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4:00pm to 4:50pm - RH 306 - Applied and Computational Mathematics Anna Konstorum - (Center for Computing Sciences / Institute for Defense Analyses (CCS/IDA)) Tensor dictionary learning for immune profiling data Tensor decompositions are being more frequently employed to discover low-dimensional features of complex datasets. In this talk, we discuss how the decomposition of immune profiling data, which has an inherent multi-index array structure, can be viewed through the lens of a tensor dictionary learning problem. We show how this approach leads to improved rank selection and interpretability of the final model. |
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4:00pm to 5:00pm - RH 340N - Geometry and Topology Steve Trettel - (University of San Francisco) Classical Physics in Curved Space When transitioning from studying Euclidean space to more Riemannian manifolds, one must first unlearn many special properties of the flat world. The same is true in physics: while one can make sense of classical physics on an arbitrary curved background space, many seemingly foundational concepts (like the center of mass) turn out to have no place in the general theory. Freed from the constraints such properties induce, classical physics on a curved background space has many surprises in store. In this talk I will share some stories related to joint work with Brian Day and Sabetta Matsumoto on understanding and simulating such situations, focusing on hyperbolic space when convenient. To give a taste, here are two such surprises: |
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4:00pm to 5:30pm - RH 440R - Logic Set Theory Julian Talmor Eshkol - (UC Irvine) Stationary Partition Relations The partition relation A→(P)^μ_λ, despite its brevity, is remarkably expressive. This fundamental combinatorial principle asserts that every λ-coloring of μ-sized subsets of A is constant on a subset in the class P. By adjusting the parameters A, μ, λ, and P, one can express a wide variety of large cardinal principles, including weak compactness, Ramsey-ness, and even supercompactness. In this talk, we focus on the case where A is an uncountable cardinal κ and P is the class of stationary subsets of κ. By work of Baumgartner 1977, it turns out that this corresponds to certain ineffability properties of κ. We also describe how this fits into a different hierarchy of ineffability properties described in current joint work with Matthew Foreman and Menachem Magidor. |
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4:00pm - RH306 - Differential Geometry Giuseppe Barbaro - (Aarhus University) Pluriclosed manifolds with parallel Bismut torsion and the pluriclosed flow We present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion. Consequently, we also establish a splitting theorem for compact manifolds that are both pluriclosed with parallel Bismut torsion and have vanishing Bismut Ricci form. Due to the relations of these conditions with the Vaisman geometry, we also analyze the behavior of the pluriclosed flow, proving that it preserves the Vaisman condition on compact complex surfaces if and only if the starting metric has constant scalar curvature. |
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3:00pm to 4:00pm - Rowland Hall 510R - Combinatorics and Probability Roman Vershynin - (UC Irvine) Can we spot a fake? The ongoing AI revolution is transforming human-computer interaction. But not all interaction is good: generative AI has made it easy to create fake data: images, news, and soon videos. But what is a fake? Can we define it mathematically? Which fakes can we detect and which cannot? I will suggest a simple probabilistic framework, where these questions can lead to concrete open (and fun!) problems in mathematics. This talk is based on a joint work with Shahar Mendelson and Grigoris Paouris: https://arxiv.org/abs/2410.18880 |
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9:00am to 9:50am - Zoom - Inverse Problems Rakesh - (University of Delaware) Fixed angle inverse scattering for velocities, Riemannian metrics and Lorentzian metrics |
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4:00pm to 5:00pm - RH 306 - Colloquium Aravind Asok - (USC) From matrices to motivic homotopy theory Recall that a square matrix P is called a projection matrix if P^2 = P. It makes sense to talk about projection matrices with coefficients in any commutative ring; the image of a projection matrix is called a projective module. This seemingly innocuous notion intercedes in geometric questions in the same spirit as the famous Hodge conjecture because of Serre's dictionary: projective modules are ``vector bundles''. If X is a smooth complex affine variety, we can consider the rings of algebraic or holomorphic functions on X. Which of the holomorphic vector bundles on X admit an algebraic structure? I will discuss recent progress on these questions, using motivic homotopy theory, and based on joint work with Tom Bachmann and Mike Hopkins.
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