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Large language models (LLMs) can use examples provided in a prompt to make predictions for new queries without updating their parameters, a capability known as in-context learning. In this talk, I will explore how transformers, the architectural backbone of many LLMs, can perform nonlinear kernel ridge regression (KRR). I will first present numerical observations showing […] |
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Let $E$ be a non-CM elliptic curve defined over $\mathbb{Q}$. We present models of curves that have 2-adic image as large as possible, given the constraint that they have a rational 2-isogeny. These curves are known to be generic, and one of the aims of this article is to make that fact explicit. Our techniques […]
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Speaker: Chris Soteros (University of Saskatchewan) Title: TBA Abstract: TBA _______ We especially welcome all undergraduates and graduate students to attend topology seminar! Room: Roberts South 103 |
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Abstract: Optimal transport describes the process of finding the most efficient way to move mass between two distributions. Wasserstein distance measures the minimal transportation cost achieved by that optimal plan. However, in higher dimensions, computing the Wasserstein distance becomes computationally expensive. The sliced Wasserstein distance offers an effective and efficient way to alleviate this burden. […] |
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This GEMS session will be facilitated by Professor Robert Sanchez from Harvey Mudd College. Title: Going with the flow: The Mathematics of Fluid Motion Abstract: Why can the depth of a river or the height of a wave tell us how fast it is moving? This lesson talks about the mathematics of fluid motion and […] |
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Please join us for the course preview of upper division undergraduate and graduate Spring 2027 courses in the Applied Mathematical Sciences. Come hear from faculty about the exciting options this upcoming Spring in applied math, data science, probability, statistics, and financial mathematics. It’s a great opportunity to learn more, ask questions, and plan your schedule! |
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This will be a sequel of my last ANTC talk on bundles of probability schemes. We introduce entropy for fiber bundles of probability schemes and higher-order entropy for hypercubes of bundles. This framework yields categorical proofs of several fundamental results about Shannon entropy and reveals correspondences between classical concepts in information theory and categorical concepts […]
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Speaker: Vin de Silva (Pomona College) Title: TBA Abstract: TBA _______ We especially welcome all undergraduates and graduate students to attend topology seminar! Room: Roberts South 103 |
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Abstract: We present our program of geometrizing cohomology on a totally disconnected space through the intrinsic Cantor function and the cohomological complex dimensions of the ternary Cantor set. The Cantor set is an uncountable, self-similar set of measure zero; yet beneath this apparent “dust” lies a remarkably rich geometry across scales. We show how cohomological […] |
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Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the permutation approach is the exchangeability condition, which determines the appropriate null sampling distribution. We explore the exchangeability condition in the […] |
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Speaker: Bahar Acu (Pitzer College) Title: TBA Abstract: TBA _______ We especially welcome all undergraduates and graduate students to attend topology seminar! Room: Roberts South 103 |
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Abstract: Dirichlet’s 1837 proof of his theorem on primes in arithmetic progressions depended on the non-vanishing of L(1,\chi) for nonprincipal characters. The Birch and Swinnerton-Dyer conjecture relates the rank of an elliptic curve to the order of vanishing of its L-function at the central point. Determining whether an individual central value vanishes can be difficult, […] |
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Atul Vyas was an outstanding CMC student who was majoring in Mathematics and Physics. He tragically lost his life in a train crash that occurred on September 12, 2008 in Chatsworth, California. The Mathematical Sciences Department at CMC fondly remembers Atul as someone who was equally excited by the power of mathematical abstraction and the […] |
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Speaker: Giuseppe Martone (Sam Houston State University) Title: TBA Abstract: TBA _______ We especially welcome all undergraduates and graduate students to attend topology seminar! Room: Roberts South 103 |
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This GEMS session will be facilitated by Professor Jasmine Camero from Pomona College. Title: Loops and Lines: What Math and Bracelets Have in Common Abstract: Can you make a bracelet out of points? Join us for an interactive adventure where beads and bracelets become a way to explore mathematical curves! We’ll discover how mathematicians find […] |
