Title: Recalibration of Predicted Probabilities Using the "Logit Shift": Why Does It Work, and When Can It Be Expected to Work Well? Abstract: In the context of election analysis, researchers frequently face the "recalibration problem." That is: they must reconcile individual-level vote probabilities, modeled prior to the election, with vote totals observed in each precinct […]
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 human intervention. As a result, UUVs are valuable for surveillance tasks, especially in the presence of hazardous environmental conditions. Specific applications of UUVs include seafloor mapping, […]
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 called purely cosmetic if the resulting 3-manifolds are homeomorphic as oriented manifolds, whereas it is said to be chirally cosmetic if they result in homeomorphic […]
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 of Farey fractions of level n—that is, the rational numbers between 0 and 1 with denominator at most n. It turns out that these distribute uniformly in the […]
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 beyond.
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 given integers? This problem and its siblings can be understood through generating functions with 0/1 coefficients according to whether or not an integer is representable. […]
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 ago, Giroux and Honda classified contact structures on lens spaces. A natural question to ask after that is how the transformations on lens spaces interact […]
