Mathematics Department

Colloquium

Upcoming Seminar

January 25, 4:40 PM in Eliot 314
Jonathan Campbell, Vanderbilt University

Most Thursday afternoons during the academic year, the Reed College Department of Mathematics hosts 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.

2017-18 Schedule

Fall

4:40-5:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.

Aug 31
Please note change in location.
Meeting with majors
Location: Psychology 105
Sept 7Lattices, finite subsets of the circle, and the trefoil knot
Kyle Ormsby, Reed College
I will explore a remarkable correspondence between
  • lattices in the complex plane (up to homothety),
  • nonempty subsets of the circle with at most three elements, and
  • the complement of the trefoil knot in the 3-sphere.
Along the way, we will encounter modular forms, Voronoi cells, and open book decompositions.  The talk should be accessible to anyone who knows how to multiply complex numbers.
Sept 14How to Win the Lottery
David Roe, Department of Mathematics, University of Pittsburgh
From 2005 through 2012, three groups in Massachusetts earned millions of dollars playing a lottery game called Cash Winfall.  I'll describe how the game worked, explain why it was exploitable, give connections with projective geometry and share stories from my participation in one of the pools.  You'll also learn why almost every other lottery is not worth playing.
Sept 21 A New Approach to Euler Calculus for Continuous Intergrands
Carl McTague, University of Rochester

The Euler characteristic satisfies an inclusion-exclusion principle χ(X∪Y)=χ(X)+χ(Y)-χ(X∩Y), which lets one regard it as a measure – a peculiar one where a point has measure 1 while a circle has measure 0. One can use it to integrate simple functions (in the sense of measure theory), and the resulting integral calculus has deep roots in algebraic geometry and has recently found surprising applications to data analysis. However, since it is only finitely – not countably – additive, it does not fit into the framework of Lebesgue integration, and there are problems integrating even the most elementary non-simple functions. I will describe a new approach to this calculus, based on differential geometry, which makes it possible to integrate a large class of non-simple functions, and which hints at new ways to apply differential geometry to data analysis.

Sept 28
Cancelled
Bicolored Trees, Shabat Polynomials and Monodromy Groups Uniquely Determined by Passport
Naiomi Cameron, Lewis & Clark College
Location: Physics 123
In this talk, I will discuss the results of an undergraduate research project focused on so-called dessin d'enfants.  Roughly speaking, a dessin d'enfant (or dessin for short) is a bicolored graph embedded into a Riemann surface.  Dessins which are trees can be associated analytically to pre-images of certain polynomials, called Shabat polynomials, and also algebraically to their monodromy group, which is the group generated from rotations of edges about its vertices.  One known invariant for dessins is called the passport, which is the multiset of the degrees of its vertices and faces.  The focus of this project was to determine the Shabat polynomials and monodromy groups for trees uniquely determined by their passport.
Oct 5 Homotopy Types as a Foundation for Mathematics
Emily Riehl, Johns Hopkins University
The Curry-Howard correspondence formalizes an analogy between computer programs and mathematical proofs. This talk will introduce alternative foundations for mathematics animated by this analogy. The basic object is called a type, which can be simultaneously interpreted as something like a set or as something like a mathematical proposition. Homotopy type theory refers to the recent discovery that a type can also be interpreted as something like a topological space. We will discuss the implications of this homotopy theoretic interpretation for the so-called univalent foundations of mathematics.
Oct 12Classifying Manifolds: Applications of Topology to Geometry and Physics
Christine Escher, Oregon State University
A fundamental and deep problem in mathematics is a classification of the objects of study: which objects are the same, which are different.  The tools for the classification of this talk come from algebraic topology but the interest and motivation for the classifications come from differential geometry and theoretical physics.   I will give an overview over which objects we study and what we mean by "the same" and "different".   In particular, I will discuss the classification of Euclidean spaces and spheres.
Oct 19Fall Break
Oct 26Azumaya Algebras: Bridging Algebra and Topology
Ben Williams, University of British Columbia
Since the discovery of Quaternions by Hamilton in 1843, noncommutative division algebras have been a topic of study in algebra. In the mid-20th century, they were generalized considerably by several people, culminating in an abstract and general definition of "Azumaya algebra" by Grothendieck in 1968. In this formulation, certain algebraic problems may admit solutions by geometric, or strictly speaking, topological, methods. I will explain what the algebraic terms mean, how Grothendieck's idea works and why it is ingenious, and how you can use it to solve problems.
Nov 2Melting of Ice, Obstacles and Walls: An Introduction to Free Boundary Problems
Mariana Smit Vega Garcia, University of Washington
Free boundary problems arise naturally in a number of physical phenomena and deal with solving partial differential equations (PDEs) in a domain Ω, a part of whose boundary is unknown in advance. A famous example of a free boundary problem is the Stefan problem, which describes the temperature distribution in a medium undergoing a phase change, for example melting of ice. In this talk we will see examples of free boundary problems, questions people are interested in answering, and some techniques used in the field to address those questions. No prior knowledge of Partial Differential Equations will be assumed.
Nov 9
Please note change in location.
Bringing Data Science to Government Surveys: Incorporating New Data Sources into Survey Estimation
Kelly McConville, Swarthmore College
Location: Physics 123

Government agencies across the world are estimating important population quantities using data collected under a complex sample design.  With the advent of big data and advancements in technology, a wealth of additional data sources, such as remotely sensed data and administrative data, are available.  In this talk, I present a class of survey estimators that seek to combine existing survey data with these new sources of data, often using machine learning methods to do so.  I then examine the utility of these modern techniques in estimating official statistics.

