Talks (unless otherwise indicated) are in Davis 301 from 4–5 PM on Mondays. Refreshments begin at 3:30 on the second floor of Davis.

To make sure you get email updates, add yourself to the mathstu (if a student) or mathothers (if not) email groups. Or check the Colby Math&Stats facebook page.

You can see next semester’s schedule.

September 9
Leo Livshits
Colby College
What is Measure Theory?

Title

Abstract

In December of 1943, few months after being invited to join the Manhattan Project at Los Alamos, Polish American mathematician Stanslaw Ulam published a short article in the American Mathematical Monthly entitled “What is Measure?” There he offered a very a brief account of the developments of a relatively new field of measure theory with some emphasis on the contributions that he had made to it. The article began thus:

The concept of measure includes the notions generalizing the old ideas of length, area, and volume of figures; all of which are among the oldest in mathematics and, in fact, as basic as the idea of number itself.

As I am offering a course on measure theory this semester, I figured that this may be a good time to give a broader student audience a gentle colloquial overview of the origins and the motivations behind the concept of measure, an area that has since become integral to mathematical analysis.

I am borrowing the title from Ulam’s article, because my original more appropriate title attempts of “Why is Measure?” and “How is Measure?” ran into problems with English grammar.

This particular colloquium is aimed at the students, and while the professionals and alike are always welcome to attend, please be warned that the talk will not offer any cutting edge material, and is not designed to impress. On the other hand, I promise the students a number of “wow” moments to illustrate a counterintuitive wonder of the intellectual world that we have created for ourselves.

 

September 16
Jan Holly
Colby College
The Unsolved Problem of Two Circles and a Square

Title

Abstract

In the early 1800s, mathematician Yamaguchi Kanzan traveled through Japan recording mathematical problems.  The focus was on sangaku, which were tablets containing mathematics that were displayed in Buddhist temples and Shinto shrines.  These tablets contained problems, and sometimes solutions, that ranged from simple to very difficult.  Yamaguchi’s travel diaries lay mostly unnoticed until the 1980s, when large portions were translated into English, resulting in books and a Scientific American article about these “Japanese Temple” problems.  Two of the problems presented were so difficult that they remained unsolved, despite being quite easy to state.  One of the problems was solved in 2018.  This talk is about the other unsolved problem, and the work of David Krumm and myself on that problem.  This year, we completed a proof that this remaining unsolved problem cannot be solved.  In other words, there is no closed-form solution.  The proof uses techniques ranging from basic geometry through calculus and advanced algebra, and is completed using computational tools in Galois theory that have only recently become available.  The talk will be accessible to all students, with a particular focus on geometry plus a little bit of calculus, and then will touch upon the more advanced algebra underlying the completion of the proof.

 

September 23
Fernando Gouvêa
Colby College
What is Number Theory?

Title

Abstract

The name of a part of mathematics seldom tells outsiders much about the actual nature of that subject. “Number Theory” seems particularly obscure, perhaps because most people associate all of mathematics with numbers. Even to insiders, it can be hard to explain why certain questions fit into “Number Theory” rather than into other parts of mathematics.

Rather than try to define Number Theory, this talk seeks to consider a range of examples. We will start with a very old problem about whole numbers and demonstrate several different ways to solve it. Each solution will suggest new questions, some of which will turn out to be very difficult. We may even run into some problems that remained unsolved.

This talk is aimed at students. High school algebra is enough to understand most of it.

 

 

September 30
Eisso Atzema
University of Maine Orono
Ferdinand Engel (1805–1866) and his Models of the Fresnel Wave Surface

Title

Abstract

The end of the 19th century was the golden age of the production of mathematical models and of their use for educational purposes. The interest in mathematical models as a visualization aid, however, goes at least as far back as the first half of the 19th century. In this talk, I will discuss the early history of the visualization of mathematical surfaces and the manufacturing of physical models for such surfaces, culminating in a discussion of the work of Christian Gottlieb Ferdinand Engel (Magdeburg,1805–New York, 1866). In particular, I will discuss his prize-winning plaster models of the Fresnel Wave Surface still on display at the University of Mississippi. Along the way, I will talk about his work under Gustav Magnus at the University of Berlin and under Alexander Bache at the Coastal Survey in Washington DC.

 

October 7 – Olin 1
Momin Malik
Berkman Klein Center for Internet & Society at Harvard University
Statistics and Machine Learning: Foundations, Limitations, and Ethics

Title

Abstract

When should we use statistics? When should we use machine learning? When should we not use either one? The basic philosophical assumptions of statistics and machine learning can be hard to see amidst practice, but they are key for seeing their limitations, appropriate uses, and ethical implications. This talks gives a broad overview of the nature of statements in statistics and machine learning, covering historical roots (about the central tendency, use of probability, and the “reduction of data”), sociological critique (around forcing the world into mold of data matrices, and modeling being connected to the exercise of power), and limitations according to statistical theory itself (such as in the bias-variance tradeoff suggesting that a “false” model can predict better than a “true” one). Understanding these limitations, we can more responsibly decide how, and indeed if, to use statistical tools, and which tools to use.

