Fall 2009

Ryan Ward, Ben Sokolowsky, Mike Lengel, Joe Ruby, Steven Duff, Will Kanegis took the challenge of this grueling and fun competition, ably supported by Professors Greg Adams and Steven Wang.

**"I Know What You Did Last Summer," Presented by Bucknell Students Dennis Fillebrown ’10 Ariel Kniss ’09 Lucas Mentch ‘10 Aaron Meyers ’10 Alyssa Okita ’10 Julie Sullivan ’10 Mary Wilson ‘10 **

**Abstract: **Do you want to know about summer options for undergraduates with mathematical interests? Seven students will share information about the research experiences and internships they had last summer, providing practical information, opinions, and advice for you!

**"The Riemann Hypothesis", David Farmer (American Institute of Mathematics)**

This year marks the 150th anniversary of the Riemann Hypothesis, the biggest unsolved problem in mathematics. November 18 is "RH Day." The Riemann Hypothesis will be celebrated by more than two dozen lectures all over the world, including this talk at Bucknell. During the talk, I will explain exactly what the Riemann Hypothesis says, why mathematicians think it is an important problem, and give some reasons why it is so difficult to prove.

For more information about the 150th anniversary celebration of the Riemann Hypothesis, visit the AIM page

**"At the crossroads of topology, algebra, and combinatorics," Matt Miller (Bucknell University) **

**Abstract: **Mathematics is sometimes portrayed as a collection of disconnected areas of study. On the other hand, solutions to mathematical problems often require tools from many different areas of mathematics. In this talk we will discuss one way in which topology, algebra, and combinatorics interact in my current research. We will describe some of the connections between subspace arrangements, a general notion of multiplication, and hypergraphs using pictures and specific examples.

Panelists who majored in Economics and Mathematics will share their work experiences to help you understand the job and internship search process and answer any questions you may have. Refreshments will be served afterward.

The panelists are:

- Victoria Boyarsky ’04, ASA, MAAA Actuarial Analyst, United Concordia Companies, Inc., Carlisle, PA
- Sam Camens ‘07 Consultant, Towers Perrin, New York, NY
- Jeff Cohen ‘02 Economics and Mathematics Teacher, Mercersberg Academy, Mercersberg, PA
- Chris Ellis ’00, Ph.D. Professor, Political Science Department, Bucknell University
- Erin Hirschbeck Mallonee ’01, MS Research Health Policy Analyst, RTI International, Rockville, MD
- Ben Wellington ’02, Ph.D. Researcher, Two Sigma Investments, New York, NY

This event is co-sponsored by the Economics and Mathematics departments and Alumni Relations and Career Services Questions? Please contact the Career Development Center at 7-1238 or cdc@bucknell.edu

**"Multitext Parsing: A Statistical Approach to Language Translation," Ben Wellington '02 (Two Sigma Investments)**

**Abstract:**** **As the amount of freely available data has exploded in recent years, advances in natural language processing (NLP) have increasingly relied on statistical techniques. This type of research involves collecting statistics from a training data set and then applying these statistics to new instances of the task. This talk will give an overview of statistical techniques in two main areas of NLP: parsing (finding the correct phrase structure for a sentence), and language modeling (building a statistical model of sentences in a language). A discussion will follow on a novel way to combine these two areas to perform machine translation (finding the best translation from one human language to another). The talk will show that with a proper grammar formalism, translation can be seen simply as a generalization of parsing.

**Kim Ruane, Tufts University**

Hosted by Adam Piggott.

Professor Ruane will give two faculty colloquia

**"To infinity...and beyond", Wednesday, October 21, 4:00pm, in Olin 372**

Suppose F is a finitely generated free group with basis S and let f be an automorphism of F. It is well-known that the subgroup of F that contains the elements of F that are fixed by f is a finitely generated subgroup of F - in fact, it is only recently that the rank of this subgroup was shown to be bounded by the rank of the ambient free group. The first proof of the finite generation was given by S. Gersten. His proof is rather long and combinatorial. We would like to present a geometric proof of this fact that was first given by D. Cooper. The idea is that we view F acting by isometries on its Cayley graph which is a metric simplicial tree. The automorphism f induces a map from the tree to itself that is well-behaved with respect to the geometry of the tree. To make this last statement precise and helpful, we will compactify the Cayley graph by adding on a boundary. Then we see that f can be extended to a unique homeomorphism of the resulting boundary. This will allow us to answer the finite generation question by studying this homeomorphism. The proof is short and elegant, but more importantly this proof motivates some of the main themes of geometric group theory. The ideas in this proof were substantially generalized to yield analogous theorems about Gromov hyperbolic groups. I will discuss these generalizations near the end of the talk.

