Mathematics Department - Graduate Pizza Seminar - Spring 2017

# Graduate Pizza Seminar - Spring 2017

### Organizer(s)

Emily Kukura, Justin Semonsen

### Website

http://www.math.rutgers.edu/~js2118/pizza/index.html

Time: 1:40 PM

## Friday, April 21st

### "What the heck is Floer cohomology?"

Time: 1:40 PM
Location: Hill 705
Abstract: Since so many people have asked me about this, I've decided to give a basic talk. The prerequisite, "What the heck is Morse cohomology?" will also be covered in my talk: Suppose you have a manifold, but you would like to know more about its topology. A natural thing that you might do is pour chocolate sauce on it, and see where the sauce forms pools and saddle points. Great! Floer cohomology is similar to this, but now you suppose that the chocolate is delicious hot fudge, and can form bubbles in the ambient manifold. These bubbles form an obstruction to displacement by "area preserving diffeomorphism" (or if you like, displacement from your couch after your ice-cream sundae).

## Friday, April 14th

### "Busy Beavers"

Time: 1:40 PM
Abstract: A Turing Machine is an idealized model of a computer program consisting of read/write memory and a finite-state control. A given Turing Machine may or may not halt (stop running) on a given input. This leads to the following question: Which n-state Turing Machines that halt use the most memory, and how much memory do they use? This problem known as the Busy Beaver Problem, turns out to be undecidable, and the corresponding function of n (the Busy Beaver Function) is not computable. In this talk, we will prove the noncomputability of the Busy Beaver Function, and then, in spite of this, we will attempt to compute some of its values.

Time: 1:40 PM

## Friday, March 31st

### "April Fool's!"

Time: 1:40 PM
Abstract: It is widely believed that different numbers typically have different values but not only will I prove that many numbers are the same, but also that all triangles are equilateral, horses are all the same color, and you can color a map with at most 4 colors. I also hope to provide many conjectures that are almost assuredly true based on huge amounts of empirical evidence. Audience participation will be appealed for!

## Friday, March 24th

### " The first big test of Einstein's General Relativity"

Time: 1:40 PM
Abstract: Any introductory book on Relativity Theory will tell you of a couple of real-life situations that cannot be explained by Newtonian physics alone, but rather require Einstein's theory. Two very common examples are the precession of Mercury and the functioning of GPS. In this talk I'd like to give an elementary introduction to General Relativity and then apply it to show how GPS works. Unfortunately it turns out GPS really is a complicated thing, so instead I'll show you how GR correctly predicts the orbit of Mercury. Einstein himself considered this as one of the three most important tests of the validity of his theory, so we'd better not fail it. And even though all this may sound like a physics talk, don't worry, it's also math. There's even differential geometry and stuff. (No prerequisite required).

## Friday, March 3rd

### " On the Logic of Time Travel: Paradoxes, Banana Peels, Cheshire Cats, and (maybe) Einstein"

Time: 1:40 PM
Abstract: We've all seen popular time travel stories on screen, from Back to the Future, to Harry Potter to Star Trek, and so on. While some popular depictions may do a decent job, from a logical perspective many more are fraught with problems, often because they rely on some version of the premise that changing the past is possible. But just because we can't change the past doesn't mean that we can't travel to it, have an impact on it, and maybe even have a nice chat with our younger selves. In this talk we'll take a trip with Tim the Time Traveler to explore whether or not we can do better than Hollywood. Along the way we will likely encounter many banana-peels, disappearing cats, and other oddities, and to see where we end up you'll just have to hop along for the ride. Time (no pun intended) permitting, we may even talk about more math-y things like relativity, and how they could potentially accommodate some apparent paradoxes we may encounter on our trip.

## Friday, February 24th

### " Origametry"

Time: 1:40 PM
Abstract: The art of paper-folding extends far beyond paper cranes; indeed, working with "infinite" paper allows us to analyze crease patterns as line configurations and gives us tools to tackle classical geometric constructions. We will work out some of these constructions and find out if origami is more powerful than our old friends, the straightedge and compass (spoiler: it is). For those who want to get their hands dirty, finite paper will be provided.

## Friday, February 17th

### "Why you should never get your bird drunk, and other random facts"

Time: 2:40 PM
Abstract: No, we aren't actually going to be getting people or animals drunk, but we are going to be talking about Random Walks and Brownian Motion. We'll start with random walks on the integers, talk about some properties, and use that to motivate the definition of Brownian Motion on the real numbers. And don't worry, this will all come back to PDEs eventually.

Time: 1:40 PM

## Friday, February 10th

### "This Computer Does and Does Not Work: Using Quantum Mechanics in Computing Systems"

Time: 1:40 PM
Abstract: While the mathematics behind quantum mechanics has been known for close to a century, it is only within the last 35 years that researchers have started asking its phenomena could be used in efficient computation of difficult problems. In this talk, I will go over some of the known algorithms that use quantum mechanics to solve otherwise time-consuming problems quickly, as well as some of the historical background behind them. Viewers can expect to leave with a full understanding of quantum computation - provided that they adjust their use of the term "understand."

Time: 1:40 PM