Algebra / Number Theory / Combinatorics Seminar

For a finite field F_q, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e., a coset of every one-dimensional linear subspace).  The finite […]

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 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, […]

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 […]