Home Program Location

All talks will be held in JWB335

9:30am Welcome!
Please join us in the LCB Loft for some coffee, snacks and sodas before the talks.
10:20am The Minimal Denominator in Function Fields
Noy Soffer Aranov (Utah)
Meiss and Sanders proposed an experiment in which they fix $\delta>0$, and study the statistics of the minimal denominator $Q$ for which there exists a rational $\frac{P}{Q}\in (x-\delta,x+\delta)$, where $x$ is varied. In this talk, I will discuss the history of this problem and its generalizations, as well as the function field analogue of the minimal denominator problem. This is based off the preprint https://arxiv.org/pdf/2501.00171.
11:20am McGehee Regularization and Collision Manifold of Planar (2+2)-Body Problem
Nathan Sill (BYU)
We use McGehee regularization to analyze the dynamics of two asteroids and a primary in a (2+2)-body problem near triple collision. We examine the manifold that describes the dynamics of the bodies during triple collision. We discuss properties of this collision manifold including equilibrium points and gradient-like flow.
12:00PM Lunch
1:30pm Almost-homogeneous Anosov Flows
Sage Yeager (Utah)
A fundamental question in dynamics is that of when one dynamical system is equivalent to another. Understanding when one such notion of equivalence, C^r-conjugacy, exists between dynamical systems provides a way to classify and compare seemingly disparate dynamics. In this talk, we will introduce (G,X)-structures on manifolds and how they can be used to define a class of Anosov flows that exhibit a rigidity phenomenon related to conjugacy. In particular, such flows have smooth stable and unstable bundles, but are not C^0-conjugate to standard examples of Anosov flows: suspensions of hyperbolic toral automorphisms and geodesic flows on surfaces of constant negative curvature. Moreover, we will discuss how these “almost-homogeneous flows” can always be described.
2:30pm Mathematical billiards
Boris Hasselblatt (Tufts)
Mathematical billiards provide a concrete context in which to raise questions dynamicists are interested in, as well as open problems that are easy to state, and connections to number theory, geometry and remarkable applications.