## Student Colloquia

#### Upcoming Seminar

February 13,
4:40 PM
in
Physics 123*Pretty Curve Pictures and Why They Matter *

Alex Striff

Most Tuesday afternoons during the academic year, the Mathematics students host a math talk. The talks are directed to our mathematics majors but are usually accessible on a variety of levels. Refreshments are served before the talks.

Please email Skye Binegar and Langston Barrett, if interested in signing up for a talk.

### 2017-18 Schedule

#### Fall

**4:40** in **Physics 123** (unless marked otherwise).

Sept 18 | The Controllability of Functional Classes in the Genetic Regulatory Network of E. coli Ananthan Nambiar Ananthan Nambiar will discuss control theory, its computations, and its application in studying dynamical systems in biology! |
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Sept 26 | An Elliptic Curve Analogue to the Ferment NumbersSkye Binegar The
This talk covers results from the 2017 Wake Forest/Davidson number theory REU. A preprint is available on arXiv: https://arxiv.org/abs/ |

Oct 2 | How does a math/cs/stats major find ways to spend their summers while staying engaged with their discipline? Kyle Ormsby, Kelly Shaw, and Heather Kitada Professors Kyle Ormsby, Kelly Shaw, and Heather Kitada will |

Oct 9 | Dependence Analysis and Automatic OptimizationBen Black Most code is written as sequential instructions. But somehow, compilers and hardware have managed to exploit significant parallelism in this sequential code. However, these are some of the most complex systems imaginable, and so reasoning about them directly is hard. Luckily, there are powerful models we can use to reason about the optimal system, and we can often use these to understand the real-world systems much more easily. And there are effective tools we can use to understand their behavior more precisely. I will use dependency graphs as a model and use it to give a brief introduction to instruction level parallelism from the hardware level and the compiler level. I will also show how to perform measurements to inspect how well the real-world hardware and software is achieving its goals relative to the optimal model. |

Nov 7 | Langston Barrett Type theory is simultaneously a programming language and an alternative to set theory as a foundation for mathematics. In this talk, we'll explore how one formal system can take on such seemingly disparate tasks. First, we'll try to understand the origins of formal systems, what they consist of, and how we can reason about them. We'll take a tour of intuitionistic propositional logic and the typed λ-calculus, discuss their similarity, and explore the consequences for mathematics and computer science. |

Dec 5 | Bidirectional Type TheoryKyle McKean Type theory is a method of axiomatizing mathematics. Unlike set theory, type theory is uniquely suited for interactions with computers allowing for mechanized reasoning of mathematical proofs. It also forms the theoretical foundation of any statically typed programming language. In this talk, we'll cover bidirectional type theory, a simpler and more effective approach to specify type theories meant for computer implementation. Specifically focusing on the typing judgements that axiomatize the theory. If time permits, we will construct the natural numbers using a type of well founded trees. |

#### Spring

**4:40** in **Physics 123** (unless marked otherwise).

Feb 13 | Pretty Curve Pictures and Why They Matter Alex Striff How do we obtain smooth curves, given only partial data on the curve? Often applications or the intractability of problems force us to look at discrete data and attempt to form a continuous picture from partial information. A variety of numerical methods will be investigated, with a focus on splines, which provide a means for "optimally" connecting the dots. Several demonstrations of these methods in use will be presented. Beyond the realm of applications, the constructions and generalizations these techniques offer deep insights into the nature of functions and what it means to be smooth. |
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