**Student Colloquium: Thursday, January 29, 12:00 noon in 268 Olin Science**

**"Another prisoners' dilemma," John Bourke (Bucknell University)**

**Abstract: **A sadistic prison warden lines up 50 prisoners in a single row, so that each one can see only the prisoners in front of him. He puts a blue or orange hat on each head, then in turn (starting from the back), each prisoner must state the color of his hat, or face execution. If the prisoners agree to cooperate in advance, how many can they save? Chagrined by the lack of executions that followed this test, the warden places an infinite number of prisoners in a row and repeats the "game". How many prisoners will survive this time? We will discuss these questions, and the role of set theory in the second answer.

**Distinguished Visiting Professor, January 12 - 16**

**Corey Dunn, California State University at San Bernardino**

Hosted by Matt Miller.

**Faculty Colloquium: Thursday, January 15, 4:00 p.m. in 372 Olin Science**

**"An Introduction to Curvature in Differential Geometry," ****Corey Dunn (California State University, San Bernardino)**

**Abstract:**There has always been a very deep relationship between the way a surface curves, and the geometry it contains. But rigorously defining an intrinsic notion of curvature has escaped mathematicians until Gauss in 1827, when he proved that inhabitants of a surface may measure its curvature. In this talk, we will discuss the development of curvature on smooth surfaces, and how it effects the geometry of these surfaces. We will also discuss invariants which are built from curvature and how they can distinguish between objects we cannot see.

**Faculty Colloquium: Friday, January 16, 4:00 p.m. in 372 Olin Science**

**"Curvature Homogeneity of Pseudo-Riemannian Manifolds," ****Corey Dunn (California State University, San Bernardino)**

**Abstract:**The metric and curvature tensor of a pseudo-Riemannian manifold is a complicated object, and it holds much of the geometric data the manifold has to offer. If a manifolds is (locally) homogeneous, then it is clear that the curvature tensor at one point is the same as the curvature tensor at any other point. What is somewhat surprising, however, is that the converse does not necessarily hold: there are non-homogeneous manifolds that have the same curvature tensor at each point--these are (proper) curvature homogeneous manifolds. After giving an introduction to the relevant differential geometric objects, we give a survey of relevant results in this field, and discuss several known examples of curvature homogeneous manifolds which are not homogeneous, along with an overview of the techniques one employs when working with these manifolds.

**Distinguished Visiting Professor, January 12 -26**

**Il Bong Jung, Kyungpook National University, South Korea**

Hosted by George Exner.

**Faculty Colloquium: Monday, January 19, 4:00 p.m. in 372 Olin Science**

**"Rank-one Perturbations of Diagonal Operators and Invariant Subspace Problem," ****Il Bong Jung (Kyungpook National University, South Korea)**

**Abstract:** The invariant subspace problem of Hilbert space operators is one of longstanding open problems, which was introduced by J. Von Neumann on 1930. We discuss the invariant subspace problem of operators on Hilbert space of the form T = D + (- , v) u where D is a diagonalizable normal operator and (- , v) u is a rank-one operator. The talk partially answers this open question of at least 30 years duration.

**Faculty Colloquium: Wednesday, January 21, 4:00 p.m. in 372 Olin Science**

**"Weak Hyponormalities of Composition Operators," ****Il Bong Jung (Kyungpook National University, South Korea)**

**Abstract:** There are many operator classes that are weaker than normal operator on Hilbert space. These include quasinormal, subnormal, hyponormal, quasihyponormal, paranormal, normaloid, and spectraloid operators. In this talk, we discuss measure theoretic composition operators in these classes. Our idea provides several interesting models for further research about these areas.

**Student Colloquium: Thursday, February 12, 12:00 noon in 268 Olin Science**

**"How Michael Met Jessica: romance and error detecting codes", Adam Piggott (Bucknell University)**

We retell an old fashioned love story which happens to involve some very pleasant mathematics.

**Economics and Mathematics-Alumni Career Panel, Monday, February 16, 5:00pm in the Gallery Theatre**

"What Can You Do With A Liberal Arts Degree?" is the focus of a recent article by Diana Gehlhaus '04. Diana, a combined Economics and Mathematics major, worked upon graduation from Bucknell as an economist for the Bureau of Labor Statistics. She has recently accepted a position as Policy Analyst for the Export-Import Bank.

Please join Diana and other Mathematics and/or Economics majors for a panel discussion on what you can do with your liberal arts degree. The panelists are:

Diana Gehlhaus Carew '04 - Policy Analyst, Export-Import Bank.

