Welcome
The Joint UNC and Duke Student Math Colloquium meets on Tuesdays, 4:305:30 pm, and is preceded by a special tea at 4 pm. To receive announcements about this program, send an email with no message and no subject to subscribestudentmathcolloq@listserv.unc.edu. This program is supported by an award from the KenanBiddle Partnership, which is funded by the William R. Kenan Charitable Trust and The Mary Duke Biddle Foundation.
Student organizers: Humberto Diaz (Duke), Katrina Morgan (UNC), Dylan Muckerman (UNC).
Faculty advisors: Linda Green (UNC), Heekyoung Hahn (Duke).
Date  Speaker  Title 

March 17, 2015 at UNC, Phillips Hall 332  Jared Wunsch (Northwestern University)  Trace formulae on smooth and singular manifolds 
April 7, 2015 at UNC, Phillips Hall 332  Farshid Hajir (University of Massachusetts, Amherst)  200 Years of Classifying Integer Solutions of d=b²4ac 
April 14, 2015 at Duke University, Gross Hall 103  John Voight (Dartmouth College)  Triangles, permutations, and (covers of) surfaces 
October 21, 2015 at Duke, Physics 119  Jeremy Rouse (Wake Forest University)  Positivedefinite quadratic forms representing all odd numbers 
Jared Wunsch
Trace formulae on smooth and singular manifolds 
Farshid Hajir
200 Years of Classifying Integer Solutions of d=b²4ac This survey talk for undergraduates is about an undergraduate student named Carl who collected together some of the mathematical thoughts of his teenage years and published them as a book when he turned 23. The book went viral, but nearly everyone who got a copy couldn’t really make head or tails of it, even though they could tell it was cool and important. One of Carl’s sharpest disciples, Pete, slept with a copy of the book under his pillow and wrote many articles over his lifetime trying to explain to himself and others what Carl was talking about. Even today, whether they know it or not, undergraduate math majors who take number theory or abstract algebra in college are indirectly studying Carl’s teenage musings. Despite thousands of papers and books written on the subject since then, verifying, amplifying, and contextualizing Carl’s ideas, including some recent work that garnered a 2014 Fields Medal, some of Carl’s most basic conjectures are still wide open. My goal for this talk is to explain enough about the classification of primitive integral binary quadratic forms of a given discriminant so that students will: (1) learn about the historical roots of some of their current curriculum and connect it with the current research of some of Carl’s disciples at UNC and Duke, (2) learn about an as yet unsolved problem in number theory, and (3) make a beeline for the library (or their laptops?) in search of a book that, in the view of some, is one of the greatest ever written. 
John Voight
Triangles, permutations, and (covers of) surfaces There is a marvelous and deep connection between: 
Jeremy Rouse
Positivedefinite quadratic forms representing all odd numbers. Given a positivedefinite quadratic form Q with integers coefficients it turns out
that Q represents every odd integer if and only if Q represents the numbers from 1 up to 451.
Rather than discussing the proof of this result, I will explain my mathematical journey in understanding the problem (including a lot of wrong turns), and a bit about how it has shaped my future as a mathematician. This talk will be accessible to mathematicians at all levels.
