MixedMath - explorations in math and programinghttps://davidlowryduda.comDavid's personal blog.en-usCopyright David Lowry-Duda (2022) - All Rights Reserved.admin@davidlowryduda.comadmin@davidlowryduda.comThu, 02 Mar 2023 13:54:58 +0000Thu, 02 Mar 2023 13:54:58 +0000mixedmathapp/generate_rss.py v0.1https://cyber.harvard.edu/rss/rss.htmlhttps://davidlowryduda.com/static/images/favicon-32x32.pngMixedMathhttps://davidlowryduda.comSlides from a talk at Concordia Universityhttps://davidlowryduda.com/slides-from-concordia-2023David Lowry-Duda<p>Today, I'm giving a talk at QVNTS on computing Maass forms. My slides are
available <a href="/wp-content/uploads/2023/02/Concordia.pdf">here</a>.</p>
<p>Please let me know if there are any questions or comments.</p>https://davidlowryduda.com/slides-from-concordia-2023Thu, 23 Feb 2023 03:14:15 +0000Paper: Sums of cusp forms coefficients along quadratic sequenceshttps://davidlowryduda.com/paper-sums-of-coeffs-along-quadraticsDavid Lowry-Duda<p>I am happy to announce that my frequent collaborators, Alex Walker and Chan
Kuan, and I have just posted a <a href="https://arxiv.org/abs/2301.11901">preprint to the
arxiv</a> called <em>Sums of cusp form coefficients
along quadratic sequences</em>.</p>
<p>Our primary result is the following.</p>
<div class="theorem">
<p>Let $f(z) = \sum_{n \geq 1} a(n) q^n = \sum_{n \geq 1} A(n) n^{\frac{k-1}{2}}
q^n$ denote a holomorphic cusp form of weight $k \geq 2$ on $\Gamma_0(N)$,
possibly with nontrivial nebentypus. For any $h > 0$ and any $\epsilon > 0$, we
have that
\begin{equation}
\sum_{n^2 + h \leq X^2} A(n^2 + h) = c_{f, h} X + O_{f, h,
\epsilon}(X^{\eta(k) + \epsilon}),
\end{equation}
where
\begin{equation*}
\eta(k) = 1 - \frac{1}{k + 3 - \sqrt{k(k-2)}} \approx \frac{3}{4} +
\frac{1}{32k - 44} + O(1/k^2).
\end{equation*}</p>
</div>
<p>The constant $c_{f, h}$ above is typically $0$, but we weren't the first to
notice this.</p>
<h2>Context</h2>
<p>We approach this by studying the Dirichlet series
\begin{equation*}
D_h(s) := \sum_{n \geq 1} \frac{r_1(n) a(n+h)}{(n + h)^{s}},
\end{equation*}
where
\begin{equation*}
r_1(n) = \begin{cases}
1 & n = 0 \\
2 & n = m^2, m \neq 0 \\
0 & \text{else}
\end{cases}
\end{equation*}
is the number of ways of writing $n$ as a (sum of exactly $1$) square.</p>
<p>This approach isn't new. In his 1984 paper <em>Additive number theory and Maass
forms</em>, Peter Sarnak suggests that one could relate the series
\begin{equation*}
\sum_{n \geq 1} \frac{d(n^2 + h)}{(n^2 + h)^2}
\end{equation*}
to a Petersson inner product involving a theta function, a weight $0$
Eisenstein series, and a half-integral weight Poincaré series. This inner
product can be understood spectrally, hence the spectrum of the half-integral
weight hyperbolic Laplacian (and half-integral weight Maass forms) reflect the
behavior of the ordinary-seeming partial sums
\begin{equation*}
\sum_{n \leq X} d(n^2 + h).
