Here is the website:

https://swc-math.github.io/aws/2026/index.html

I was in a study group, not a project group. I was already familiar with one section, computational modular forms. However, I learned a great deal from the other three sections, particularly on point counting and cryptography.

The zeta function. Let C/FqC / \mathbb{F}_q be a hyperelliptic curve of genus g⩾1g \geqslant 1. The sequence of point counts #C(Fqr)\# C\left(\mathbb{F}_{q^r}\right), for r=1,2,…\mathrm{r}=1,2, \ldots, may be encoded into a generating function (formal power series) called the the zeta function of C . This is defined by the formula

ZC(T):=exp⁡(∑r=1∞#C(Fqr)rTr)∈Q⟦T⟧.\begin{equation*} Z_{C}(T):=\exp \left(\sum_{r=1}^{\infty} \frac{\# C\left(\mathbb{F}_{q^r}\right)}{r} T^{r}\right) \in \mathbb{Q} \llbracket T \rrbracket . \end{equation*}

Here exp denotes the usual exponential of power series, i.e.,

Theorem 3.3.2 (Weil Conjectures). Let C/FqC / \mathbb{F}_{q} be a hyperelliptic curve of genus g⩾1\mathrm{g} \geqslant 1. Then the zeta function of C is a rational function of the form

ZC(T)=LC(T)(1−T)(1−qT)′Z_C(T)=\frac{L_C(T)}{(1-T)(1-q T)^{\prime}} where LC(T)∈1+TZ[T]L_C(T)\in 1+TZ[T] is a polynomial of degree 2g2g

About isogeny-based cryptography, I was impressed by the use of Deuring Correspondence in SQISign and the application of Kani's Lemma to break SIDH."

On March 9th, we visited the Arizona-Sonora Desert Museum.

The travel experience, however, was not very pleasant.