## “The Dynamics of Continued Fractions” at noon on Thursday 4/11 in Olin 268

Student Colloquium talk by Professor Daniel Visscher, Ithaca College

Title: The Dynamics of Continued Fractions

Abstract: While only rational numbers have a fraction representation, all real numbers have a continued fraction representation. Continued fractions illuminate interesting structure in real numbers, for example, by giving a way to express how close a real number is to being rational. In this talk, we investigate continued fractions from the point of view of a dynamicist, framing the topic in terms of iterating a function and asking questions about how orbits distribute. Multiple flavors of π will be present, and the golden ratio will make approximately 1.618 appearances.

## “When is the best time to stop?” at noon on Monday 3/25 in Olin 268

Student Colloquium talk by Professor Ryan Hynd, University of Pennsylvania

Title: When is the best time to stop?

Abstract:Suppose that you are observing a sequence of events, and need to decide when to stop. Your goal could be to maximize an expected gain or give yourself a good chance to make the best choice possible.  We will discuss several instances of this type of problem and talk about ways to use math to solve them.

## “Mathematics of Outbreaks: Exploring Infectious Disease Transmission and Control with Mathematical Models” at noon on Thursday 3/21 in Olin 268

Student Colloquium talk by Professor Michael A. Robert, University of the Sciences

Title: Mathematics of Outbreaks: Exploring Infectious Disease Transmission and Control with Mathematical Models

Abstract: Mathematical models have long been used to study the spread of infectious diseases. From smallpox to influenza to Zika virus, mathematical models help us understand how infectious diseases spread and how we can potentially control their spread. Models are also powerful tools for making predictions about how infectious diseases may emerge and spread in the future. In this talk, I will introduce mathematical models developed to study infectious diseases, and I will discuss my recent work in using mathematical models to study the spread and control of dengue fever and Zika virus, two diseases transmitted by mosquitoes. Dengue fever is found throughout tropical regions of the world and impacts millions of people each year. In recent years, dengue has begun to spread into more temperate areas of the world. Zika virus first emerged in 2015 and spread rapidly throughout the world, infecting millions of people. The recent rapid spread of both viruses is the result of a number of factors including an increasingly connected world and a rise in global surface temperatures caused by climate change. I will discuss how I utilize mathematical models to understand how these two factors play a role in transmission of dengue and Zika. I will specifically discuss how human movement and temperature variation impact the potential for the spread of dengue and Zika in certain U.S. cities and how the potential for emergence of the viruses may change if global surface temperatures continue to rise. I will also briefly discuss how models are being used to plan control strategies for infectious diseases, including strategies involving the release of genetically modified mosquitoes to help control mosquito-borne diseases.

## “An Orchestra without a Conductor: The Mathematics of Synchronizing Fireflies” at noon on Thursday 2/28 in Olin 268

Student Colloquium talk by Professor Matthew Mizuhara ’12 of The College of New Jersey

Title: An Orchestra without a Conductor: The Mathematics of Synchronizing Fireflies

Abstract: In Amphawa, Thailand trees are lined with thousands of fireflies spontaneously flashing in near perfect unison. However, there is no “leader” driving this coordination. The Kuramoto model, a non-linear system of differential equations, describes the firefly flashes. Using numerical simulations, we can capture this spontaneous emergence of synchronization and explore other, new patterns which can arise. No background in differential equations is required to enjoy this talk!

## “Using Genetic Algorithms for U.S. Army Robot Design” at noon on Thursday 2/14 in Olin 268

Student Colloquium talk by Professor Lucas Waddell of Bucknell University

Title: Using Genetic Algorithms for U.S. Army Robot Design

Abstract: In recent years, Operations Research practitioners have increasingly utilized nature-inspired algorithms (NIAs) to solve real-world, large-scale optimization problems. One of the most popular NIAs is the Genetic Algorithm (GA), which is based on ideas from Darwin’s theory of evolution. This talk will provide an introduction to GAs through the lens of a project that Lucas worked on for the U.S. Army during his time as an Operations Research Analyst at Sandia National Laboratories.