 

October 14
Mahlet Tadesse
Georgetown University
Title

 

October 28
Tamar Friedmann, Michael Dougherty, Nicholas Owad
Colby College
Meet our new Mathematics faculty!

Title

Abstract

We are fortunate to have several new faculty in our department. Come meet them and find out something about their research and teaching.

 

November 4
Álvaro Lozano Robledo
University of Connecticut
What is an Elliptic Curve?

Title

Abstract

In this talk we will define what is an elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were prominently featured in Wiles’ proof of Fermat’s last theorem, but there are many other problems that lead to a question about elliptic curves. We will discuss some of the open problems related to elliptic curves, and a number of conjectures, some of which are quite controversial!

 

November 12 (Tuesday) 3:30 PM
Mathematics and Statistics Candidate
Feature-specific inference for penalized regression models using local false discovery rates

Title

Abstract

Regression modeling is a powerful statistical tool with well-studied inferential methods available for common models including least squares linear regression, logistic regression, Cox proportional hazards regression, and others.  However, these classical models break down when the number of explanatory variables exceeds the sample size. Penalized regression models provide an attractive approach to analyzing high-dimensional data, but their inferential tools are less well-developed than their un-penalized counterparts.  Many popular penalization approaches, most notably the LASSO, naturally perform variable selection, prompting the question “how confident can we be in these selections?” as starting point for inference.  In this talk we seek to answer that question, beginning with an introduction to LASSO regression and progressing to use the optimization conditions that characterize the LASSO solution to develop feature-specific local false discovery rate estimates for each explanatory variable under consideration.  We demonstrate the validity of this approach and compare it with several other inferential methods currently available for the analysis of high-dimensional data.

 

November 14 (Thursday) 4:00 PM
Mathematics and Statistics Candidate
Exploring and Evaluating Patterns in Data Through Model-Based Clustering and Partition Agreement

Title

Abstract

Clustering is a method of unsupervised machine learning that seeks to uncover group structure in data by classifying observations when little or no a priori information about groups is available. In this talk, I will introduce the audience to statistical clustering with a special focus on model-based clustering and model assessment via partition agreement.

 

November 19 (Tuesday) 3:30 PM
Mathematics and Statistics Candidate
Title

 

November 21(Thursday) 4:00 PM
Mathematics and Statistics Candidate
A Novel Agreement Statistic using Data on Uncertainty in Ratings

Title

Abstract

The first step in identifying biopsy-based markers of kidney disease progression is to assess agreement among pathologists’ marker ratings. Unfortunately, existing agreement statistics make assumptions about chance agreement that are often implausible in kidney pathology. We propose a novel agreement statistic that accounts for the empirical probability of chance agreement, estimated by collecting additional data on rater uncertainty for each rating. We also derive a standard error estimator for our proposed agreement statistic. Simulations studies show our proposed statistic has less bias than existing statistics for estimating the probability of agreement after removing chance agreement. Finally, we apply our proposed statistic to a real data example to estimate pathologist agreement in rating kidney biopsy markers.

 

December 2 – Olin 1
Isabel Fulcher
Harvard Medical School
Improving the delivery of healthcare to pregnant women in sub-Saharan Africa with statistics and data science

Title

Abstract

Nearly 250 million women of childbearing age live in sub-Saharan Africa and face significant obstacles in receiving vital health care. Despite significant improvements over the past two decades, pregnant women in this region still lack access to quality care during pregnancy, including skilled birth attendants during childbirth. Specifically, an estimated 1 in 38 women die of a pregnancy-related complication, a rate 50 times higher than the United States. Almost all of these deaths are preventable. In response to these alarming rates, a wide variety of health interventions have been implemented in many regions of sub-Saharan Africa. However, the efficacy of these interventions has often been left unquantified, leaving many pressing questions, including: Does a particular intervention improve health outcomes among pregnant women? Are there certain populations of women not benefitting from the intervention? How can we fine-tune the intervention to accelerate improvements? Statistics and data science approaches, specifically the application of causal inference and machine learning methods, are needed to provide answers to these open questions. As anecdotes of unique challenges that arise in such contexts, I will discuss my ongoing work with two very different interventions – a large-scale digital maternal health program in Zanzibar and the introduction of ultrasound machines at rural health clinics in Rwanda. The goal of this talk is to elucidate some of the exciting ways that applied statistics can be used to inform medical and policy decisions in global health contexts.