\end{equation*}</p>
<p>A broader class of sums was studied by Blomer.<span class="aside">Blomer. <em>Sums of Hecke
eigenvalues over values of quadratic polynomials</em>. <strong>IMRN</strong>, 2008.</span></p>
<p>Let $q(x) \in \mathbb{Z}[x]$ denote any monic quadratic polynomial. Then Blomer
showed that
\begin{equation*}
\sum_{n \leq X} A(q(n)) = c_{f, q}X + O_{f, q, \epsilon}(X^{\frac{6}{7} + \epsilon}).
\end{equation*}
Blomer already noted that the main term typically doesn't occur.</p>
<p>More recently, Templier and Tsimerman<span class="aside">Templier and Tsimerman.
<em>Non-split sums of coefficients of $\mathrm{GL}(2)$-automorphic forms</em>.
<strong>Israel J. Math</strong> 2013</span></p>
<p>showed that $D_h(s)$ has polynomial growth in vertical strips and has
reasonable polar behavior. This allows them to show that
\begin{equation*}
\sum_{n \geq 0} A(n^2 + h) g\big( (n^2 + h)/X \big)
=
c_{f, h, g} X + O_\epsilon(X^{\frac{1}{2} + \Theta + \epsilon}),
\end{equation*}
where $\Theta$ is a term that is probably $0$ coming from a contribution from
potentially exceptional eigenvalues of the Laplacian and the Selberg Eigenvalue
Conjecture, and where $g$ is a smooth function of sufficient decay.</p>
<p>Templier and Tsimerman approach their result in two different ways: one studies
the Dirichlet series $D_h(s)$ with the same initial steps as outlined by
Sarnak. The second way is more representation theoretic and allows greater
flexibility in the permitted forms.</p>
<h2>Placing our techniques in context</h2>
<p>Broadly, our approach begins in the same way as Templier and Tsimerman —
we study $D_h(s)$ through a Petersson inner product involving half-integral
weight Poincaré series. The great challenge is to understand the discrete
spectrum and half-integral weight Maass forms, and we deviate from Templier and
Tsimerman sharply in our treatment of the discrete spectrum.</p>
<p>For each eigenvalue $\lambda_j$ there is an associated type $\frac{1}{2} +
it_j$ and form
\begin{equation*}
\mu_j(z) = \sum_{n \neq 0} \rho_j(n) W_{\mathrm{sgn}(n) \frac{k}{2}, it_j}(4\pi \lvert n \rvert y) e(nx),
\end{equation*}
where $W$ is a Whittaker function and the coefficients $\rho_j(n)$ are very
mysterious. We average Maass forms in long averages over the eigenvalues and
types (indexed by $j$) <em>and</em> long averages over coefficients $n$. We base the
former approach average on Blomer's work above, and for the latter we improve
on (a part of) the seminar work of Duke, Friedlander, and
Iwaniec.<span class="aside">Duke, Friedlander, Iwaniec. <em>The subconvexity problem for
Artin $L$-functions</em>. <strong>Inventiones</strong>. 2002.</span></p>
<p>For this, it is necessary to establish certain uniform bounds for Whittaker functions.</p>
<p>To apply our bounds for the discrete spectrum, Maass forms, and Whittaker
functions, we use that $f$ is holomorphic in an essential way. We decompose $f$
into a sum of finitely many holomorphic Poincaré series. This is done by Blomer
as well. But in contrast, we study the resulting shifted convolutions whereas
Blomer recollects terms into Kloosterman and Salié type sums.</p>
<p>Ultimately we conclude with a standard contour shifting argument.</p>
<h2>Additional remarks</h2>
<h3>Continuous vs discrete spectra</h3>
<p>The quality of our bound mirrors the quality of our understanding of the
discrete spectrum. This is interesting in that the continuous and discrete
spectra are typically of a similar calibre of size and difficulty.</p>
<p>But here we are examining a half-integral weight object into half-integral
weight spectra. The continuous spectrum comes from Eisenstein series, and it
turns out that the coefficients of real-analytic half-integral weight
