How many sublattices of Zn have index at most X? If we choose such a lattice L at random, what is the probability that Zn/L is cyclic? What is the probability that its order is odd? Now let R be a random subring of Zn. What is the probability that Zn/R is cyclic? We will see how these questions fit […]
We welcome all undergraduates and graduate students to attend topology seminar! Speaker: Qing Zhang (UC Santa Barbara) Title: Super-modular categories from near-group centers Abstract: A super-modular category is a unitary pre-modular category with Müger center equivalent to the symmetric unitary category of super-vector spaces. The modular data for a super-modular category gives a projective representation […]
Title: A Survey of Diophantine Equations Speaker: Edray Herber Goins, Professor of Mathematics and Statistics, Pomona College Abstract: There are many beautiful identities involving positive integers. For example, Pythagoras knew $3^2 + 4^2 = 5^2$ while Plato knew $3^3 + 4^3 + 5^3 = 6^3$. Euler discovered $59^4 + 158^4 = 133^4 + 134^4$, and even […]
Title: Developments in Noncommutative Fractal Geometry Abstract: As a noncommutative fractal geometer, I look for new expressions of the geometry of a fractal through the lens of noncommutative geometry. At the quantum scale, the wave function of a particle, but not its path in space, can be studied. Riemannian methods often rely on smooth paths to encode […]
Title: Geometric Optimization Involving Partial Differential Equations and Its Applications Speaker: Professor Chiu-Yen Kao, Claremont McKenna College, Claremont, CA USA Abstract: Optimal geometric design for energy functionals, which depends on solutions to partial differential equations, provides a vast number of interesting and challenging mathematical problems. One of the famous problems is that L. Rayleigh conjectured that the disk […]
I will give a brief introduction to well-rounded lattices and to their utility in wireless communications and post-quantum security. We will see how the lattice theta series naturally arises in these contexts and discuss its connections to well-rounded lattices. The talk is based on joint work with Laia Amoros, Amaro Barreal, Taoufiq Damir, Oliver Gnilke, […]
We welcome all undergraduates and graduate students to attend topology seminar! Speaker: Jim Hoste (Pitzer College) Title: Variations on the Kauffman Bracket Abstract: Forty years ago, Lou Kauffman formulated his "bracket" polynomial, a function from link diagrams to Laurent polynomials in one variable. This elementary construction leads to a simple definition of the Jones Polynomial. […]
For the next CCMS Colloquium on April 3rd Wednesday, we invite all MATH faculty, and students intending to enroll in upper division math courses to attend the Fall 2024 Course Preview Session of all the upper division math courses offered across the consortium in Fall 2024. Faculty, We strongly encourage you to attend so that […]
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 […]
