Abstract: Is your view of mathematics an endless cycle of Lemma → Proof → Theorem → Repeat? Does the world of math ever feel like a story with no characters? Prepare to change your mind! In this talk, we will reveal some of the dramatic and chaotic stories behind math - focusing more on the mathematicians and less on the math itself - through a fun quiz. We will journey through documented history, famous folklore, and some stories that are simply too good to be true.
Abstract: Did you know that except for 6, all numbers are prime powers? What about that at least half of all numbers are Fibonacci numbers? I checked for all numbers less than 10 and it's true, and if it holds for so many cases it must be true! In this talk we will explore many other wonderful "theorems" and the numbers that disproved them.
Abstract: Many familiar theorems in topology, algebra and analysis are traditionally proved using the axiom of choice. However, surprisingly often, these theorems admit a stronger version: alternative proofs exist with no appeal to choice. In this talk, I will sketch various common, unnecessarily choicey proofs, and present a choice-free alternative.
Title: How Far Can You See In An Orchard, or, What Is It Like To Live In Various Topological Spaces?
Abstract:
Imagine...an orchard. Trees everywhere, except for the spot you're standing. Specifically, you're standing at the origin, and there's a tree at every integer lattice point. How far can you see, if you choose the correct direction? We'll also consider what it feels like to live in various manifolds (with or without boundary), and how validly deck transforming the universal cover determines what you can see.
Abstract: In this talk the speaker will employ rhetorical devices and sometimes math to explain how everything* is just a collection of disks glued together in funky ways
Abstract: I will present the classic packing problems in a probabilistic context and discuss how sophisticated global structures emerge from simple geometric exclusion and evolve with increasing packing density, along with some proof ideas.
Abstract: We will play Jeopardy on Friday. It will be awesome. There will be math questions. There will be non-math questions (actually not really - maybe one or two). It will be really awesome. Really. Awesome.
Abstract: In the spirit of Halloween, let's go trick-or-treating in the Platonic realm and meet some of the spooky inhabitants of the mathematical universe.
Abstract: Any introductory graph theory course worth its salt will include at least one graph theory game, so naturally a pizza seminar talk ought to have three! We will play some games, prove a couple of interesting results, and learn a little bit of graph theory while we’re at it. This will be an interactive talk, so please bring paper and a writing implement and prepare to draw some graphs.
Abstract: My original plan was to talk about some large numbers, but then Riley did that, so I had to change my talk. On that note, I will be talking about some moderate numbers and how they naturally appear in the proof of van der Waerden's theorem: for any c,k there is n such that any c-coloring of [n] contains a monochromatic arithmetic progression of length k.
Title: About the Classification of finite simple groups.
Abstract: As we know, finite simple groups are classified. It is fair to say that Rutgers played a key role in the proof of this result. In this Pizza Seminar, I would like to talk about the history of the classification theorem and some curiosities around it. In particular, my goal is to transmit my admiration of the main characters of this proof. Time permitting, I will provide a full proof starting from scratch (abstracts for this seminar are supposed to be funny).
Abstract: Think of the best pizza seminars you could possibly imagine. Proving the Riemann hypothesis has to be pretty darn near the top of that list. I was hoping to present a proof but it probably won’t be until the five-minute talks that I’m able to figure out all the details. Instead, I’ll talk about a different kind of RH, the Riemann hypothesis for varieties over finite fields.
Title: How To Think About the Continuum Hypothesis, As Explained by a Non-Logician
Abstract: Continuing the theme of "pizza talks about named mathematical hypotheses", let's talk about the Continuum Hypothesis! Its independence from ZFC is a well-known fact, but a lot of people don't understand what that actually means. In this pizza talk I will dispel much of the mysticism around the independence of CH by looking deeper into the statement of CH itself as well as the mathematical notion of independence. Also, if any of you are interested in hearing about nonstandard analysis, I'll be doing some of that too! Surely it won't tie together in the end.
Title: Shor's Algorithm and the Hidden Subgroup Problem
Abstract: Have you ever wanted to be able to factor efficiently on a quantum computer? After this talk, you will!* I will present Shor’s famous efficient quantum algorithms for factoring and discrete log, and briefly discuss the cryptographic schemes threated by these efficient algorithms. I will talk about the generalization to the hidden subgroup problem for arbitrary groups, and (time permitting) applications of solving this problem for the symmetric and dihedral groups. Somewhat lesser known than his quantum computation results are Peter Shor’s poems. If you are a quantum skeptic, at least come for the limericks!
*Note: quantum computer not included.
Abstract: In Flatland, you can be anything you want to be (within reason) just by cutting corners, but not in the real world. I'll demonstrate this surprising truth while posing some solvable and unsolvable puzzles for you to try.
Abstract: We're going to play some games on a triangle, and then we're going to look at equilibria in games. Bring your board games for afterwards and get ready to game!
Abstract: Get ready for a hat trick of hat puzzles! In this interactive talk I'll present a few hat puzzles along with their solutions. I'll highlight some connections with measure theory, equivalence relations, and the axiom of choice. If there's time, I'll also present a puzzle about numbers in boxes!
Abstract: Last time we played Jeopardy!, it was awesome. Some people were saying it was the most awesome thing. So we will play it again. But this time, it will not be awesome. It will be LEGENDARY. And probably pretty awesome too.
Title: The Law of Excluded Middle is dead, and we have killed it.
Abstract: I am sorry to inform you all that by the end of this talk, you will no longer trust what you likely believe to be true: the law of excluded middle. Based off of an article by Andrej Bauer, I will lead you through the 5 stages of accepting constructive mathematics. After healing from the loss of LEM, we may rejoice in what new frontiers of math there are to explore!
Title: Elliptic curves are really cool (and the Weil conjectures I guess)
Abstract: We'll be talking about elliptic curves, their group structure over arbitrary fields first and eventually over finite fields. The goal is to convince you that the Weil conjectures in this setting are actually not too difficult to prove. No heavy algebraic geometry background needed!
Abstract: Here is a simple exercise. Consider a circle with diameter AB. Suppose P is a point on AB, and l is a line through P that is different from AB and intersects the circle in C, D. Show that tan∠CBA ⋅ tan∠DBA does not depend on l.
I will present two proofs of this, one algebraic and one geometric. I will then explain:
(1) Why they technically prove two different things.
(2) Why they essentially prove the same thing, thanks to work of Euclid, Hilbert and Gödel, showing a harmony between algebra and geometry. One of the keywords here is Gödel's completeness theorem (not the incompleteness theorem)
Abstract: They say a magician never reveals their secrets, but as mathematicians, we demand proof. Surprisingly, the intersection of math and magic is not empty, with many tricks having a rich mathematical structure in the background. Conversely, many mathematical tricks and methods feel like magic. In this talk, be ready to learn plenty of secrets, as well as some applications of prime numbers and elliptic curves. It's a show to die for.
Abstract: Sooner or later it comes for us all: empl*yment. Finding a j*b is hard, and the goal of this talk is to make it a little less hard for everyone to find a j*b. Come with any and all questions you have for this panel about finding a j*b in academia post graduation.
5-Minute Talks
Riley Guyett: untitled (Mario the Myth vs Mario the Man)
Timothy Bates: untitled (Uniqueness Methods in Pure Axiomatic Topology)
