Mathematics Department

Student Colloquia

Upcoming Seminar

February 13, 4:40 PM in Physics 123
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.

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 18The 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!
Sept 26An Elliptic Curve Analogue to the Ferment Numbers
Skye Binegar

The Fermat numbers have many notable properties, including order universality, coprimality, and definition by a recurrence relation. We use arbitrary elliptic curves and rational points of infinite order to generate sequences that are analogous to the Fermat numbers. We demonstrate that these sequences have properties similar to those of the Fermat numbers, and we discuss results about the prime factors of sequences generated by specific curves and points.

 

This talk covers results from the 2017 Wake Forest/Davidson number theory REU. A preprint is available on arXiv: https://arxiv.org/abs/1708.03804

Oct 2How 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 OrmsbyKelly Shaw, and Heather Kitada will provide some resources and answer questions about the opportunities available. We will discuss topics such as Research Experience for Undergraduates (REUs), industry internships, Reed faculty projects, camps, and independent studies. Additionally, there will be students with previous summer experiences to talk about how they got there and what it was like.
Oct 9Dependence Analysis and Automatic Optimization
Ben 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 7Langston 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 5Bidirectional Type Theory
Kyle 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 13Pretty 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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