Brandi Herman '02 - MBA candidate, Wharton

John Stith '95 - Senior Data Analyst, Environmental Defense Fund

Lauren Donnelly '05 - Industry Economist, Federal Railroad Administration

Jeffrey Cohen '02 - Mathematics and Economics Teacher, Mercersburg Academy

Refreshments will be served after the discussion.

This event is open to all students and the community. It is sponsored by the Economics Department, Mathematics Department, and Alumni and Career Services

**Distinguished Visiting Professor, February 22 - 28**

**James Wilson, The Ohio State University**

Hosted by Pete Brooksbank.

**Faculty Colloquium: Tuesday, February 24, 4:00 p.m. in 372 Olin Science**

**"How to Find a Direct Product of Groups," James Wilson, The Ohio State University**

**Abstract:**It is easy to create a group by forming the direct product of two groups, but when is a group a direct product of proper nontrivial subgroups? The ﬁrst polynomial-time solution to this question is a surprising mix of group theory, bilinear maps, and commutative rings. Yet, the fundamental steps will be explained using only dihedral groups and matrices.

Student Colloquium: Thursday, February 26, 12:00 noon in 268 Olin Science

**"Game Theory and a simple poker game," Jeff Bowen (Bucknell University, Department of Physics and Astronomy)**

**Abstract: **The Theory of Games as constructed by Von Neumann and Morgenstern originally sought to identify ways to maximize expected positive outcomes in situations where the actual outcome depends on individual choices of several players. In this talk, I will outline their theory of two-person zero-sum games. Then we will, with lots of audience participation, apply the theory to a simple poker game and determine an exact maximal strategy for playing it. Come prepared to do some calculations for the team!

**Faculty Colloquium: Thursday, February 26, 4:00 p.m. in 372 Olin Science**

**"Decomposing p-Groups," James Wilson, The Ohio State University**

**Abstract: **The groups of order p^{7} (of which there are more than 3p^{5}) were classiﬁed in 2006, but there is yet no understanding of the structure of such a quantity of groups. One approach is to introduce a family of decompositions, which generalize central products. A theorem is proved on the uniqueness of these decompositions. Also an asymptotic estimate is provided for the number of decomposable and indecomposable groups (there are roughly equal numbers of each type), and implicit within the theorem's proof is an algorithm which can identify the decompositions of a given p-group. In joint work with P. A. Brooksbank, algorithms of this sort are now computing with groups as large as p^{200}, for any p> 2.

**36th Professor John Steiner Gold Mathematical Competition.**

**Tuesday, March 10 in Trout Auditorium of the Vaughan Literature Building. Registration is at 9:30 a.m. **

### 23rd Annual Workshop on Automorphic Forms and Related Topics,

March 10-13, 2009

For more information, visit the conference webpage.

Image courtsey of Tom Boothby.

**Distinguished Visiting Professor, March 14 - 22**

**Nils Skoruppa, Universität Siegen, Germany**

Hosted by Nathan Ryan.

**Faculty Colloquium: Tuesday, March 17, 4:00 p.m. in 372 Olin Science**

**"Poor Man's Elliptic Curve," ****Nils Skoruppa (Universität Siegen, Germany)**

**Abstract: **Over the last 50 years the theory of elliptic curves became a vast subject with several deep results whose proofs required often very advanced techniques. In this talk we show that conic sections exhibit many parallels to elliptic curves, but have the advantage that corresponding results can be easily deduced from scratch and require only a basic knowledge of projective geometry.

**Student and Faculty Party: Thursday, March 19 at noon in 383 Olin Science**

**Pi-Day 2009**

Due to the inconvenient value of pi (spring break), the department in agreement with the students declares that the value of pi for this year is 3.19 - this Thursday. Come for various Pi's, soda and a contest: who can recite the closest decimal approximation of pi? (Current departmental record by Nicole to around 200 decimal places!)

**Faculty Colloquium: Thursday, March 19, 4:00 p.m. in 372 Olin Science**

**"Finite Quadratic Modules, Representations of SL(2,Z) and Modular Forms****," Nils Skoruppa (Universität Siegen, Germany)**

**Abstract: **Many questions in the theory of automorphic forms require the study of vector valued elliptic modular forms on SL(2,Z), which in turn requires a deeper understanding of representations of the groups SL(2,Z/NZ). Any such representation is contained in a Weil representation, whose theory is intimately connected to the theory of quadratic modules.

Distinguished Visiting Professor, March 21 - 28

**Joe McKean, Western Michigan University**

Hosted by John Kloke.

