Title: The Chronicles of Fractal Geometry: Fractal Strings, and Functorial Harps Abstract: In this talk, we explore the colorful analytical world of fractal geometry. We introduce fractal strings in the sense of Lapidus, both intuitively and by way of rigorous constructions. We examine rich illustrations of higher dimensional fractals and p-adic fractal strings. Then, we […]
Title: Numerical studies to the Chaplygin gas system and Pressureless Euler Equations Speaker: Ying Wang University of Oklahoma, USA Abstract In this talk, we will discuss the numerical solutions to the Riemann problem for Chaplygin gas equation, which is the Euler equations equipped with the state equation p = -1/\rho, as well as the 2D […]
In late March, students, staff, and faculty were invited to help collaboratively build a large-scale geometric sculpture on the campus of Harvey Mudd College, demonstrating a relationship between truncated octahedra and rhombic dodecahedra, which are two examples of space-filling polyhedra. I’ll talk about the process of designing and building the sculpture, some geometry and combinatorics […]
The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K, called a primitive element. In fact, it is clear from the proof of this theorem that not only there are infinitely many such primitive elements in K, but in fact most elements in […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Ryan Maguire (Dartmouth College) Title: Relative Strengths of Knot Invariants by Experiment Abstract: Four knot polynomials have been well studied by topologists, graph theorists, and algebraists alike: The Alexander, Jones, HOMFLY-PT, and Khovanov polynomials. It is known that the Khovanov polynomial is […]
Title: Structural Ramsey Theory and Logic Speaker: Lynn Scow, Professor of Mathematics, California State University, San Bernardino Abstract: The connection between Ramsey theory and logic goes back to Frank P. Ramsey's 1929 paper in which he announced his famous Ramsey theorem for finite sequences. This theorem states that for any partition of all sequences of length […]
Title: On Nonlinear Schrödinger Type Equations: Wave Modulation and Mathematical Analysis Abstract: The nonlinear Schrödinger (NLS) equation describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media. The NLS equation with soliton solutions is one of the significant and widely pursued research areas on the nonlinear wave motions. Sub-studies on […]
Imagine the hands on a clock. For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we ``move'' twelve times then we get back to where we […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Joe Breen (University of Iowa) Title: Open books in all dimensions Abstract: I will discuss recent work (joint with K. Honda and Y. Huang) on establishing a relationship, first discovered by Giroux, between "contact structures" and "open books". This relationship has been […]
Title: Review of differential geometry Abstract: 1. Given the embedding of a sphere of radius rho centered at the origin of \R^3 from spherical coordinates, what is the pullback of the flat metric in \R^3? i.e., what is the "round metric" on the 2-sphere of radius rho? 2. If we impose a complex structure on S^2 via […]
Title: The fractional p-Laplacian operator. Motivation for its definition and related boundary value problems Abstract: Last decades, nonlocal operators, as the fractional Laplacian, have gained to much attention due to its applications to several physical Phenomena. In this talk we aim to motivate the definition of the fractional laplacian operator through a simple but quite […]
