The mathematics of democracy, from theory to practice Mathematics has played a largely unseen role in democracy for centuries, influencing everything from how votes are counted to how political boundaries are drawn. Today, classical mathematical ideas are finding unexpected new applications, while unprecedented computational resources are opening new avenues for analyzing and improving democratic systems. […]
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 […]
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 […]
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
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. […]
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 […]
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!
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 […]
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
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 […]
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 […]