**Faculty Colloquium: Tuesday, March 24, 4:00 p.m. in 372 Olin Science**

**"Side-by-Side Analyses: Traditional and Robust," ****Joe McKean, Western Michigan University**

**Abstract: **Applied Statisticians often do not use diagnostic tools to check model and quality of fit. Even if they do traditional diagnostics are not robust. They are sensitive to outliers, which can mask their effect. Another way to easily obtain diagnostic information on an analysis is to run several analyses, along with some simple (but robust) diagnostics that detect differences in fits. Besides the traditional (LS) analysis, we suggest running two robust analyses, a highly efficient analysis and a high breakdown analysis. Several examples are given to illustrate this approach. The simple geometry of the robust fits and their robustness properties are briefly discussed.Applied Statisticians often do not use diagnostic tools to check model and quality of fit. Even if they do traditional diagnostics are not robust. They are sensitive to outliers, which can mask their effect. Another way to easily obtain diagnostic information on an analysis is to run several analyses, along with some simple (but robust) diagnostics that detect differences in fits. Besides the traditional (LS) analysis, we suggest running two robust analyses, a highly efficient analysis and a high breakdown analysis. Several examples are given to illustrate this approach. The simple geometry of the robust fits and their robustness properties are briefly discussed.

**Student Colloquium: Thursday, January 29, 12:00 noon in 268 Olin Science**

**"Traffic Circles and Sudoku Puzzles: A Contest in Mathematical Modeling," Mike Lengel '11, Bryan Ward '11 and Ryan Ward'11 (Bucknell University) **

**Abstract: **Which traffic control methods optimize the flow of cars through a traffic circle? How should Sudoku boards be generated to yield puzzles with unique solutions of varying difficulties? These questions were featured in the past two years in the Mathematical Contest in Modeling. We will discuss the general format of the contest, our methodologies and solutions to these problems, and potential improvements to our work.

**Faculty Colloquium: Friday, March 27, 4:00 p.m. in 372 Olin Science**

**"Use of Adaptive Robust R Procedures on Bioequivalence Type Problems," ****Joe McKean, Western Michigan University**

**Abstract: **Adaptive procedures for R estimators of regression coefficients are discussed. Several of these exploit an optimality result for R estimators. Shomrani and McKean (2003) developed an extension of an adaptive procedure for tests in simple 1 ocation models as proposed byHogg, Fisher and Randles (1974). This procedure selects one of a set of scores for the R estimation based on the residuals from an initial fit. It can be used for an analysis but, also, as a method to explore what type of scores are useful for a specified class of problems. Using this procedure and recent results for R estimators in mixed models (Kloke, McKean and Rashid, 2008), we explore the use of R methodology for bioequivalence type problems focusing on the modeling and statistical approaches as mandated by the FDA.

**Distinguished Visiting Professor, April 6 - April 10 **

Nathan Feldman, Washington and Lee University

Hosted by Paul McGuire.

**Faculty Colloquium: Tuesday, April 7, 4:00 p.m. 372 Olin Science**

**"A Unified Approach to some Major Theorems in Topology," ****Nathan Feldman, Washington and Lee University.**

**Abstract: **We shall present a single theorem that has as a corollary several major theorems from topology, including the Stone-Weierstrass Theorem, The Stone-Cech Compactification, The Tychonoff Theorem, the Tietze-Extension Theorem, and a classification of all compactifications of completely regular spaces.

**Student Colloquium: Thursday, April 9, 12 noon in 268 Olin Science**

**"Which Line Best Approximates a Function?" ****Nathan Feldman, Washington and Lee University.**

**Abstract: **One often says that the tangent line for a function f at a point x=a gives the "best approximation" to f near the point a. In one sense this is true, but in another sense it is not. We will discuss how to find the line that is (uniformly) closest to a (convex) function on a given interval.

**Student Colloquium: Thursday, April 23, at 4:00 p.m. in 268 Olin Science**

**"Extreme Waves in Shallow and Deep Water" ****Diane Henderson, William G. Pritchard Fluid Mechanics Laboratory, Penn State University.**

**Abstract: **Extreme waves, including tsunamis in shallow water and rogue waves in deep water, are important phenomena to society because of the damage they can cause to life and property. They also present interesting mathematical challenges to investigators trying to understand and predict them. In this talk, we will discuss some of the mathematical ideas and (laboratory) experimental results used to study and model these waves.

**Annual Math. Department BBQ/Picnic: Tuesday, April 28th, from 4:00pm in Olin/Cassidy Quad **

**Any and all math students and guests, faculty and families are invited. **