For a lattice L in the plane, we define the affiliated deep hole lattice H(L) to be spanned by a shortest vector of L and the furthest removed vector from the lattice contained in the triangle with sides corresponding to the shortest basis vectors. We study the geometric and arithmetic properties of deep hole lattices, […]
Title: Generating families on Lagrangian cobordisms Abstract: An important question in contact topology is to understand Legendrian knots and their relations given by Lagrangian cobordisms. In the contact manifold T*M x R, an important tool to study Legendrian knots and their Lagrangian cobordisms is called generating families or generating functions, which are generalizations of the […]
Title: What is a moduli space? Speaker: Javier Gonzalez Anaya, Department of Mathematics, Harvey Mudd College Abstract: A natural endeavour in mathematics is to classify objects according to their properties. For example, we can readily identify straight lines in the plane, or recognize different kinds of triangles depending on their symmetries. Less intuitive, however, is that […]
Title Control algorithms for unmanned underwater vehicles: new approaches based on Hamilton-Jacobi equations and reinforcement learning. Abstract Unmanned underwater vehicles (UUVs) are defined by their ability to operate without direct […]
We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs, and show that the spectral properties of different matrix representations of these classes of trees provide insight into the linguistic properties that characterize these classes. More generally, our […]
Title: Cosmetic Surgeries on Knots and Heegaard Floer Homology Abstract: A common method of constructing 3-manifolds is via Dehn surgery on knots. A pair of surgeries on a knot is […]
Title: Slope gap distributions of translation surfaces Speaker: Taylor McAdam, Department of Mathematics, Pomona College Abstract: How “random” are the rational numbers? To make sense of this question, let us consider the set […]
During this student-centered Applied Math Seminar, there will be discussion and presentations about upcoming courses offered in applied mathematics, to help students make their enrollment choices for Spring 2024 and […]
We study variants of the Frobenius coin-exchange problem: Given n positive relatively prime parameters, what is the largest integer that cannot be represented as a nonnegative integral linear combination of the […]
Title: Contact structures and the mapping class group of lens spaces Abstract: One important problem in contact topology is to classify contact structures on a given manifold. Around 20 years […]
Title: Lonely Runners and My Favorite Polyhedron Speaker: Matthias Beck, Department of Mathematics, San Francisco State University Abstract: We study the Lonely Runner Conjecture, conceived by Wills in the 1960's, and originally phrased in terms of Diophantine approximation: Given positive integers n_1, n_2, ..., n_k, there exists a positive real number t such that for all […]
