Spring 2011

Department Picnic, Tuesday, May 3, 4:00pm on Olin Quad

** **All math students and faculty are invited to celebrate the end of the year!

Study Break: Monday, May 2nd, 7:00 p.m. in Olin 383

Take a break and enjoy "Freeze" Ice Cream Cakes. This event is sponsored by the MAA student mathematics club.

ECMA Majors Picnic, Thursday, April 28, 5:00pm on Olin Quad

** **All ECMA students and faculty are invited to celebrate the end of the year!

Student Colloquium: Thursday, April 28th, 12:00 noon in Olin 268

**Cryptography, presented by Paul Jenkins (Brigham Young University) **

How can information be kept secure when others can read or listen to every message that is sent? We discuss some mathematics and some history behind classical and modern ways of encrypting messages, and explain why using your credit card on the Internet is (probably) safe. GAHZ HZ XQF XM GAF ZHJECFS RSPEGXZPZGFJZ BF BHCC CFDSQ DKXNG.

Distinguished Visiting Professor Colloquium: Monday, April 25th, 4:00 pm in Olin 372

**Weakly Holomorphic Modular Forms, presented by Paul Jenkins (Brigham Young University) **

Modular forms play a central role in modern number theory. They encode information about objects such as partitions and singular moduli, and they play a critical role in the proof of Fermat's Last Theorem. We discuss recent work on the location of the zeros and on the prime factors of the Fourier coefficients of some of the simplest examples of modular forms: weakly homomorphic modular forms on SL(2,Z). Some results are joing work with W. Duke (UCLA) or Darrin Doud (BYU)

Student Colloquium: Thursday, April 21st, 12:00 noon in Olin 268

**The Survivable Network Design Problem, presented by Mihai Banciu (Bucknell University) **

Given a graph G = (V, E), a cost vector c(E), and a set of connectivity requirements conn(V), the survivable network design problem seeks to find a set of edges that satisfy all connectivity requirements, at minimum cost. The real-world applications of this problem span multiple domains, from evacuation and humanitarian logistics planning, to telecommunications network design. In this talk, we will see why this problem is hard to solve exactly in a reasonable amount of time and discuss an alternative approach used for generating good solutions, called tabu search.

Pi Mu Epsilon Honor Society Banquet: Thursday, April 14th, 5:30 p.m., Refectory

**The 87th Initiation & Banquet **

At the annual banquet of the Mathematics Honor Society, Pi Mu Epsilon, new inductees were initiated into the society. Professor Greg Adams entertained the attendees with the lecture: e, A Natural Love Affair.

Field Trip to Broadway: Sunday, April 10th

Students and faculty spent the day in New York City to see Tom Stoppard's Broadway play, Arcadia.

Student Colloquium: Thursday, April 7th, 12:00 noon in Olin 268

**Designing a Better Black Box, presented by Linda Smolka (Bucknell University) **

"In science and engineering, a black box is a device, system or object which can be viewed solely in terms of its input, output and transfer characteristics without any knowledge of its internal workings, that is, its implementation is "opaque" (black). Almost anything might be referred to as a black box: a transistor, an algorithm, or the human mind." (from Wikipedia)

In this talk, we'll discuss the central role mathematics plays in developing numerical algorithms that are used by society as "black boxes," e.g., as algorithms in mathematical software such as MatLab. Without careful design and understanding of the underlying theory, unexpected results can arise that may lead to catastrophic consequences. We'll investigate how things can go awry by developing a numerical algorithm for the heat equation.

"π Day Celebration", Tuesday, March 29, 12:00 noon, Olin 363

** **Bucknell students and faculty celebrated (admittedly belated) that most delicious ratio by consuming pizza π's, fruit π's, salad π's, and chocolate π's.

Distinguished Visiting Professor Colloquium: Thursday, March 24th, 4:00 pm in Olin 372

**You can't hear the shape of a manifold, presented by Carolyn Gordon (Dartmouth College) **

Inverse spectral problems ask how much information about an object is encoded in spectral data. For example, Mark Kac's question "Can you hear the shape of a drum?" asks whether a plane domain, viewed as a vibrating membrane, is determined by the Dirichlet eigenvalue spectrum of the associated Laplacian, equivalently, by the characteristic frequencies of vibration. The lecture will focus on Kac's question and its generalizations to Riemannian manifolds. We will consider methods for constructing manifolds with the same spectral data and compare examples of such "sound-alike" manifolds.

Student Colloquium: Thursday, March 24th, 12:00 noon in Olin 268

**Stayin' alive with Mathematical Demography, presented by Tom Cassidy (Bucknell University) **

Demographers study characteristics of populations and how these characteristics change over time. Demography is a very broad topic, with applications in economics, biology, history and medicine. I will explain how mathematical demography can advance these fields, with a particular focus on an example from biology.

Student Colloquium: Thursday, March 10th, 12:00 noon in Olin 268

**Dating the Demise of the Dinosaurs, presented by Steve C. Wang (Swarthmore College)**

Why did the dinosaurs go extinct, and when? And how do we know? Most of our knowledge of the history of life comes from the fossil record. But the fossil record is notoriously incomplete, and as a result, potentially misleading. How, then, can we learn anything about life on earth millions of years ago? In this talk I will discuss my research on how we can use statistics to recognize mass extinctions -- such as the one that killed the dinosaurs -- from imperfect clues in the fossil record. Along the way we will explore some seemingly unrelated topics, including how the Allies estimated the strength of enemy forces during World War II.

Student Colloquium: Thursday, March 3rd, 12:00 noon in Olin 268

**The Art of Tomography, presented by Tim Feeman (Villanova University) **

We will look at how an algorithm from linear algebra, called Kaczmarz's Method, can be used to create a CAT scan image from X-ray data." (This will be completely accessible to undergraduates, though some familiarity with vectors and the dot product is helpful.)

Career Panel: Thursday, February 17th, 5:30-6:30 pm in O'Leary 232

**Mathematics Alumni Career Panel Discussion, sponsored by the Mathematics Department and Alumni Relations/Career Development**

This interactive panel discussion will examine different career paths of Bucknell alumni. Come hear advice and perspectives from Bucknell alumni who will discuss their work and available opportunities, also with a question and answer period. The event is followed by a networking reception. Food and drinks will be served.

Student Colloquium: Thursday, February 10th, 12:00 noon in Olin 268

**"Protection for Sale: A Mathematical Model of How Politics and Lobbying Affect Tariffs", presented by Chris Magee (Bucknell University)**

Grossman and Helpman (1994) develop a mathematical model that explains how tariffs can emerge from a lobbying process in which firms offer campaign contributions to a policy maker in exchange for protection. Empirical estimates of this model offer a puzzling result: governments do not seem to care at all about campaign contributions in setting trade policy; instead trade policies are chosen largely to maximize social welfare. This result contrasts with a long list of government policies (such as the sugar quota) that seem to reduce social welfare. I present the mathematics behind the Grossman and Helpman model and discuss why this puzzling empirical result emerges when the model is estimated. I also show how the puzzle can be resolved if firms free ride on the contributions of others and are not able to sustain perfect cooperation with each other when they lobby the government.

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