# AMS Student Chapter Seminar

The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.

**When:**Wednesdays, 3:00 PM – 3:30 PM**Where:**Van Vleck, 9th floor lounge**Organizers:**Laura Cladek, Ryan Julian, Xianghong Chen, Daniel Hast

Everyone is welcome to give a talk. To sign up, please contact the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.

## Spring 2015

### January 28, Moisés Herradón

Title: Winning games and taking names

Abstract: So let’s say we’re already amazing at playing one game (any game!) at a time and we now we need to play several games at once, to keep it challenging. We will see that doing this results in us being able to define an addition on the collection of all games, and that it actually turns this collection into a Group. I will talk about some of the wonders that lie within the group. Maybe lions? Maybe a field containing both the real numbers and the ordinals? For sure it has to be one of these two!

### February 11, Becky Eastham

Title: A generalization of van der Waerden numbers: (a, b) triples and (a_1, a_2, ..., a_n) (n + 1)-tuples

Abstract: Van der Waerden defined w(k; r) to be the least positive integer such that for every r-coloring of the integers from 1 to w(k; r), there is a monochromatic arithmetic progression of length k. He proved that w(k; r) exists for all positive k, r. I will discuss the case where r = 2. These numbers are notoriously hard to calculate: the first 6 of these are 1, 3, 9, 35, 178, and 1132, but no others are known. I will discuss properties of a generalization of these numbers, (a_1, a_2, ..., a_n) (n + 1)-tuples, which are sets of the form {d, a_1x + d, a_2x + 2d, ..., a_nx + nd}, for d, x positive natural numbers.

## Fall 2014

### September 25, Vladimir Sotirov

Title: The compact open topology: what is it really?

Abstract: The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition.

### October 8, David Bruce

Title: Hex on the Beach

Abstract: The game of Hex is a two player game played on a hexagonal grid attributed in part to John Nash. (This is the game he is playing in /A Beautiful Mind./) Despite being relatively easy to pick up, and pretty hard to master, this game has surprising connections to some interesting mathematics. This talk will introduce the game of Hex, and then explore some of these connections. *As it is a lot more fun once you've actually played Hex feel free to join me at 3:00pm on the 9th floor to actually play a few games of Hex!*

### October 22, Eva Elduque

Title: The fold and one cut problem

Abstract: What shapes can we get by folding flat a piece of paper and making (only) one complete straight cut? The answer is surprising: We can cut out any shape drawn with straight line segments. In the talk, we will discuss the two methods of approaching this problem, focusing on the straight skeleton method, the most intuitive of the two.

### November 5, Megan Maguire

Title: Train tracks on surfaces

Abstract: What is a train track, mathematically speaking? Are they interesting? Why are they interesting? Come find out!

### November 19, Adrian Tovar-Lopez

Title: Hodgkin and Huxley equations of a single neuron

### December 3, Zachary Charles

Abstract: An addition chain is a sequence of numbers starting at one, such that every number is the sum of two previous numbers. What is the shortest chain ending at a number n? While this is already difficult, we will talk about how addition chains answer life's difficult questions, including: How do we compute 2^4? What can the Ancient Egyptians teach us about elliptic curve cryptography? What about subtraction?