Eisenstein series are (essentially) Dirichlet $L$-functions — and these
are relatively easy to understand.</p>
<p>Existing bounds for half-integral weight Maass forms are much weaker than
corresponding bounds for full-integral weight Maass forms.</p>
<p>In principle, there is also a residual spectrum to consider here (in contrast
to weight $0$ spectral expansions). But in practice this is perfectly handled
by in the work of Templier and Tsimerman and presents no further difficulty.</p>
<h3>Two too-brief summaries</h3>
<p>One too-brief-to-be-correct summary of this paper is that <em>by restricting to a
smaller class of quadratic polynomials than Blomer, it is possible to prove a
stronger result</em>. In reality, we restrict to a class of quadratic polynomials
that allows the corresponding Dirichlet series to be easily recognized as a
Petersson inner product involving a standard theta function and a half-integral
weight Poincaré series.</p>
<p>Another too-brief-to-be-correct summary of this paper is that <em>examining
Whittaker functions and Bessel functions even closer reveals that they control
all of multiplicative number theory</em>. Actually, this might be
correct.<span class="aside">As a corollary, I guess all multiplicative number theory is
controlled by monodromy?</span></p>https://davidlowryduda.com/paper-sums-of-coeffs-along-quadraticsFri, 27 Jan 2023 03:14:15 +0000On Mathstodonhttps://davidlowryduda.com/on-mathstodonDavid Lowry-Duda<p>I've been on Mastodon for just over 6 weeks now, inspired by obvious events
approximately two months ago. Specifically, I've been on the math-friendly
server <a href="https://mathstodon.xyz/"><em>Mathstodon</em></a>, which includes latex rendering.</p>
<p>In short: I like it.</p>
<p>Right now, <em>Mathstodon</em> is a kind place. The general culture is kind and
inviting. I'm reminded a bit of young StackExchange sites, which are often so
happy to come into existence that it seems like every new post is
treasured.</p>
<p>Given the similarities to twitter, it is natural to compare and contrast.
Twitter is not kind. Outrage evidently boosts engagement and snark generates
retweets and likes. On <em>Mathstodon</em>, moderators maintain civility. I don't pay
much attention to other Mastodon servers — they have different moderators
and possibly different cultures.</p>
<p>But it's also true that Mastodon (and <em>Mathstodon</em>) are growing rapidly, and I
don't know any social media sites that managed to maintain a positive culture
while growing larger. Math.StackExchange<sup>1</sup>
<span class="aside"><sup>1</sup> Which I've helped moderate for
a decade and which is dear to me.</span>
used to be much friendlier than it is
now, but I think it's impossible to bring that positivity back.<sup>2</sup>
<span class="aside"><sup>2</sup> I have
thought much about this. See my other posts <a href="/challenges-facing-community-cohesion-and-math-stackexchange-in-particular/">Challenges facing cohesion at
MSE</a>,
<a href="/ghosts-of-forums-past/">Ghosts of forums past</a>, and <a href="/splitting-mathse-into-novicemathse-is-a-bad-idea/">Splitting MSE into
NoviceMathSE is a bad idea</a>
for more.</span></p>
<p>Is the Mastodon system of having separate instances with separate cultures the
answer? I don't know. Conceivably if <em>Mathstodon</em> starts to feel bad, I could
pick and and move elsewhere — or of course run my own. Time will tell.</p>
<h2>The Algorithm</h2>
<p>I wasn't sure if I would like or not like the lack of <strong>the algorithm</strong>, the
mysterious ordering system. But to my surprise, I miss essentially nothing
about twitters algorithm.</p>
<p>Maintaining a reasonable signal-to-noise ratio on social media is a struggle.
