Bryn Mawr College Math Department: Research

Research

Faculty Research
Titles of Recent Ph.D. Dissertations
Titles of Recent M.A. Theses
Titles of Recent A.B. Honors Theses

Faculty Research

Victor Donnay

My area of research is Dynamical Systems, particularly systems that exhibit chaotic (ergodic) behaviour. I work on geometric systems such as geodesic flow on surfaces and billiard motion. I study the mechanisms that produce chaotic behavior as well as trying to understand the transition from chaotic to non-chaotic motion.
I am interested in bringing the beauty and excitement of mathematics to the general public; Bryn Mawr students working with me have made a computer generated movie of the Costa Surface that was exhibited at the Maryland Science Center, an interactive web site about chaotic billiard motion and computer generated pictures of surfaces whose geodesic flow is chaotic. More information about these and other projects can be found at this website: http://www.brynmawr.edu/math/people/donnay/

Helen G. Grundman

My mathematical research interests span a wide range of topics in the areas of algebra and number theory. My primary work is in the areas of algebraic number theory and computational algebraic geometry. Specifically, my research involves exploiting the connections between Hilbert modular varieties and certain algebraic number fields, studying the fields to determine classifications of the varieties. Additional research topics include:

Galois embedding problems: characterizing fields that have field extensions with specified small 2-groups as Galois groups.
Elementary number theory: discovering properties of the integers and interesting subsets of the integers, such as Niven numbers and happy numbers.
Modular forms: studying properties of multiplier systems of functions similar to modular functions arising from considerations of modular equations.
Diophantine equations: using algebraic number theory and computational methods to solve Diophantine equations over number rings.

Lisa Traynor

My research interests are in geometry and topology. More specifically, I work in symplectic topology and contact geometry. I have worked on the symplectic camel problem, symplectic homology, symplectic packings, and legendrian knots. To learn more about the types of problems that interest me, click on the research interests link below.

http://www.brynmawr.edu/math/people/traynor/research.html

Titles of Recent Ph.D. Dissertations

Generating Family Invariants for Legendrian Links, Jill Jordan, December 2005. Advisor: Lisa Traynor.
Smooth Approximation of Singular Perturbations of the Laplacian, Walter Huddell, 2002. Advisor: Rhonda Hughes.
The Arithmetic Genus of Threefolds Defined by Extended Hilbert Modular Groups, Amber Salzman, 2002. Advisor: Helen Grundman.
Symplectic Packings of Cotangent Bundles of Tori, Jean Mastrangeli, 1997. Advisor: Lisa Traynor.
Sewn up and Surgered Swen up Link Exteriors: Surgery Presentations & Formulas for Lescop’s Invariant, Gowri Meda, 1997. Advisor: Paul Melvin.

Titles of Recent M.A. Theses

Thomas's Work on Split Families of Cubic Thue Equations, Wen Gao, 2007. Advisor: Helen Grundman.
Arnold's 4-Cusp Conjecture, Devasish Majumdar, 2005. Advisor: Lisa Traynor.
Tangling Legendrian Knots, Cristina Nistor, 2005. Advisor: Paul Melvin.
The Arnold Invariants of Plane Curves, Emi Arima, 2005. Advisor: Lisa Traynor.
Class Numbers and Other Numerical Invariants of Imaginary Quadratic Fields, Laura Hall, 2004. Advisor: Helen Grundman.
Morse Theory, Kim Urso, 2004. Advisor: Lisa Traynor.
Producing Positive Lyapunov Exponents on the Sphere, Gina Calderaio, 2003. Advisor: Victor Donnay.
A Simple-Homotopy Classification of Certain CW-Complexes by Reidemeister Torsion, Ben Allen, 2002. Advisor: Paul Melvin.
Constructing Brownian Motion with Wavelets, Beth Campbell, 2002. Advisor: Rhonda Hughes.
Chekanov’s Decomposition Invariant for Legendrian Knots, Jane Holsapple, 2002. Advisor: Lisa Traynor.
Power Basis Generators in Cyclotomic Fields, Jill Jordan, 2002. Advisor: Helen Grundman.
Weight Systems, Rachael Thomas, 2001. Advisor: Paul Melvin.
On Galois Realizability of Groups of Order 32, Grisha Stewart, 2001. Advisor: Helen Grundman.

Titles of Recent A.B. Honors Theses

Isospectral Lattices and Quadratic Forms, Katie Haymaker, 2007. Advisor: Paul Melvin.
Intrinsic Linking Numbers of Complete Graphs, Cara Petonic, 2007. Advisor: Paul Melvin.
Thurston-Bennequin Numbers of Legendrian Links, Danny Tang, 2007. Advisor: Paul Melvin.
A Wavelet Analysis of Event Related Potentials, Ananya Misra and Sarah Williams, 2003. Advisors: Rhonda Hughes and Jeana Mastrangeli.
Valuation of American Barrier Options, Alexis Iwanisziw, 2003. Advisors: Leslie Cheng and Walter Stromquist.
The Valuation of Asian Options, Ayako Fukui, 2002. Advisor: Leslie Cheng.
Elements of Representation Theory, Emma Haddad, 2002. Advisor: Paul Melvin.
Equidissections of Polygons, Emily Turner, 2002. Advisor: Jeana Mastrangeli.
Fundamental Units in Quartic Rings With Two Real and Two Complex Embeddings, Juliana V. Belding, 2001. Advisor: Helen Grundman.
A New Example of an Embedded Surface with Chaotic Geodesic Flow, Gina Calderaio, 2001. Advisor: Victor Donnay.
Random Walks on String Links, Debra Ciucci, 2001. Advisor: Paul Melvin.
New Solutions of a Diophantine Equation, Laura L. Hall, 2001. Advisor: Helen Grundman.
Expanding the Definition of a Horseshoe, Emily Hill, 2001. Advisor:Victor Donnay.
On the Unknotting Numbers of Rational Knots, Anna Hu, 2001. