Title: A Math History Pop Quiz
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.

Title: The Strong Law of Small Numbers
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.

Title: Don't choose if you don't have to
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.

Title: It’s All Disks (and spheres)
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

Title: Structures of random packings
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.

Title: Jeopardy! (but math)
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.

Title: Trick-or-treating in the Platonic realm
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.

Title: Graph Games Galore!
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.

Title: Van der Waerden's theorem
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).

Sammy Thiagarajan and Anupam Nayak: Commutative Algebra 101
Joy Hamlin: 17 17 facts in 17 seconds each
Riley Guyett: Complex Written Qual in 5 minutes
Adam Earnst: Proof of Fermat's Last Theorem
Michalis Lolis: The abc saga
Anupam Nayak: (Conditional) Proof of Fermat's Last Theorem* (using abc conjecture*)
Jakub Niksinski: An important consequence of Fermat's Last Theorem
Austin Lei: Who is Austin?
Anupam Nayak: Proof of abc conjecture*
Danae Rupp and Sammy Thiagarajan: (untitled) Piano Man

Rutgers Graduate Pizza Seminar AY25-26