A deep problem I've faced on twitter is that I like to read things written by
people who write about Hard Problems for a living. To ensure they get
sufficient audience on twitter, it's necessary to post and repost the same
essay/story (possibly with lightly different titles or formats). If any of
these gets sufficient following, then it will bubble up to the feed.</p>
<p>This is too noisy for me.</p>
<p>The Mastodon system is closer to an interleaved set of RSS feeds.<sup>3</sup>
<span class="aside"><sup>3</sup> The
ActivityPub protocol that Mastodon implements is sort of like a souped up
RSS/Atom protocol that allows more rapid updates.</span>
Everything is strictly
in the order that they're made. I love RSS, so perhaps it is no surprise that I
like this system.</p>
<p>And the system allows unimaginatively-named "lists", which are feeds containing
various specific accounts.</p>
<p>At least at the moment, this has a great signal-to-noise ratio.</p>
<h2>Lack of Trending</h2>
<p>The notable exception is the lack of <strong>trending</strong> information. Mastodon does
not have an answer to trending local content.</p>
<p>Concretely, I thought about this when the Boston MBTA screeched to a halt (as
it has a recent tendency to do) a bit before Christmas. If I had opened
twitter, I might have been able to find the source of the disruption —
not because I follow any MBTA accounts, but because this type of kerfluffle
would cause enough activity that it would have populated the feed.</p>
<p>But I don't have twitter on my devices, and I don't currently see myself
reinstalling twitter. In principle, the various MBTA twitter posts could have
appeared on Mastodon as well — but I wouldn't see them. I suppose I could
look for the tag #MBTA, or maybe #Boston? These aren't sufficient yet.</p>
<p>One can debate the merits of having twitter be the de facto place for random
civic and political organizations to post news, but this is common. And this is
another place where Mastodon is currently lacking.</p>https://davidlowryduda.com/on-mathstodonSun, 01 Jan 2023 03:14:15 +0000Implementation notes on modular curve visualizationshttps://davidlowryduda.com/modcurvevizDavid Lowry-Duda<p>The LMFDB will soon have a new section on modular curves. And as with modular
forms, each curve will have a <em>portrait</em> or <em>badge</em> that gives a rough
approximation to some of the characteristics of the curve.</p>
<p>I wrote a note on some of the technical observations and implementation details
concerning these curves. This note can be <a href="/wp-content/uploads/2022/12/VisualizingModularCurves.pdf">found
here</a>. I've also
added a link to it in the unpublished notes section of my <a href="/research">research
page</a>.</p>
<p>Instead of going into details here, I'll refer to the details in the note. I'll
give the core idea.</p>
<p>Each modular curve comes from a subgroup $H \subset \mathrm{GL}(2,
\mathbb{Z}/N\mathbb{Z})$ for some $N$ called the <em>level</em>. To form a
visualization, we compute cosets for $H \cap \mathrm{SL}(2,
\mathbb{Z}/N\mathbb{Z})$ inside $\mathrm{SL}(2, \mathbb{Z}/N\mathbb{Z})$, lift
these to <em>nice</em> elements in $\mathrm{SL}(2, \mathbb{Z})$, and then translate
the standard fundamental domain of $\mathrm{SL}(2, \mathbb{Z}) \backslash
\mathcal{H}$ by these cosets.</p>
<p>We show this on the Poincaré disk, to give a badge format similar to what we
did for modular forms.</p>
<p>This is not a perfect representation, but it captures some of the character of
the curve.</p>
<p>Here are a few of the images that we produce.</p>
<figure class="center shadowed">
<img src="/wp-content/uploads/2022/12/mcportrait.8.24.1.13.png"
width="400px" />
</figure>
<figure class="center shadowed">
<img src="/wp-content/uploads/2022/12/mcportrait.10.18.0.1.png"
width="400px" />
</figure>
<figure class="center shadowed">
<img src="/wp-content/uploads/2022/12/mcportrait.10.72.1.1.png"
