Mathematics Department

Student Colloquia

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.
Feb 27Exploring Data Quality and Times Series Event Detection in 2016 U.S. Presidential Election Polls
Kaelyn Rosenberg
Public opinion regarding political polling has declined after the last presidential election. In this talk, I will explore 2016 U.S. presidential election polls from 196 pollsters from November 2015 through November 2016.  Literature supports that social desirability bias is significant in interview type modes rather than in self-administered modes, and there is evidence to suggest that the data quality, particularly the  mode of survey administration (web or telephone), may have influenced polling results. After examining initial exploratory data analysis involving survey mode effect and time series event detection, I will discuss the challenges that have arisen with modeling this type of data.
Mar 6A Conversation on Inclusivity
The intention for this week's student colloquium is to have a discussion about the state of diversity and inclusivity within the mathematics community at large and at Reed. We would like to stress that this meeting is open for all students of the Reed mathematics department to attend.
Our plan for the meeting is as follows:
The first half will be about “inclusivity in the mathematics community at large,” and will be led by Skye Binegar and Aja Procita. They will discuss articles relating the experiences of members of underrepresented groups in mathematics. They will pinpoint some of the societal issues at play affecting the experiences of members of underrepresented groups in mathematics. Since this is supposed to be more of an “educational” section, do note that faculty may be present for this half.
The second half will be for “inclusivity in Reed mathematics,” where the floor will be opened for students to discuss their experiences. Here, we want to ask about “what works” and “what doesn’t” regarding inclusivity in Reed mathematics. We welcome all input, and we stress that faculty will not be present during this section of the meeting. Skye will be compiling a document for students who wish for their experiences to be anonymously related to the faculty.
Since this is a sensitive topic, we will discuss some ground rules about engagement during the meeting, but we do so in the hopes of having people feel safe to speak. We cannot stress enough that this meeting is intended to improve the health of the Reed math community (and in the big picture, the larger math community), so we highly encourage students of all backgrounds to attend.
Apr 3What is Biostatistics?
Miriam Elman and Meike Niederhausen, OHSU-PSU School of Public Health
When you read a New York Times article about a new drug or special diet that reduces risk of heart disease, a newly discovered gene that increases risk for diabetes, or the discovery that children not vaccinated for a certain disease may cause an outbreak, it is not just biologists doing the work. These breakthroughs come from collaborations, where biostatisticians often play a key role in designing studies, analyzing and visualizing data, and interpreting the results.
Statistics offers interesting and exciting work in diverse areas along with many opportunities to make a positive difference; it is also a rapidly expanding field with jobs projected to grow much faster than the average: 34% between 2016 and 2026, according to U.S. Bureau of Labor Statistics. Statistical analysis and data mining was listed as #2 in the “Top Skills Companies Need Most in 2018” by LinkedIn, #2 best STEM and #1 Business jobs in 2018 by US News, and Fortune magazine ranked statistics among the top graduate degrees based on salary, growth, and job satisfaction.
At this colloquium, OHSU Biostatisticians will give an overview of the field of biostatistics and talk about the research they do and how they use their analytical skills to collaborate with many types of scientists and clinicians on exciting and meaningful research problems and clinical studies. They will also discuss the Biostatistics graduate programs at OHSU.
Apr 10 Elliptic Functions, Curves, and Modular Forms
Young Jin Kim
Elliptic functions are of interest to many branches of mathematics. They have many fascinating properties, have deep connections with combinatorics and number theory, and even have a practical use in evaluating integrals and providing explicit solutions to certain differential equations. In this talk, I will introduce the concept of elliptic functions and explore some of their properties. This will give rise to a discussion about elliptic curves and their structure. Through this, I aim to motivate an elementary introduction to the theory of modular forms.

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