Department Colloquium

ACADEMIC YEAR 2017-2018

Fall 2017

September 15, 2017
Learning Models of Language, Action and Perception for Human-Robot Collaboration
Professor Stefanie Tellex
Brown University

Robots can act as a force multiplier for people, whether a robot assisting an astronaut with a repair on the International Space station, a UAV taking flight over our cities, or an autonomous vehicle driving through our streets.  To achieve complex tasks, it is essential for robots to move beyond merely interacting with people and toward collaboration, so that one person can easily and flexibly work with many autonomous robots.  The aim of my research program is to create autonomous robots that collaborate with people to meet their needs by learning decision-theoretic models for communication, action, and perception.  Communication for collaboration requires models of language that map between sentences and aspects of the external world.  My work enables a robot to learn compositional models for word meanings that allow a robot to explicitly reason and communicate about its own uncertainty, increasing the speed and accuracy of human-robot communication.  Action for collaboration requires models that match how people think and talk, because people communicate about all aspects of a robot’s behavior, from low-level motion preferences (e.g., “Please fly up a few feet”) to high-level requests (e.g., “Please inspect the building”).  I am creating new methods for learning how to plan in very large, uncertain state-action spaces by using hierarchical abstraction.  Perception for collaboration requires the robot to detect, localize, and manipulate the objects in its environment that are most important to its human collaborator.  I am creating new methods for autonomously acquiring perceptual models in situ so the robot can perceive the objects most relevant to the human’s goals.  My unified decision-theoretic framework supports data-driven training and robust, feedback-driven human-robot collaboration.

Stefanie Tellex is the Joukowsky Family Assistant Professor of Computer Science and Assistant Professor of Engineering at Brown University.  Her group, the Humans To Robots Lab, creates robots that seamlessly collaborate with people to meet their needs using language, gesture, and probabilistic inference, aiming to empower every person with a collaborative robot.  She completed her Ph.D. at the MIT Media Lab in 2010, where she developed models for the meanings of spatial prepositions and motion verbs.  Her postdoctoral work at MIT CSAIL focused on creating robots that understand natural language.  She has published at SIGIR, HRI, RSS, AAAI, IROS, ICAPs and ICMI, winning Best Student Paper at SIGIR and ICMI, Best Paper at RSS, and an award from the CCC Blue Sky Ideas Initiative.  Her awards include being named one of IEEE Spectrum’s AI’s 10 to Watch in 2013, the Richard B. Salomon Faculty Research Award at Brown University, a DARPA Young Faculty Award in 2015, a NASA Early Career Award in 2016, a 2016 Sloan Research Fellowship, and an NSF Career Award in 2017.  Her work has been featured in the press on National Public Radio, BBC, MIT Technology Review, Wired and Wired UK, as well as the Smithsonian. She was named one of Wired UK’s Women Who Changed Science In 2015 and listed as one of MIT Technology Review’s Ten Breakthrough Technologies in 2016.

October 13, 2017
Outer billiards and the plaid model
Professor Richard Schwartz
Brown University

Outer billiards is a dynamical system that involves a point circulating around the outside of a convex shape in the plane sort of like the earth orbiting around the sum.  The name comes from the fact that the rules for the system resemble the rules for ordinary billiards.  I show some computer pictures and demonstrations of outer billiards, and then narrow the focus and explain how I figured out a combinatorial model (which I call the plaid model) for what happens when the convex shape is a kite.

Rich Schwartz got his Ph.D. in math from Princeton in 1991 and since then has had a number of university jobs, the last one being the Chancellor’s Professor of Mathematics at Brown University.  In his spare time, Rich enjoys drawing, listening to music, computer programming, cycling, walking on the beach, and working out at the gym.

October 24, 2017
Suspect something fishy? How statistics can help detect it, quickly.
Aleksey S. Polunchenko, Ph.D.
State University of New York at Binghamton

Suppose you are gambling at a casino in a game where you and a dealer take turns rolling a die. Naturally, you would expect the die to be fair. However, what if at some point into the game the dealer-without you seeing-replaced the die with a look-alike unfair one, so as to steer the course of the game favorably to the casino. As the die’s appearance hasn’t changed, you would continue to gamble without suspecting anything. The obvious question is: as the game progresses, can you somehow “detect” that the die has been tampered with, and do so as promptly as possible? The time at which the die was replaced (if it was replaced) is referred to as the change-point, and it is not known.

Your “detection strategy” would clearly be sequential, and based solely on the scores observed so far. The desire to detect the change quickly makes the question a gamble on its own. On the one hand, it would be desirable to find out that the die is no longer fair as fast as possible, so as to quit the game to prevent further losses and subsequently file a lawsuit against the casino. On the other hand, if you are too trigger-happy there is a risk of stopping the game too quickly, i.e., stopping the game before the fair die was replaced with the unbalanced one, which is not desirable. How does one go about solving this problem? Statistics can help!