width="400px" />
</figure>
<p>I had studied how to produce space efficient SVG files as well, though I did
not go in this direction in the end. But I think these silhouettes are
interesting, so I include them too.</p>
<figure class="center shadowed">
<img src="/wp-content/uploads/2022/12/mc8.24.1.13.svg"
width="400px" />
</figure>
<figure class="center shadowed">
<img src="/wp-content/uploads/2022/12/mc10.72.1.1.svg"
width="400px" />
</figure>https://davidlowryduda.com/modcurvevizWed, 07 Dec 2022 03:14:15 +0000Slides on Maass forms, nearing completionhttps://davidlowryduda.com/slides-agntc-dec22David Lowry-Duda<p>I'm giving an update today on my project to compute Maass forms. Today, I
describe the final steps about how to make the computation rigorous. This
complements a <a href="/talk-on-computing-maass-forms">talk I gave two years ago</a> about
how to implement a <em>heuristic</em> evaluation.</p>
<p>The slides for my talk today <a href="/wp-content/uploads/2022/12/SimonsDec2022_maass.pdf">are available here</a>.</p>
<p>I hope to have a preprint describing this algorithm and its implementation
shortly. I also hope to have a beta update to LMFDB with this information by
the next meeting of the collaboration.</p>https://davidlowryduda.com/slides-agntc-dec22Fri, 02 Dec 2022 03:14:15 +0000Slides on Modular Forms and the L-functions, a talk at the Simons Center for Geometry and Physicshttps://davidlowryduda.com/slides-scgp2022David Lowry-Duda<p>I'm giving a talk today on modular forms and their $L$-functions at the Simons
Center for Geometry and Physics. The slides for this talk are <a href="/wp-content/uploads/2022/11/SCGP.pdf">available
here</a>.</p>
<p>I refer to many things that I have done before in this talk.</p>
<p>For references and proofs of the various aspects of Dirichlet series associated
to half-integral weight modular forms, I wrote a series of notes stemming from
<a href="/zeros-of-dirichlet-series-masthead/">this post</a>.</p>
<p>For more information on computing and working with Maass forms, see <a href="/talk-computing-and-verifying-maass-forms/">notes from
another talk I gave</a>.</p>
<p>And finally, many of the objects discussed are <a href="https://www.lmfdb.org/">in the
LMFDB</a>.</p>https://davidlowryduda.com/slides-scgp2022Wed, 09 Nov 2022 03:14:15 +0000Supplement to Langlands surveyhttps://davidlowryduda.com/scgp-langlandsDavid Lowry-Duda<p>Today, I gave an introductory survey on the Langlands program to a group of
mathematicians and physicists at the Simons Center for Geometry and Physics at
Stonybrook University.</p>
<p>Many of these connections are well-illustrated on the <a href="https://www.lmfdb.org">LMFDB</a>.
I highly suggest poking around and clicking on things — on many pages
there are links to related objects.</p>
<p>Part of the Langlands program includes the modularity conjecture for elliptic
curves over $\mathbb{Q}$. On the LMFDB, this means that we can go look at
<a href="https://www.lmfdb.org/EllipticCurve/Q/">elliptic curves over $\mathbb{Q}$</a>,
take some arbitrary elliptic curve like
\begin{equation*}
y^2 + xy + y = x^3 - 113x - 469,
\end{equation*}
(which has <a href="https://www.lmfdb.org/EllipticCurve/Q/105/a/1">this homepage in the LMFDB</a>),
and then see that this corresponds to <a href="https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/105/2/a/a/">this modular form on the
LMFDB</a>. And
they have the <a href="https://www.lmfdb.org/L/2/105/1.1/c1/0/1">same L-function</a>.</p>
<p>During the talk, Brian gave an example or an Artin representation of the
symmetric group $S_3$ on three symbols. For reference, he pulled data <a href="https://www.lmfdb.org/ArtinRepresentation/2.23.3t2.b.a">from
this representation page on the LMFDB</a>.</p>
<p>From one perspective, the Langlands program is a monolithic wall of imposing,
intimidating mathematics. But from another perspective, the Langlands program
