*STUDENT COLLOQUIUM SERIESThursday - February 1 NOON - OLIN 268 *

**Howard Smith Department of Mathematics Bucknell University **

*Title: "Axiom Systems, Consistency and Completeness"*

*STUDENT COLLOQUIUM SERIESThursday - March 22 NOON - OLIN 268*

**Nicholas Bennett Deep Imaging Program: Mathematics and Modeling Department, Schlumberger-Doll Research (Cambridge, MA) Research Affliliate: Yale University**

*Title: "Imaging Challenges when Placing an Oil Well"*

**Abstract:** Placing an oil well in a layer of the Earth containing hydrocarbons can be challenging. One can easily drill through the layer, overcorrect, and end up with an uneconomic well. The proper placement of wells is also very important when preparing to sequester carbon dioxide in the Earth's subsurface and thereby reduce global warming due to the greenhouse effect.Real-time imaging of the geology around the well, particularly using electromagnetics and acoustics measurements, is critical for decision making while drilling. I will discuss some of the mathematics challenges inherent in this process which are somewhat similar to those found in medical imaging. After the talk, I will also share some of my own experiences along the road towards a career in applied mathematics.

*STUDENT COLLOQUIUM SERIESThursday - March 1 NOON - OLIN 268*

**Ed Sandifer Western Connecticut State University**

** Title: "Euler and the Two Gammas"** Leonhard Euler is responsible for two things we now call "gamma," Gamma the function and gamma, the Euler-Mascheroni constant. Both gammas have their origins in the same letter, Euler's first letter to his mentor Christian Goldbach. We describe how the same ideas led to the two different objects.

Abstract:

*STUDENT COLLOQUIUM SERIESThursday - March 22 NOON - OLIN 268*

**Kathy McKeon Connecticut College**

**Title: "Symmetry Breaking in Graphs"**

**Abstract: **Suppose you have a circular key ring with *n* indistinguisable keys. What's the minimum number of colors required to mark the keys so that they are all distinguishable? This question leads to a vertex coloring problem for graphs. The distinguishing number of a graph is the minimum number of colors required to destroy all symmetries of the graph. In this talk, we'll look at the distinguishing numbers for different families of graphs and at the relationship between the symmetry group and distinguishing number of a graph.

**Distinguished Visiting Professor**

Professor Margaret Smith - University of Pittsburgh

April 1-9, 2007

*Seminar Talk - Thursday - April 5 - OLIN 372 - 4:00*

*Title: "Tracing the development of teachers' understanding of proportionality in a practice-based course"*

**Abstract:** Research suggests that teachers, particularly at the elementary and middle school levels, often have limitations in their knowledge of the mathematical ideas that are central to the curriculum they are teaching. One area that has proven to be particularly problematic for teachers is proportional reasoning. Research indicates that teachers cannot differentiate situations in which the comparisons between quantities is multiplicative rather than additive, that they tend to use additive strategies when multiplicative approaches would be appropriate, and that they do not recognize ratios as a multiplicative comparison. Using implementation and outcome data from a practice-based course, I will trace the development of teachers' understanding of proportionality and the course experiences to which their learning appears to be related. An analysis of pre- and post-test data suggests positive changes in teachers' ability to analyze the nature of the relationships between quantities, to flexibly solve problems that involve proportional relationships, and to provide mathematical justifications for their approaches.

**Distinguished Visiting Professor**

Professor Rachel Levy - Duke University

April 8-14, 2007

**Seminar Talk - Tuesday - April 10 - OLIN 372 - 4:00**

**Title: "Gravity-driven thin film flow with insoluble surfactant: smooth traveling waves"**

**Abstract:**The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant, which lowers the surface tension of the fluid and induces a Marangoni driving force. Traveling waves are obtained for a system of lubrication equations describing the free surface fluid height and the surfactant concentration. The solutions are investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic-degenerate parabolic and admits piecewise linear weak solutions. For any value of the surfactant volume, there is a traveling wave with that volume that is piecewise constant in height and piecewise linear in surfactant concentration. The one-parameter family of traveling waves persists when any or all of the small parameters are nonzero, but the structure has some surprises, which are investigated with a combination of analysis and numerical simulation.

Rachel Levy and Linda Smolka

*STUDENT COLLOQUIUM SERIESThursday - April 19 NOON - OLIN 268*

*Title: "A shocking discovery: nonclassical waves in thin liquid films" *

**Abstract:** When a thin film flows down an inclined plane, a bulge of fluid, known as a capillary ridge, forms on the leading edge and is subject to a fingering instability in which the fluid is channeled into rivulets. This process is familiar to us in everyday experiments such as painting a wall or pouring syrup over a stack of pancakes. It is also observed that changes in surface tension due to a temperature gradient can draw fluid up an inclined plane. Amazingly, in this situation the capillary ridge broadens and no fingering instability is observed. Numerical and analytical studies of a mathematical model of this process led to the discovery that these observations are associated with a nonclassical shock wave previously unknown to exist in thin liquid films.

**Distinguished Visiting Professor**

Professor Stephanie van Willigenburg - University of British Columbia

April 14-21, 2007

*Seminar Talk - Tuesday - April 17 - OLIN 372 - 4:00*

**Title: "A combinatorial classification of skew Schur functions"**

**Abstract:** Littlewood-Richardson coefficients arise in a number of areas including algebraic geometry, algebra, and representation theory. However, computing them is #P-complete. One way to reduce the number of coefficients needed to be computed is to find classes of coefficients that are equal. In this talk we investigate the question of Littlewood-Richardson coefficient equality via the study of skew Schur function equality. More precisely, we define an equivalence relation on diagrams such that two diagrams are equivalent if and only if their corresponding skew Schur functions are equal. When the diagrams are of a certain type this reduces to an equivalence relation on integer compositions. We give a combinatorial interpretation of this integer composition relation and relate it to other known combinatorial objects. If time permits we will also discuss how the combinatorial interpretation can be generalised. No prior knowledge of any of the above is required. This is joint work with a number of people that I will mention including Peter McNamara.

*STUDENT COLLOQUIUM SERIESThursday - April 19 NOON - OLIN 268*

*Title: "Using graphs to cure instant insanity"*

**Abstract:** Graph theory has been used to solve many problems during the past 300 years, from knights touring chessboards to computers mapping the internet. In this talk, we will introduce graphs and use them to solve the puzzle known as Instant Insanity that sold 12m copies in 1966-7.

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