallis test for functional data which exhibits good test characteristics as well. Finally, we illustrate the use of doubly ranked tests in functional data contexts from material science, climatology, and public health policy.