is most interesting because it organizes and connects seemingly different
phenomena.</p>
<p>It's not necessary to understand each detail — instead it's interesting
to note that there are many fundamentally different ways of producing highly
structured data (like $L$-functions). And remarkably we think that <em>every</em> such
$L$-function will behave beautifully, including satisfying their own Riemann
Hypothesis.</p>https://davidlowryduda.com/scgp-langlandsThu, 03 Nov 2022 03:14:15 +0000Notes from a survey talk by Jeff Lagarias on the Collatz problemhttps://davidlowryduda.com/lagarias-collatzDavid Lowry-DudaThis post is larger than 10000 bytes, which is above the limit for this RSS feed. Perhaps it is long or has embedded images or code. Please view it directly at the url.https://davidlowryduda.com/lagarias-collatzWed, 02 Nov 2022 03:14:15 +0000Paul R. Halmos -- Lester R. Ford Awardhttps://davidlowryduda.com/halmos-ford-awardDavid Lowry-Duda<p>This is an update with (unexpected) good news. My collaborator <a href="https://people.bath.ac.uk/mw2319/">Miles
Wheeler</a> and I were given the <a href="https://www.maa.org/programs-and-communities/member-communities/maa-awards/writing-awards/paul-halmos-lester-ford-awards">Paul R.
Halmos – Lester R. Ford Award</a>
for our paper <a href="https://doi.org/10.1080/00029890.2021.1840879">Perturbing the mean value theorem: implicit functions, the morse
lemma, and beyond</a><sup>1</sup>
<span class="aside"><sup>1</sup>The
<a href="https://arxiv.org/abs/1906.02026">arxiv version</a> of this paper is called <em>When
are there continuous choices for the mean value abscissa</em>, and is slightly
longer than the final published form.</span></p>
<p>This was an unexpected honor. Partly, this is due to the fact that we first
wrote this paper years ago and it was accepted in 2019. But the publication
backlog meant that it wasn't published until January of 2021, and thus eligible
for the 2022 award. But also it's always sort of a nice surprise to hear that
people <em>read</em> what I write.</p>
<p>I described <a href="/paper-continuous-choices-mvt/">this paper before</a>, and
wrote <a href="/choosing-functions-for-mvt-abscissa/">an additional note on how we chose our functions and made the figures</a>.</p>
<p>When my wife learned that this paper won an award, she asked
if this "was that paper you really liked that you wrote wtih Miles during grad
school"? Yes! It is that paper. I really do like this paper.</p>
<h2>Origin story</h2>
<p>The string of ideas leading to this paper began when I first began to TA
calculus at Brown. I was becoming aware of the fact that I would soon be
teaching calculus courses, and I began to really think about why we structured
the courses the way we do.<sup>2</sup>
<span class="aside"><sup>2</sup>I don't have a completely satisfactory
explanation for everything, especially for the "integration bag of tricks" or
the "series convergence bag of tricks" portion. But upon reflection, I can
understand the purpose of <em>most</em> portions of the calculus sequence.</span></p>
<p>One of my least favorite questions was the <em>verify the mean value theorem for
the function $f(x)$ on the interval $[1, 4]$ by...</em> sort of question. The
problem is that this question is really just a way to check that one
understands the statement of the mean value theorem — and this statement
<em>feels</em> very unimportant.</p>
<p>But it turns out that the mean value theorem is <em>extremely</em> important. The mean
value theorem and intermediate value theorems are the two sneaky abstractions
that encapsulate underlying topological ideas that we typically brush aside in
introductory calculus courses.</p>
<h3>We don't do calculus on real valued functions over the rationals</h3>
<p>We illustrate this with two examples in the analogous case of functions
\begin{equation*}
f: \mathbb{Q} \longrightarrow \mathbb{R}.
