Tag Archives: talks

Slides from a talk on Quantitative Hilbert Irreducibility

I’m giving a talk today on my recent and forthcoming work in collaboration with Theresa Anderson, Ayla Gafni, Robert Lemke Oliver, George Shakan, Frank Thorne, Jiuya Wang, and Ruixiang Zhang. The slides for my talk can be found here.

This talk includes some discussion of our paper to appear in IMRN (link to the arXiv version, which is mostly the same as what will be published). (See also my previous discussion on this paper). But I’ll note that in this talk I lean towards a few ideas that did not make it into the paper, but which we are using in current work.

In particular, in our paper we don’t need to use group actions or classify orbit sizes, but it turns out that this is a very strong idea! I’ll note that in a very particular case, Thorne and Taniguchi have applied this type of orbit counting method in their paper “Orbital exponential sums for prehomogeneous vector spaces” to gain extremely strong, specific understanding of Fourier transform for their application.

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Slides from a talk on Visualizing Modular Forms

Yesterday I gave a talk at the University of Oregon Number Theory seminar on Visualizing Modular Forms. This is a spiritual successor to my paper on Visualizing modular forms that is to appear in Simons Symposia volume Arithmetic Geometry, Number Theory, and Computation.

I’ve worked with modular forms for almost 10 years now, but I’ve only known what a modular form looks like for about 2 years. In this talk, I explored visual representations of modular forms, with lots of examples.

The slides are available here.

I’ll share one visualization here that I liked a lot: a visualization of a particular Maass form on $\mathrm{SL}(2, \mathbb{Z})$.

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Talk on computing Maass forms

In a remarkable coincidence, I’m giving two talks on Maass forms today (after not giving any talks for 3 months). One of these was a chalk talk (or rather camera on pen on paper talk). My other talk can be found at https://davidlowryduda.com/static/Talks/ComputingMaass20/.

In this talk, I briefly describe how one goes about computing Maass forms for congruence subgroups of $\mathrm{SL}(2)$. This is a short and pointed exposition of ideas mostly found in papers of Hejhal and Fredrik Strömberg’s PhD thesis. More precise references are included at the end of the talk.

This amounts to a description of the idea of Hejhal’s algorithm on a congruence subgroup.

Side notes on revealjs

I decided to experiment a bit with this talk. This is not a TeX-Beamer talk (as is most common for math) — instead it’s a revealjs talk. I haven’t written a revealjs talk before, but it was surprisingly easy.

It took me more time than writing a beamer talk, most likely because I don’t have a good workflow with reveal and there were several times when I wanted to use nontrivial javascript capabilities. In particular, I wanted to have a few elements transition from one slide to the next (using the automatic transition capabilities).

At first, I had thought I would write in an intermediate markup format and then translate this into revealjs, but I quickly decided against that plan. The composition stage was a bit more annoying.

But I think the result is more appealing than a beamer talk, and it’s sufficiently interesting that I’ll revisit it later.

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