You probably have seen all sorts of function spaces before, be it in your sophomore year in undergrad, or a few weeks ago, or, when you were in fourth grade, and you might feel that it is a zoooo. Just in case you would like to be a function space zoooologist this Friday afternoon, you are welcome to join me, and let's scratch the surface a bit more. Why should(n't) we care about $L^{p}$, for $p\in(0,1)$? How shall we define a limit of a family of topological spaces? What is $H^{1}$, and what about $h^{1}$? How shall we interpret fractional derivatives, and negative derivatives? What about .... In the case you don't care about any of these, you are still welcome to join for a surprise (?) at the end.
Why does music make my brain go brrr?
Chris Dunstan
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DRL A4
We’ll give a mathematical introduction to music theory and use our framework to explore current theories about why humans like music. Live music will be provided :)
Abelian Groups Gone Wild
David Zhu
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DRL A4
Are you struggling to compute ∞-colimits in the ∞-category of ∞-categories? Have p-adic Galois representations attached to elliptic curves haunt your dreams? And what, if anything, is a derived Artin stack with prescribed Tor-amplitude? Sometimes I wish things were as simple as abelian groups…
Gnomes and Glomes
Nikita Borisov
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DRL A4
Can you decompose Euclidean 3-space as a disjoint union of lines such that no two are parallel? Come find out as we explore various cartographic map projections, the Hopf fibration, and the glome; a famous mathematical object named by paleontologist George Olshevsky.
High Scores in Guitar Hero
Colton Griffin
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DRL A4
Guitar Hero is a series of rhythm games that were released between 2005-2010. In the game, you press notes to the rhythm of a song using a guitar-shaped controller, and you are awarded points for successfully doing so. However, there is a specific game mechanic that makes it surprisingly difficult to compute the maximum possible score you could be awarded in any given song. This is an example of a combinatorial optimization problem, like Traveling Salesman or other graph theory problems. In this talk, I'll discuss some of the mechanics of the game and how people have developed approximate solutions to the problem of determining maximum possible scores.
Abstract Nonsense
Riley Shahar
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DRL A4
Our originally scheduled speaker was unfortunately sick, so Riley filled in with some discussion about the nlab, abstract nonsense, and philosophy.
Top 10 Proofs of The Infinitude of Primes
Luis Modes Castillo
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DRL A4
During this talk, we will give several interesting proofs from various areas of math of Euclid's theorem: There are infinitely many prime numbers. Feel free to bring your favorite proof to share!
Minesweeper: Logic, Computation, ... Physics?
Jasper Ty
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DRL A4
Minesweeper is a famous puzzle game that was shipped with various versions of Windows operating system, where one aims to assign mines to a board of undetermined squares via local counting rules. We will survey various logical and complexity-theoretic analyses of the game, culminating in an experimental result by two (bored) physicists, demonstrating a phase transition phenomenon for Minesweeper closely related to that of random SAT.
The Jordan Curve Theorem
Carmine Ingram
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DRL A4
The Jordan Curve Theorem has always gotten a bad rap. Historically, Jordan's original proof was regarded as insufficient "even for the case of a polygon", and even today the proof of the Jordan curve theorem is regarded as highly technical, and many graduate students have never seen a proof of the theorem, which I believe is a very sad state of affairs. I will give some historical background, discuss what the Jordan curve theorem actually states, present a straightforward proof, and defend Jordan's original proof.
viXra Day
viXra Day
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DRL A6
Continuing the tradition started by Colton and Yam last year, we will hold a viXra day! viXra (arXiv backwards, https://vixra.org/) is a collection of articles that were rejected by the arXiv. In their words, they serve "the whole scientific community"; in my words, they serve very entertaining crackpots. So let's have fun learning together about the brilliant mathematical discoveries that those of us in academia are just too hegemonic to appreciate. If you want to participate, feel free to pick your favorite article in advance and plan a mini-talk on it, or to show up on the day of and just read us selections from an article you find entertaining!