\end{equation*}
I would expect that many introductory students would think these functions
<em>feel intuitively about the same</em> as functions from $\mathbb{R}$ to
$\mathbb{R}$. But in fact both the intermediaet value theorem and mean value
theorem are false for real-valued functions defined on the rationals.</p>
<p>The intermediate value theorem is false here. Consider the function
\begin{align*}
f(x): \mathbb{Q} &\longrightarrow \mathbb{R}\\
x &\mapsto x^2 - 2.
\end{align*}
On the interval $[0, 2]$, for example, we see that $f(0) = -2$ and $f(2) = 2$.
But there is no $x \in \mathbb{Q} \cap [0, 2]$ such that $f(x) = 0$.</p>
<p>The mean value theorem is false too. Consider the function
\begin{align*}
f(x): \mathbb{Q} &\longrightarrow \mathbb{R} \\
x &\mapsto \begin{cases} 0 & \text{if } x^2 > 2, \\
1 & \text{if } x^2 > 2.
\end{cases}
\end{align*}
For this function, $f'(x) = 0$ everywhere, even though the function isn't
constant. (But it is <em>locally constant</em>). We try to avoid pathological examples
initially.<sup>3</sup>
<span class="aside"><sup>3</sup>It is a funny thing. Initially, we pretend that everything
is as nice as possible to build intuition. Then we see that there are
pathological counterexamples and use these to sharpen intuition. Seeing these
too early is potentially misleading. Implicit within the order is an idea of
what <em>usually</em> hapens and what behavior is <em>exceptional</em>.</span></p>
<p>It turns out that the topological space the functions are defined on <em>really
matter.</em></p>
<h3>Mean value theorem as abstraction</h3>
<p>I don't talk about this in a typical calculus class because topological
concerns are almost entirely ignored. We work with the practical case of
real-valued functions defined over the reals. And the key tools we use to hide
the underlying topological details are the intermediate and mean value
theorems.</p>
<p>I didn't fully realize this until I wondered whether we could teach calculus
<em>without</em> covering these two theorems.</p>
<p>It might be possible. But I decided that it was a bad idea.</p>
<p>Instead, I think it's a good idea to give students a better idea of how these
two theorems are two of the most important ideas in calculus. I kept this idea
in mind when I wrote <a href="/an-intuitive-introduction-to-calculus/">An intuitive introduction to
calculus</a> for my students in 2013.</p>
<p>And more broadly, I began to investigate just how many things we could reduce,
as directly as possible, to the mean value theorem. Miles realized we could
investigate the continuity of the mean value abscissa with a low dimnsional
implicit function theorem and baby version of Morse's lemma, and the rest is
history.</p>
<p>I've collected so many random facts and questions tangentially related to the
mean value theorem over the years. But I could always collect more!</p>
<h3>MathFest</h3>
<p>I attended <a href="https://www.maa.org/meetings/mathfest">MathFest</a>
for the first time to receive this award in person. MathFest was an
extraordinary and interesting experience. I was particularly impressed by how
many sessions and talks focused on actionable ways to improve math education
in the classroom <em>now</em>.</p>https://davidlowryduda.com/halmos-ford-awardMon, 17 Oct 2022 03:14:15 +0000Slides from a talk at Maine-Quebechttps://davidlowryduda.com/slides-mq2022David Lowry-Duda<p>This weekend I'm at the
<a href="https://archimede.mat.ulaval.ca/QUEBEC-MAINE/22/qm22.html">Maine-Québec</a>
number theory conference. This year, it's in Québec!</p>
<p>I'm giving a talk surveying ideas from <a href="https://arxiv.org/abs/2204.01651"><em>Improved bounds on number fields of
small degree</em></a>, joint work with Anderson,
Gafni, Hughes, Lemke Oliver, Thorne, Wang, and Zhang.</p>
<p>The slides for this talk are <a href="/wp-content/uploads/2022/10/MaineQuebec2022_DLD.pdf">available
here</a>.</p>https://davidlowryduda.com/slides-mq2022Sat, 15 Oct 2022 03:14:15 +0000