**The Graduate Colloquium**

Department of Mathematics

University of South Carolina

*Spring 2016 Lectures and Events*

Time |
Place |
Speaker |
Title |

February 2 4:30pm |
LC 412 | Robert Vandermolen |
The Beauty of Breaking The Rules |

February 16 4:30pm |
LC 412 | Alicia Lamarche |
Generating composite sequences |

March 8 |
Spring Break |
||

April 5 4:30pm |
LC 412 | Frank Thorne, Adela Vraciu |
An Invitation to Upcoming Graduate Courses |

April 7 4:30pm |
LC 412 | Michael Filaseta, George McNulty |
An Invitation to Upcoming Graduate Courses |

April 12 4:30pm |
LC 412 | Josiah Reiswig |
Arrow’s Impossibility Theorem and the Theory of Social Choice |

April 21 4:30pm |
LC 412 | Matthew Ballard |
Categories, strings, and things |

April 26 4:30pm |
LC 412 | Various graduate students |
Everything you always wanted to know about exams (but were afraid to ask) |

Abstracts

** Robert Vandermolen ** - In this talk we will explore systems of differential operators which obey the Leibniz rule and compare them to systems of discrete differential operators which satisfy a generalized q-deformed Leibniz rule, and under a special condition build a universal imbedding from one to the other.

** Alicia Lamarche ** - In 1849, Alphonse de Polignac conjectured that every odd positive integer larger than 3 can be written in the form $2^n + p$ for some integer $n\geq 1$ and prime $p$. This is easily seen to be false; the smallest counterexample is 127, as Polignac himself discovered soon after making the conjecture. Much later, in 1950, Paul Erdos provided infinitely many counterexamples to this conjecture. In this talk, we will examine Erdos' proof and use it to construct composite sequences of various forms.

** Upcoming Graduate Classes ** - Frank, Michael, George, and Adela will give meet-and-greet talks for what to expect in their courses coming up in the fall. Everyone is welcome.

**Josiah Reiswig** - In a society, it is (generally) desired that the actions of the society as a whole act as a function of the aggregated preferences of the individual members of the society. Additionally, it is (generally) desired that this function adhere to notions of “fairness” and “equality.” In his seminal 1950 paper “A Difficulty in the Concept of Social Welfare,” economist Kenneth Arrow provided a mathematical proof that a modest set of axioms enforcing fairness and equality upon the function were mutually exclusive. This result led to the development of Social Choice Theory. Time permitting, we will examine the mathematics of Arrow’s proof as well as extensions of the theorem.

**Matthew Ballard** - I'll talk a bit about the physics behind mirror symmetry and how it leads naturally to considering categories of boundary conditions, or branes.

** Everything you always wanted to know about exams (but were afraid to ask) ** - Graduate students in the 2nd, 3rd and 4th year will talk about their experiences with qualifying and comprehensive exams and answer questions.

For more information about The Graduate Colloquium, contact ballard@math.sc.edu.