In this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To the best of our knowledge this is the first Jacobi-Perron type algorithm for which the cubic periodicity is proven. This provides an answer in the […]
Title: Topic Models, Methods, and Medicine Speaker: Prof. Jamie Haddock (Harvey Mudd College) Abstract: There is currently an unprecedented demand for efficient, quantitative, and interpretable methods to study large-scale (often multi-modal) data. One key area of interest is that of topic modeling, which seeks to automatically learn latent trends or topics of complex data sets, […]
Title: Eigenvector Methods for Community Detection in Hypergraphs Abstract: Hypergraphs are generalizations of graphs in which edges are allowed to contain arbitrary numbers of nodes. Hypergraphs are well-suited for modeling complex data sets with multi-body interactions. Familiar examples include email threads with multiple participants, projects with multiple collaborators, and forum posts with multiple tags. The hypergraph […]
When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. Explanatory proofs, in the sense of Steiner, transform what might initially seem mysterious or even magical into […]
Sam Nelson will wow us with his maths.
Title: Quantitative Approaches to Social Justice Prof. Chad Topaz (he/him/his) Co-Founder and Executive Director of Research, QSIDE Institute Professor of Mathematics, Williams College Abstract: Civil rights leader, educator, and investigative journalist Ida B. Wells said that "the way to right wrongs is to shine the light of truth upon them." This talk will demonstrate how […]
Title: Mixing and Pumping on the Microscale Abstract: Mixing and pumping in microfluidics devices is difficult because the traditional methods of mixing and pumping at large length scales don’t work at small length scales. Experimental work has suggested that rotating helical flagella may be used to effectively mix and pump fluid in microfluidics devices. To […]
The Kauffman bracket skein algebra was originally defined as a generalization of the Jones polynomial for knots and links on a surface and is one of the few quantum invariants where the connection to hyperbolic geometry is fairly well-established. Explicating this connection to hyperbolic geometry requires an understanding of the non-commutative structure of the skein algebra, […]
Robert Bowden will tell us fantastic things he did at PSU.
Title: Virtual Trivalent Spatial Graphs and Virtual Niebrzydowski Algebras Speaker: Prof. Sherilyn Tamagawa Visiting Assistant Professor Pomona College Abstract: If you were given two tangled up circles of string, could you untangle one to look like the other without cutting and reattaching the string? How could you tell? Knot theory explores answers to these questions. In this […]
Title: Traditional Applied Math, and then, Working with High Dimensional Biological Data Abstract: I will give an overview of my interests in two parts. The first part will be on passive tracer problems – with the goal of finding formulas of descriptive statistics (mean, variance, skewness) for a solute distribution advected by a smooth flow […]
A Belyi map $\beta: \mathbb{P}^1(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})$ is a rational function with at most three critical values; we may assume these values are $\{ 0, \, 1, \, \infty \}$. […]