**"Using the boundary", Thursday, October 22, 4:00pm, in Olin 372.**

In this talk, I will define the visual boundary of a proper geodesic metric space in a more formal way than in my first talk. I will give several examples that arise naturally in the study of nonpositively curved (i.e. CAT(0)) groups. A CAT(0) group is a group G that acts geometrically on a CAT(0) metric space X. The prototypical example is the fundamental group of a compact nonpositively curved Riemannian manifold acting on its universal cover. In this case, the visual boundary is a sphere. There is a natural extension of the action of G on X to the visual boundary as in my first talk. We will analyze this action by first understanding how a single element g in G acts on the boundary - in particular, we can describe the fixed point set of g in the boundary. We will then use this to characterize those elements of G that are "virtually" central as those that act like the identity on the boundary.

**"Computer Forensics: I Know What You Do Online," Scott Inch (Bloomsburg University) **

**Abstract: **Your computer stores a massive amount of data about your behavior without your knowledge. Learn how computer forensics can be used to acquire and analyze this data for use in criminal investigations. Examples from real cases will be shown.

**Brett Wick, Georgia Institute of Technology**

Hosted by Julien Giol.

Professor Wick will give a talk in two parts on "The Corona Problem in One and Several Variables."

Colloquium (Part I): Wednesday, October 7, 4:00pm, in Olin 372

Seminar (Part II): Thursday, October 8, 4:00pm, in Olin 372

**Abstract:** Carleson's Corona Theorem from the 1960's has served as a major motivation for many results in complex function theory, operator theory and, harmonic analysis. In its simplest form, the result states that for two bounded analytic functions, f_{1} and f_{2}, on the unit disc with no common zeros, it is possible to find two other bounded analytic functions, g_{1} and g_{2}, such that f_{1}g_{1}+f_{2}g_{2}=1. Moreover, the functions g_{1} and g_{2} can be chosen with some norm control.

In this series of talks we will discuss an exciting new generalization of this result to certain function spaces on the unit ball in several complex variables. In the first talk (Faculty Colloquium), we will discuss some of the problem's background and some potential generalizations of this famous result. Particular attention will be paid to connections that the Corona Problem has with other areas of mathematics. The second talk (Research Seminar) will focus on the technical aspects behind the proofs of these theorems.

**"A life and death application of mathematics," Peter McNamara (Bucknell University)**

**Abstract: **While you, Sarah Palin and Dick Cheney are out on a hunting trip, an argument ensues as to why the Republicans lost the last election. Soon enough, you find yourselves in a three-way shootout. Unfortunately for you, you only hit your target a third of the time, Sarah Palin hits her target half the time, and Dick Cheney never misses. The good news is that you get to shoot first, while Dick Cheney goes third. Emotions and politics aside, where should you aim your first shot? We will answer this question and determine your chances of being the last one standing.

**"A Spin Through Flatland," Paul Taylor (Shippensburg University)**

**Abstract: **Can you imagine a four-dimensional object? Not with time as a fourth dimension, but another space dimension like the three we normally perceive? Learn some tips and tricks for visualizing higher dimensional objects described and inspired by Flatland.

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The Mathematics Department invites you to submit your funny, profound, topical or just plain ridiculous limericks, haiku or other poetry that is mathematically related or inspired. Send your entry to adam.piggott@bucknell.edu by Wednesday September 23.

The contest is open to all members of the Bucknell community.

Click here to see the entries, including the favorites of the judges.

Come join the fun, games and food with others interested in Mathematics. This event is organized by the MAA Club-Bucknell University Students.

**"Finding Mathematics in Poetry," JoAnne Growney**

**A Brief Bio of Speaker: **JoAnne Growney is co-editor of "Strange Attractors: Poems of Love and Mathematics", (published by A K Peters, 2008) and author of "My Dance is Mathematics", (published by Paper Kite Press, 2006) and the soon to be released "Angles of Light" (published by Finishing Line Press, October 2009). She was a professor of mathematics at Bloomsburg University before moving to Maryland where her primary activity is poetry.

**Abstract:** Students (and possibly others) will join guest poet-mathematician JoAnne Growney for readings (and occasional commentary) of poems with mathematical connections. Contributions from audience members will be welcomed as time permits.

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