Nov 14
Please note change in date.
Please note change in location.
The Social and Demographic Dimensions of an Online Fitness Community
Zack Almquist , University of Minnesota
Location: Physics 123

Increased attention is being paid to the promotion of healthy habits via mobile applications, which foster online fitness communities and offer users the ability to track their physical fitness. At the intersection of social media and activity tracking, these platforms represent affordable, scalable technologies for capturing information about both physical activity and peer-to-peer interactions. Importantly, the large-scale behavioral trace data archived by these platforms offers researchers a novel and powerful opportunity to examine health-related behaviors. In this study, we explore the characteristics and dynamics of social exercise (i.e. fitness activities with at least one peer physically co-present), using data collected from an online fitness community popular with cyclists and runners. Our analysis of the personal networks of the online fitness users uncovers a strong gender-based homophily between users, as well as distinct generative processes for network formation across genders. We further examine how performance and social feedback vary by the number/gender of people participating in an activity; our results indicate that when peers are physically co-present for fitness activities (i.e. when users participate in group workouts) (i) exercise tends to be of higher performance (e.g., longer distance, higher heart rate), and (ii) users receive more online feedback from other users. These effects of co-present activity partners are true for both men and women, though we do find that women are proportionately more likely to engage in group activities. Altogether, these results improve our understanding of how technological solutions such as mobile apps and online communities may be utilized in developing affordable and large-scale health intervention strategies.

Nov 16
Please note change in location.
Genotyping Polyploids
David Gerard, University of Chicago
Location: Physics 123
Modern genomics has revolutionized how we answer questions about evolution, population dynamics, medicine, and plant and animal breeding. To answer these questions, we must first be able to detect and quantify (or "genotype") differences in individual genomes. Many scientists have used next generation sequencing technologies to genotype diploid individuals (those with two copies of their genomes). However, methods to genotype polyploids (those with more than two copies of their genomes) are just emerging. We present two main contributions: (1) many datasets feature related individuals, and so we use the structure of Mendelian segregation to borrow strength between polyploid siblings to improve genotyping; (2) we additionally draw attention to and then model common aspects of next generation sequencing data: sequencing error, allelic bias, overdispersion, and outlying observations. We verify our method in simulations and apply it to a dataset of hexaploid sweet potatoes.
Nov 21
Please note change in date.
Please note change in location.
Too many parameters! Covariance, cancer, and cells.
Shannon McCurdy, University of California, Berkeley
Location: Physics 123
Covariance, a measure of the joint variability of random variables, is an important quantity in statistics.  Estimating covariance is challenging in the high dimensional setting, where the number of features is much greater than the number of samples.  I will introduce approaches for estimating covariance and discuss applications to biomedical and biological data: cancer genomics and mouse brain cell gene expression.
Nov 23Thanksgiving Break
Nov 28
Please note change in date.
Please note change in location.
Personalism and Dempster-Shafer Analysis for the 21st Century
Paul Edlefsen, Fred Hutchinson Cancer Research Center
Location: Physics 123
Personalism, like its more familiar cousins objectivism and subjectivism, is a perspective on the role of the statistician (or more generally, the scientist: "you") in the conduct of science. The differences among these perspectives usually impact little on the daily conduct of statisticians, to our great relief. We are already sufficiently aware of our expected role on a paper or grant to ensure that the science is reproducible. However we are also not unaware of the several difficult issues that we face in statistical science including our contribution to the too-often disappointing performance of phase 3 trials, which results in a high cost for the biomedical enterprise and possibly in lost opportunity for quality human living. There are a host of thorny issues we must face, including how to maximize information yield from research investments while accounting for multiple testing and post-hoc inference. Furthermore, "p>>n" problems (high dimensional covariates with low numbers of observations) arise increasingly often in clinical trials. Can "Fisher's Greatest Blunder" (which is how Brad Efron described Fisher's "Fiducial" methodology) possibly offer an insight into a solution to all of these problems? I will begin by introducing the personalist perspective on the role that "you" play in the scientific process and I will briefly describe Dempster-Shafer (DS) methodology for statistical inference and prediction. I will argue that DS potentially offers a path toward a truly cohesive statistical inference framework for the 21st century.
Nov 30Garbled Circuits: New Results for Arithmetic and High Fan-In Computations
Mike Rosulek, Oregon State University
Secure computation is a cryptographic technique in which parties can perform a computation on private data to learn only the outcome of the computation while revealing nothing about the inputs. One of the most promising approaches for secure computation is a technique called *garbled circuits*, which can be thought of as a way to "encrypt" a boolean circuit in a particular way.
In the first half of this talk I will give an introduction to garbled circuits. Standard constructions for garbled circuits are only feasible for computations expressed in terms of low fan-in, boolean (bit-level) operations. However, boolean circuits are often a poor model in which to express many computations of interest. I will spend the second half of the talk presenting new garbled circuit constructions that natively support arithmetic operations directly over the integers and high-fan-in boolean operations. These new constructions offer exponential cost improvements over standard boolean circuits, for some natural kinds of computations. These results are joint work with Marshall Ball & Tal Malkin.

Spring

4:40-5:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.

Jan 25Jonathan Campbell, Vanderbilt University
Feb 1
Feb 8Emily Peters, Loyola University Chicago
Feb 15
Feb 22
Mar 1Igor Kriz, University of Michigan
Mar 8Symmetries of Noncommutative Algebras: The What? The How? And the Why Care?
Chelsea Walton, Temple University & University of Illinois Urbana-Champagne
Mar 15Spring Break
Mar 22
Mar 29Asher Auel, Yale University
Apr 5José Perea, Michigan State Universtiy
Apr 12Maja Taskovic, University of Pennsylvania
Location: Physics 123
Apr 19
Apr 26

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