Statistics is a branch of mathematics concerned with rational decision-making among uncertainty. This is essential in real life, as only a well-thought-out decision can enable one to take the best action available given the circumstances. This talk’s aim is to provide a gentle introduction to the nook of statistics that deals with cases when a solution has to be worked out “on-the-go”, i.e., when time is a factor as well. Specifically, the talk will focus on the so-called quickest change-point detection problem. Also known as sequential change-point detection, the subject is about designing fastest ways to detect sudden anomalies (changes) in ongoing phenomena. One example would be the above biased die detection problem. However, there are many more, arising in a variety of domains: military, finance, quality control, communications, environment-to name a few. We will consider some of the subject’s applications, and touch upon its basic ideas.

Dr. Aleksey S. Polunchenko is an Assistant Professor in the Department of Mathematical Sciences at Binghamton University in New York.  Dr. Polunchenko’s area of research is mathematical statistics and specifically studying the problem of sequential (quickest) change-point detection.   He is currently focusing on the case of composite hypotheses.

November 17, 2017
Measurement error: What is it? Does it matter? What to do about it?
John P. Buonaccorsi
Professor Emeritus, Department of Mathematics and Statistics
University of Massachusetts-Amherst

Frequently variables that enter into a statistical analysis are not able to be observed exactly. Examples include dietary intake or physical activity over a certain period of time, population abundance, disease rate,  chemical or biological properties of water or soil samples, genetic quantities including methylation rate, expenditure or income,  disease status (and many other variables with a yes/no status), etc.  The “measurement error” or as it is known for a qualitative variable, misclassification, can arise for a variety of reason including instrument error, sampling error (often from sampling over time and/or space), recall bias and a variety of other reasons. In this talk I will give a (non-technical) overview of the nature of measurement errors, what happens if you ignore it in a variety of problems, including estimating means and proportions, contingency table analysis and regression analysis, and what strategies are available to correct for measurement error. Examples will be presented from a variety of disciplines.

John Buonaccorsi is Professor Emeritus of Mathematics and Statistics at the University of Massachusetts-Amherst. He received his B.A. from Providence College in 1975, his M.S. and Ph.D. degrees from Colorado State University and has been at the University of Massachusetts since 1982. He was a long-time member of the University’s Statistical Consulting Center and coordinator of the graduate options in Statistics for many years. He is the author of over 70 articles and book chapters and is author of the 2010 book “Measurement Error: Models, Methods and Applications”, part of the Chapman-Hall series on interdisciplinary statistics. His original research interests were in optimal experimental design, estimation of ratios and calibration, followed by a focus on measurement error, an area he has worked in for over 25 years. He has also published extensively in various applied areas including quantitative ecology, with a recent emphasis on population dynamics. He has a long-standing collaboration with colleagues at the University of Oslo Medical School addressing measurement error methods in epidemiologic contexts.

ACADEMIC YEAR 2016 – 2017

Fall 2016

September 23, 2016
Using Computational Methods to Understand Microorganism Motility
Sarah Olson, Ph.D.
Worcester Polytechnic Institute

Microorganisms such as the bacteria E. coli and sperm are able to swim and navigate in complex environments. Developing an understanding of swimming microorganisms through computational models could lead to insight on the development of artificial micro swimmers for a variety of applications, including drug delivery. We will illustrate how vector calculus can be used to rewrite the fluid governing equations and how computational algorithms can be used to solve for the resulting fluid flow. Time permitting, we will show simulations of sperm motility and flagellar bundling of E. coli.

Sarah Olson is an Assistant Professor in the Department of Mathematical Sciences at Worcester Polytechnic Institute and is interested in mathematical biology, fluid dynamics, and numerical methods. She started her undergraduate studies at Providence College, majoring in both Mathematics and Biology, and continued at NC State for a Ph.D. and at Tulane University as a Postdoctoral Scholar. She has mentored many students on different research projects and recently received an NSF CAREER award, recognizing her integration of research and education.

October 14, 2016
Financial Derivatives: The Use and Pricing of Options and Futures
Professor Edward Szado

Financial derivatives are the cornerstone of risk management in financial institutions and corporate America. This discussion provides a brief overview of options and futures. I discuss their use in risk management, the impact of non-linear payoffs and their relative advantages and disadvantages. In addition, I provide a brief overview of pricing options using models based on the Black Scholes Merton option pricing model as well as a discussion of the characteristics of options and their underlying securities that determine the value and risk exposure of the options.