Proof that e is algebraic
Marc Muhleisen
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DRL A6
When I was an undergrad, like, eight years ago, a friend told me about a probability puzzle he claimed to have solved. It was shrouded in mystery because apparently the answer was “(e-1)/(e+1) or something like that,” and also he’d forgotten how he solved it. Vaguely tantalized by the presence of Euler’s number, I worked on it passively for a long time. Assuming my friend was right, I will derive for you a contradiction in ZFC by showing that the answer is also a certain algebraic number. On the way, we’ll learn about generating functions. (The puzzle itself is also kind of goofy—you’ll see what I mean…)
∞-Oreo
Vicente Bosca
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DRL A6
In this talk I will introduce the ∞-Oreo, probably changing the food industry forever. We will explore other ∞-foods and conclude with a conjecture.
SET-free sets
Nikita Borisov
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DRL A6
We will look at the mathematical aspects of the game of SET (where the goal is to find certain triplets called SETs) and the affine cap problem over integers mod 3. We will then see how counting how often no SETs appear relates to hyperplane arrangements, posets, Mobius inversion, etale cohomology and finally representation stability.
Halloween Special: Eldritch horrors in dimensions 0 and 2
Ellis Buckminster
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DRL A6
An Integration Calculus based on the Euler Characteristics, Revisited
Mattie Ji
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DRL A6
The Euler characteristic, as an alternating count of the number of cells, satisfies a finite additivity condition on nice spaces. This suggests that the Euler characteristic can perhaps be viewed as a finitely additive signed measure! Following this observation, Viro and Schapira independently proposed an integration theory with respect to the Euler characteristic, now known as the Euler calculus. In this talk, I will introduce the setting of o-minimal structures (which can be thought of as "measurable sets" for Euler integrations) and the theory of Euler calculus on them. I will then discuss some interesting properties and applications of Euler calculus. If time permits, I will also discuss an extension of this theory to Lefschetz numbers from the Lefschetz trace formula. The theories presented here have promising applications in the applied sciences, although we probably will not discuss that.
The Mathematics of Gerrymandering
Jacob Monzel
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DRL A6
We’ll look at how math can be used to detect and even prevent unfair districting in elections. I’ll introduce the basic ideas behind measuring “compactness” of districts, how randomness and geometry come into play, and what makes drawing fair maps such a surprisingly difficult mathematical problem.
Building Your Achievement Set
James Opre
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DRL A6
We will be discussing Achievement Sets which are the set containing every subsum of a given series. We will see my method for building achievement sets and explore a handful of examples to see what different types of sets can be built.
The extension theorem and aperiodic tilings of the plane
Luis Modes Castillo
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DRL A6
In this talk, we will prove the following intuitive result: If we can tile arbitrarily large disks of the plane with finitely many bounded tiles, then we can tile the whole plane. We will explore what happens if we remove some hypotheses, and we will discuss its relation with aperiodic tilings of the plane (where the number of tiles needed can range from 20426 to 1).
Can you put this graph on a torus? Maybe!
Maxine Calle
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DRL A6
In this talk, we will explore how to embed graphs in surfaces, focusing on the connection between graph topology and surface genus. My favorite invariant from algebraic topology will appear (spoiler: it's the Euler characteristic) and we will draw some fun pictures.
Funny Consequences of the Axiom of Choice
Carmine Ingram
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DRL A6
Many of us are familiar with the Banach-Tarski paradox, but do you know of nonlinear solutions to the equation f(x+y)=f(x)+f(y), or of tricks where it seems as though we can infer an uncountably infinite amount of things from only a countably infinite amount of information? We will discuss some silly tricks you can do with the axiom of choice, and, time permitting, some of its alternatives, and the silly things you can do with them.
The sequence 1, 11, 21, 1211, ... (its name is a spoiler!)
Riley Shahar
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DRL A6
This talk is about a very playful sequence, originally studied by John Conway, whose first terms are displayed in the title. We'll define the sequence, prove some of its basic properties, and then discuss Conway's "cosmological theorem," which determines the limiting behavior of the sequence. A surprising role is played by a particular endomorphism of the free monoid on 92 generators.