## “What Did You Do Last Summer?” at noon on Thursday 11/1 in Olin 268

Student Colloquium talk presented by Bucknell Students

Moderator: Nate Mattis ’19

Presenters:

• Hannah Bokma ’20, Teaching Experience for Undergraduates, Brown University
• Nate Lesnevich ’19, Undergraduate Research (Pure Mathematics), Bucknell University
• Christina Sweeney ’19, Data Analytics, Slalom Consulting
• Xeniya Tsoktoyeva ’19, Finance, PNC Bank
• Yili Wang ’21, Undergraduate Research (Applied Mathematics), Bucknell University

Abstract: There are many exciting summer opportunities for students in the mathematical sciences! These range from internships with financial companies to research experiences at other universities to leadership development programs. In this week’s colloquium, a panel of your peers will tell you their experiences. What did they enjoy about their experiences? When did they apply? There will also be ample time for questions and answers. These varied opportunities, as well as being terrific fun, are also immensely valuable as you begin to think about your careers after Bucknell.

## Assigning Students to Schools to Minimize Socioeconomic Variation between Schools: An Introduction to Optimization Modeling at noon on Thursday 10/18 in Olin 268

Student Colloquium talk by Professor Dick Forrester of Dickinson College

Title: Assigning Students to Schools to Minimize Socioeconomic Variation between Schools: An Introduction to Optimization Modeling

Abstract: Numerous studies have found that a student’s academic achievement is as much determined by the socioeconomic composition of their school as their own socioeconomic status. In this talk we provide a methodology for assigning students to schools so as to balance the socioeconomic compositions of the schools while taking into consideration the total travel distance. Our technique utilizes a bi-objective general 0-1 fractional program that is linearized into a mixed 0-1 linear program which can be submitted directly to a standard optimization package. If you didn’t understand that last sentence, don’t worry, the purpose of this talk is to introduce you to optimization modeling.  As a test case for our approach we analyze data from the Greenville County School District in Greenville, South Carolina.

## Listening to Orbifolds and Orbigraphs at noon on Thursday 10/4 in Olin 268

Student Colloquium talk by Professor Liz Stanhope of Lewis and Clark College (Visiting Professor at Bucknell University)

Title: Listening to Orbifolds and Orbigraphs

Abstract: Spectral geometry is a lively area of mathematical research motivated by the question `Can you hear the shape of a drum?’ My work in spectral geometry has been to study the spectral properties of objects called orbifolds.  Questions in spectral geometry have useful analogs in graph theory.  Because of this we’ll discuss how to make sense of the concept of orbifold in the setting of spectral graph theory.

## Bioinformatics and the Challenges of Visualizing Big Data at noon on Thursday 9/20 in Olin 268

Student Colloquium talk by Professor Ken Field of Bucknell University

Title: Bioinformatics and the Challenges of Visualizing Big Data

Abstract: Bioinformatics and next generation sequencing have revolutionized biology and medicine. The increasing affordability of next generation sequencing has made it possible to use whole-genome and whole-transcriptome approaches to answer questions in the lab, the field, and the clinic. However, working with these large datasets presents several computational and statistical challenges. As an example, we will discuss the importance of data exploration and multiple testing corrections. In addition, visualizing complex multi-dimensional data is also difficult and we will discuss approaches using interactive data displays and virtual reality.

## Proofs Without Witnesses: Zero Knowledge Proofs at noon on Thursday 9/6 in Olin 268

Title:  Proofs Without Witnesses: Zero Knowledge Proofs

Abstract:  Peggy wants to convince Victor that she possesses a secret. Victor doesn’t believe that Peggy is telling the truth while Peggy doesn’t trust Victor enough to show him the secret. Zero knowledge proofs provide a method by which Peggy can convince Victor that she has the secret without giving Victor any information about the secret itself. In this talk we’ll construct and analyze several zero knowledge proofs, and discuss how they can be used in a wide array of areas including computer security and nuclear disarmament.