Dr. Szado is an Assistant Professor of Finance at Providence College, and holds pro bono positions as the Director of Research at the Institute for Global Asset and Risk Management and the Director of Research at the Center for International Securities and Derivatives Markets. Ed earned a Ph.D. in Finance from the Isenberg School of Management, University of Massachusetts – Amherst, an MBA from Tulane University and a BComm from McMaster University. He has taught at Boston University, Clark University, Providence College and the University of Massachusetts – Amherst. He is a former options trader and has worked extensively on asset allocation and risk managed investment programs. He was a founding Editor of the Alternative Investment Analyst Review (AIAR) and currently a member of the editorial board of the Journal of Alternative Investments (JAI). He is a Chartered Financial Analyst and has consulted to the Options Industry Council, the Chicago Board Options Exchange, the Chartered Financial Analyst Institute, the Alternative Investment Analyst Association and the Commodity Futures Trading Commission.

He has published more than fifteen journal articles, and coauthored four books in the areas of derivatives, alternative investments, and risk management. His research has been featured in a wide variety of media, including: Barron’s, Bloomberg, Dow Jones Newswires, Futures Magazine, Hedge World, Market Watch, Pensions and Investments, Reuters, Smart Money, Swiss Derivatives Review, and the Wall StreetJournal.

October 21, 2016
The James Function
Professor Christopher Hammond
Connecticut College

We investigate the properties of the James Function, associated with Bill James’s so-called “log5 method,” which assigns a probability to the result of a game between two teams based on their respective winning percentages.  We also introduce and study a class of functions, which we call Jamesian, that satisfy the same a priori conditions that were originally used to describe the James Function.  (This talk represents joint work with Warren P. Johnson and Steven J. Miller.)

Christopher Hammond grew up in Durham, North Carolina, where he had the privilege of watching Duke basketball in its heyday.  After graduating from the North Carolina School of Science and Mathematics, he earned his bachelor’s degree at the University of the South in Sewanee, Tennessee.  He received his doctorate at the University of Virginia, after which he had the good fortune to obtain his current position at Connecticut College.  All of his mathematical research, apart from this project, has pertained to composition operators acting on spaces of analytic functions.

November 11, 2016
Bayes’ Rule and the Law
Professor Leila Setayeshgar

Dr. Leila Setayeshgar is an Assistant Professor of Mathematics at Providence College. She received her Ph.D. from the Division of Applied Mathematics at Brown University in 2012. She is passionate about teaching mathematics, and is equally enthusiastic about teaching mathematics to majors and non-majors. She teaches courses ranging from calculus to statistics and probability, and is broadly interested in doing research in probability and stochastic processes.

November 18, 2016
Grit and Character
Professor Jason Price
Nichols College

Do you give all that you have? The philosopher William James posited a gap between potential and its actualization. “The human individual lives usually far within his limits; he energizes below his maximum and he behaves below his optimum.” (The Powers of Men – 1907) Angela Duckworth defines Grit as perseverance and passion for long-term goals. I am involved in a study that is investigating the effect of Grit on various aspects of academic life. It is of particular interest to me that an individual’s grit score can be decomposed into two components, passion and perseverance, with both components seeming to drive success in different areas. The decomposition Grit = Passion + Perseverance is reminiscent of the decomposition of a character of a finite group into irreducible characters.

In this talk, I will discuss my career journey starting as an undergraduate at Providence College. I will give an introduction to the Grit study that I am involved in. I will also introduce group representations and characters. This part of the talk will pull in elements of Linear Algebra and Abstract Algebra although no knowledge of either is presupposed.

Jason Price is the Associate Dean for Liberal Arts and an Associate Professor of Mathematics at Nichols College. His research interests include number theory and educational technology. He studied at Providence College and the University of Vermont. He enjoys teaching a number of subjects, particularly Abstract Algebra, and spending time with his wife and baby girl.

Spring 2017

March 17, 2017
Permutations, Peaks Polynomials, and a Positivity Conjecture
Professor Pamela E. Harris
Williams College

From the basic ordering of n objects, solving a rubik’s cube, and establishing the unsolvability of the general quintic via radicals, permutations have played many important roles in mathematics. In this talk, we present some recent results related to the concept of peaks of permutations. A permutation π = π1π2?πn∈ Gn is said to have a peak at i if πi-1 <πi>πi+1. We let P(π) denote the set of peaks of π and, given any set S of positive integers, we define PS(n) = {π ∈ Gn : P(π) = S}. In 2013 Billey, Burdzy, and Sagan showed that for all fixed subsets of positive integers S and sufficiently large n, |PS(n)|= ps(n)2n-|S|-1for some polynomial pS(x) called the peak polynomial of S. Billey, Burdzy, and Sagan conjectured that the coefficients of pS(x) expanded in a binomial coefficient basis centered at max(S) are all nonnegative. We end this talk by sharing a new recursive formula for computing peak polynomials, which we then use to prove that their “positivity conjecture” is true.

