# Fields Medal Symposium 2012

The Fields Medal Symposium (see link for program) is a newly created annual gathering of mathematicians from around the world at the Fields Institute in Toronto, Canada to celebrate the work of a fields medalist.

The first Symposium will occur this year on October 15-October 18 on the topic of Ngô’s work on the fundamental lemma. This event will include lectures at a variety of levels, including a panel for high school students and undergraduates and public lectures on the Langlands program.

This is tremendously exciting because so many famous people in the field will be at this Symposium, and thus students working on various aspects of the Langlands program and the fundamental lemma will benefit greatly from attending.

Also, I hope to write a few blog posts while I am in Toronto covering some aspects of the Symposium. Stay tuned!

Those who have registered should also get the free tickets for the public opening.

Aside from the schedule, the Symposium is on Twitter and there is the Symposium Blog.

# Strasbourg 2012 Part 3: More Rigid Cohomology

In Strasbourg Part 2, I gave a bit of motivation for rigid cohomology, but I skirted defining anything substantial, except for the zeta function. Recall that we have an smooth algebraic variety $X$ of pure dimension $d$ defined over the finite field $\mathbb{F}_q$, and initially we were interested in the rational points $X(\mathbb{F}_q)$ of $X$. This led us to define the zeta function

$Z(X,t) = \mathrm{exp}( \sum_{r=1}^\infty N_r(X)t^r/r)$.

of $X$. Furthermore, I asked the reader to have faith that there are rigid cohomology spaces $H_\mathrm{rig}^i(X)$ of $X$, that the Frobenius extends to an operator $F$ on each of them, and that we have a product expansion

$Z(X,t) = \prod_{i=0}^{2d}\mathrm{det}(1 – tq^dF^{-1}|_{H_\mathrm{rig}^i(X)})^{{-1}^{i+1}}$.

Obviously many details have been left out, but this will suffice for continuing. I should state the disclaimer that from now on things will be a bit more sketchy since I’m not familiar with the more specialized material, and eventually I will just give references. As I have mentioned previously, I am not an expert in these areas, and I ask the patience of the reader since these summaries may lack some of the polish of my usual posts.
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