Bucknell Mathematics Department Blog

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.

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.

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.

Student Colloquium talk by Professor Aimee Johnson of Swarthmore College

Abstract:  We all wish we could see into the future!  In dynamical systems, we formalize what this might mean and explore to what extent it might be done.  One useful tool in this task is to investigate the fixed points of the system.  In this talk, we will explore three different examples of dynamical systems, find the fixed points for each one, and then see how they can help us learn about other points in the system.  In this way, we can try to tell a little bit about the future (at least for these examples!).

Karen Saxe, Director of Government Relations for the American Mathematical Society and DeWitt Wallace Professor of Mathematics at Macalester College

 

Abstract:  Societal inequalities pose some of the biggest and most intractable challenges facing our nation today. Can mathematical concepts help us understand and analyze social inequality? What is the relationship between various imbalances in the U.S. today such as those we see in income distribution and political polarization? Many say that gerrymandering contributes to political polarization; can we use a quantitative strategy to determine the validity of this assertion? This talk will focus on quantitative approaches that mathematicians and political scientists use to measure social inequalities and fairness in redistricting. I will also discuss my advocacy work for the American Mathematical Society, and we’ll have plenty of time for Q & A. No mathematical background required.

Graciela Chichilnisky, lead architect of the carbon market of the Kyoto Protocol and a professor of economics and mathematical statistics at Columbia University, will give the keynote presentation for the 2018 Sustainability Symposium on Thursday, March 22, at 7 p.m. in Leanne Freas Trout Auditorium. Bucknell President John Bravman will introduce Chichilnisky, who also contributed to reports of the Intergovernmental Panel on Climate Change (IPCC), the organization that shared the 2007 Nobel Peace Prize with Al Gore, “for their efforts to build up and disseminate greater knowledge about man-made climate change, and to lay the foundations for the measures that are needed to counteract such change.”

Getting Started in Analytics

Meghan Kent Harward, Analytical Consultant, Advanced Analytics Lab, SAS Institute Inc.

Thursday, March 8, 12:00 p.m. Room 268 in the Olin Science Building.

Abstract: We hear buzz words like “big data” and “the internet of things” more and more in our media, but do we really know what analytics is? In this talk we will explore paths to jobs in data science, what it means to be an analyst, and some keys to success in the field.

Iterates, invariance, and chaos

Thursday, January 25, 12:00 p.m. Room 268 in the Olin Science Building.

Abstract: We will consider what happens when we repeatedly compose a given function with itself, focusing particularly on where this repeated composition (known as iteration) sends individual inputs.  Various phenomena will be discussed, including the notions of invariance and what some might call chaos.

 

Evolutionary game theory: the mathematics of cooperation

Thursday, February 8, 12:00 p.m. Room 268 in the Olin Science Building.

Why do we (or any living organisms) cooperate? Cooperation, the act of expending one’s own energy or resources for the good of the group, is a necessary part of life, but is also exploitable by so-called “defectors” who choose not to help out yet still reap the benefits that cooperation yields. In fact, under fairly general assumptions, every rational individual will (theoretically) choose to defect, thereby extinguishing cooperation and dooming society. Of course, cooperation has not been extinguished and is in fact quite common in the natural world. This observation brings us back to the question posed at the beginning of this abstract. In this talk, I will discuss a mathematical framework through which cooperation is often studied called evolutionary game theory, and present several classic and recent results from the field.