A classical principle in algebraic geometry is that a general hyperplane section of a variety should have singularities no worse than those of the variety itself. Over the complex numbers, […]
Speaker: Jim Hoste (Pitzer) Title: Enumerating 2-bridge knots Abstract: A new proof of an old theorem. This is joint work with Patrick D. Shanahan (Loyola Marymount University). _______ We especially welcome […]
Abstract: Rings containing a finite field mathbb{F}_p (such as the ring of polynomials with coefficients in mathbb{F}_p) admit a map called the Frobenius homomorphism which sends every element to its […]
This paper examines how initial conditions shape the long-run impact of large temporary shocks on economic geography. Using WWII supply contracts in the United States, we show that temporary spending […]
Let $C$ be a smooth, projective, geometrically integral hyperelliptic curve of genus $g \ge 2$ over a number field $k$. We investigate the structure of the $\mathbb{P}^1$-parameterized density degree set $\delta_{\mathbb{P}^1}(C/k)$ (equivalently, the Lüroth semigroup) for such curves, consisting of degrees arising from morphisms to $\mathbb{P}^1$. Building on foundational frameworks for parameterized points, we provide […]
Speaker: Robert Cass (CMC) Title: TBA Abstract: TBA _______ We especially welcome all undergraduates and graduate students to attend topology seminar! Room: Roberts South 103
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. […]
