Though mirror symmetry requires much technical background, it gained traction in the mathematical community when physicists Candelas-de la Ossa-Green-Parkes discovered enumerative invariants counting the number of rational degree d curves […]
There is a rich connection between homogeneous dynamics and number theory. Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for […]
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 […]
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 […]
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 […]
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 […]
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. […]
For a finite group G, a G-module M, and a field F, an element u in H^d(G,M) is negligible over F if for each field extension L/F and every continuous […]
What are the possible angles between two integer vectors in R^n? If we fix one such possible angle and one integer vector x, is there always another integer vector y […]
In order to understand a topological space X, it is often easier to understand X in terms of an action by a group G. When X is a compact complex […]
Biquandle module enhancements are invariants of knots and links generalizing the classical Alexander module invariant. A quiver categorification of these invariants was introduced in 2020. In this work-in-progress (joint with Yewon Joung from Hanyang University in Seoul) we take the next step by defining invariant quiver representations. As an application we obtain new polynomial knot […]
A modification of the cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels gives a virtual resolution of the diagonal for smooth projective toric varieties and toric Deligne-Mumford stacks which are […]
