We talk about building knots using mosaics which were as introduced as a way of modeling quantum knots by Lomonaco and Kauffman and a newer variant, hexagonal mosaics, introduced by […]
The Field Committee Meeting is our chance to socialize with our colleagues and coordinate our course offerings for the coming academic year (2022-2023). Please come to discuss course offerings and […]
Title: Connections between Iterative Methods for Linear Systems and Consensus Dynamics on Networks Abstract: There is a well-established linear algebraic lens for studying consensus dynamics on networks, which has yielded significant theoretical results in areas like distributed computing, modeling of opinion dynamics, and ranking methods. Recently, strong connections have been made between problems of consensus […]
We describe a natural way to continuously extend arithmetic functions that admit a Ramanujan expansion and derive the conditions under which such an extension exists. In particular, we show that the absolute convergence of a Ramanujan expansion does not guarantee the convergence of its real variable generalization. We take the divisor function as a case […]
The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3-manifolds by Reshetikhin-Turaev using quantum groups. Khovanov homology is a categorification of the Jones polynomial of a knot in R^3, analogously to how ordinary homology is a categorification of the Euler characteristic of a […]
Title: The 6 Cs - Covid and the 5 Claremont Colleges Speaker: Maryann E. Hohn, Department of Mathematics and Statistics, Pomona College Abstract: The Claremont Colleges' (5Cs) environment consists of students, faculty, and staff that congregate together in indoor spaces, creating a higher risk for possible COVID-19 infection. Additionally, a majority of the students live on […]
Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently, peg solitaire has been studied extensively in two colors on […]
Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) […]
Title: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior Speaker: Prof. Rustum Choksi, Department of Mathematics and Statistics, McGill University Abstract: Given a set of N distinct points (generators) in […]
Title: Viscoelastic Effects of Spontaneous Oscillations of Elastic Filaments in the Follower-Force Problem. Abstract: It is well know that microorganisms, such as bacteria and eukaryotes, often move in intricate environments […]
In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at […]
During this student-centered Applied Math Seminar, there will be discussion and presentation about upcoming courses in applied mathematics to help students make their enrollment choices for Fall 2022 and beyond.
