# 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, 3:30 PM – 4:00 PM**Where:**Van Vleck, 9th floor lounge (unless otherwise announced)**Organizers:**Daniel Hast, Ryan Julian, Cullen McDonald, Zachary Charles

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

The schedule of talks from past semesters can be found here.

## Fall 2016

### October 12, Soumya Sankar

Title: Primes of certain forms and covering systems

Abstract: A lot of classical questions revolve around primes of the form 2^n + k, where k is an odd integer. I will talk about such primes, or the lack thereof, and use this to convert coffee into covering systems. Time permitting, I'll talk about a few cool results and conjectures related to the notion of covering systems.

### October 19, Daniel Hast

Title: A combinatorial lemma in linear algebra

Abstract: I'll talk about a fun little lemma in linear algebra and its combinatorial interpretation. (It might be "well-known" to someone, but I'd never heard of it before.) If there's time, I'll discuss some possible generalizations.

### October 26, Brandon Alberts

Title: An Introduction to Matroids

Abstract: What if you wanted to do linear algebra, but couldn't use addition or scalar multiplication? Can we still have a notion of independence and bases? The answer is yes, and these are called matroids. Not only will I introduce matroids, but I will give an example that shows not all matroids arise from vector spaces.

### November 2, Vlad Matei

Title: Hadamard Matrices

Abstract: A Hadamard matrix is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. The most important open question in the theory of Hadamard matrices is that of existence. The Hadamard conjecture proposes that a Hadamard matrix of order 4k exists for every positive integer k. The Hadamard conjecture has also been attributed to Paley, although it was considered implicitly by others prior to Paley's work.

### November 9, David Bruce

Title: Some Numbers Are Sometimes Bigger Than Others (Sometimes...)

Abstract: I will write down two numbers and show that one of them is larger than the other.

### November 16, Solly Parenti

Title: The Congruent Number Problem

Abstract: To add to the over-romanticization of number theory, I will talk about a simple to state problem about triangles that quickly leads into very difficult open problems in modern number theory.

### November 30, Iván Ongay Valverde

Title: TBA

Abstract: TBA

### December 7, Will Mitchell

Title: An unsolved isomorphism problem from plane geometry

Abstract: A geometric n-configuration is a collection of points and lines in the Euclidean plane such that each point lies on exactly n lines and each line passes through n points. While the study of 3-configurations dates to the nineteenth century, the first example of a 4-configuration appeared only in 1990. I will say a few things about 4-configurations and state an unsolved problem, and I hope that someone in the audience will decide to work on it. There will be nice pictures and a shout-out to the singular value decomposition.