Pamela E. Harris is an Assistant Professor in the department of Mathematics and Statistics at Williams College. Her research interests are in algebra and combinatorics, particularly as these subjects relate to the representation theory of Lie algebras. She received her B.S. from Marquette University, and M.S. and Ph.D. in mathematics from the University of Wisconsin-Milwaukee. She often co-organizes research symposia sessions and professional development sessions for the national SACNAS conference. She was an MAA Project NExT (New Experiences in Teaching) Fellow from 2012-2013, and is a member of the AMS, AWM, MAA, NAM and SACNAS.

March 24, 2017
Soap Bubbles and Mathematics
Professor Frank Morgan
Williams College

A soap bubble is round because the round sphere provides the least-perimeter way to enclose given volume, as was proved mathematically by Schwarz in 1884. Similarly the familiar double bubble, which forms when two bubbles come together, is the least-perimeter way to enclose and separate the two given volumes, although we didn’t prove this until 2000. If space is given a density, very popular since its appearance in Perelman’s proof of the Poincaré conjecture, the question gets even more interesting. The show will include a little guessing contest with demonstrations and prizes. No prerequisites; all welcome.

Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His proof with colleagues and students of the Double Bubble Conjecture is featured at the NSF Discoveries site. Morgan went to MIT and Princeton, where his thesis advisor, Fred Almgren, introduced him to minimal surfaces. He then taught for ten years at MIT, where he served for three years as Undergraduate Mathematics Chairman, received the Everett Moore Baker Award for excellence in undergraduate teaching, and held the Cecil and Ida Green Career Development Chair. Morgan also served at Williams as Mathematics Department Chair and founding director of an NSF undergraduate research project. He is currently Webster Atwell ’21 Professor of Mathematics, Emeritus, and Editor-in-Chief of Notices of the American Mathematical Society.

April 7, 2017
Mathematics of Options Pricing and Hedging
Professor Lucy Kimball
Bentley University

The pricing and hedging of financial options is an active area of research in mathematical finance.  Classic approaches rely on assuming a binomial model or a stochastic differential equation for the evolution of the underlying stock price process. Our work is based on an extension of the binomial model to include stock price jumps that fall in a closed interval rather than just the two point distribution assumed by the classic model.  This model allows for the development of a unique approach to finding an optimal hedging strategy based on real market data. In this talk I will give an introduction to financial options, some of the mathematical principles underlying classic approaches to pricing and hedging and give an overview of our work.  No previous exposure to financial options is required.

Dr. Lucy Kimball is a Professor of Mathematical Sciences at Bentley University.  At Bentley she served as Actuarial program Coordinator, Internship Coordinator and Math Club Advisor for many years prior to becoming Chair of the Department of Mathematical Sciences. While chair she was instrumental in developing the department’s undergraduate major in Actuarial Science and graduate degree program in Business Analytics. She is currently the Wilder Teaching Professor and Chair of the Bentley University Learning and Teaching Council.

Dr. Lucy Kimball does research in Mathematical Finance and has over thirty publications on a variety of topics including atmospheric modeling, optimization for large scale problems in electric power systems and mathematical models for pricing and hedging of financial options.

Dr. Lucy Kimball received a Bachelor of Science from the University of Massachusetts, Lowell and received a Master of Science and Doctor of Philosophy from Worcester Polytechnic Institute.

April 21, 2017
Tropical Mathematics: A New Dialect
Professor Catherine Buell
Fitchburg State University

If mathematics is truly the language of the universe, then surely there must be different dialects to describe the vast number of physical phenomena we observe and create; one such dialect is Tropical Mathematics.  Tropical Mathematics is also known as min-plus algebra or max-plus algebra because addition is defined as x ⊕ y ? the maximum of x and y and multiplication is defined as    x ⊗ y = x + y.  Questions in Tropical Mathematics cross the disciplines of computer science, pure and applied mathematics, physics, and biology.  In this talk, we will explore this new language through arithmetic, graphs, and ultimately discuss the implications of Tropical Mathematics to industrial problems and network analysis.

Dr. Catherine Buell is an assistant professor of mathematics at Fitchburg State University in Massachusetts. She has also taught at Bates College in Maine. Her research areas include algebraic group theory, visual stylometry, and undergraduate education (equity in inquiry and social justice mathematics). Her dog Donny serves as a (unofficial) math anxiety dog at the university.