## Conference road trips

Each year, MUSA organizes a road trip for undergraduates to attend the
Northern California Undergraduate
Mathematics Conference, which is held in March at a local university. The conferences provides an opportunity
for undergraduates to talk about their senior theses, REUs, or DRP projects.

The trip is partially funded by MUSA and the ASUC.

### 2018

In 2018, the conference was held at Fresno State University. Two of the talks were given by Berkeley students:

#### Norm-Euclidean ideal classes of Galois cubic fields

Clark Lyons

Lenstra introduced the notion of a norm-Euclidean ideal class as a generalization of norm-Euclideanity of a number field. He classified all quadratic number fields possessing a norm-Euclidean ideal class. We investigate the Galois cubic case. We show that up to discriminant 10^{11} precisely two such number fields possess a nontrivial norm-Euclidean ideal class, and we conjecture no more exist. In an attempt to settle our conjecture, we prove explicit bounds on the first few non-residues of cubic characters under the generalized Riemann hypothesis.

#### On the invariants of numerical monoids

Sung Hyup Lee and Brandon Van Over

Numerical monoids are frequently of import for additive combinatorics, but also arise naturally from factorization theory, where one measures failures of unique factorization. In particular, numerical monoids which are minimally generated by arithmetic sequences are known to be particularly well-behaved, in the sense that invariants difficult to compute in the general case admit closed-forms in the arithmetical case. Thus it is a natural question to analyze what happens to their invariants when one starts to omit some of their generators. We will begin by motivating their study by some examples, define some of the relevant invariants, and present our recent results that reduce the calculation of invariants of any almost-arithmetic monoids to their extremal generators under specific conditions.

### 2017

In 2017, the conference was held at Sonoma State University, and five of the talks were given
by Berkeley students:

- Mahrud Sayrafi on “Computations in Local Rings using Macaulay2 Software”
- Carl Plant on “Topological Graph Theory as a Lens for Analyzing Voting Rules”
- Hugo Jenkins on “Diophantine Equations from Pascal's Triangle”
- Renjun Zhu & Ana Wright on “Mixing Times For the Generalized Rook's Walk”
- Tram Pham on “Finite Difference Method for Partial Differential Equations”