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 […]
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 […]
Title: On the Composition of Classical Mechanical Systems Abstract: Compositionality is a basic principle for understanding the physical world. The underlying idea is to study a system by studying the ways in which the components of the system compose to form the system. Category theory is an area in mathematics that is particularly well-suited for […]
True Grit: Writing the History of Women at Yerkes Observatory, 1895–1950 Abstract: Women at Yerkes Observatory earned advanced degrees, conducted their own research, collaborated on projects with peers of both sexes, and authored publications in their own names in the first half of the Twentieth Century. Yet Alice Hall Farnsworth, Mary Murray Hopkins, Harriet McWilliams […]
The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P, introduced by Felix Breuer in 2012, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors, […]
On November 14th, Tuesday from 3-4pm in Fletcher 110, Geometry and Topology Seminar invites students and faculty to a course preview session devoted to a discussion and presentations about upcoming Spring 2024 courses in geometry, topology and/or with applications in geometry and topology to help students make their enrollment choices. We will have some refreshments […]
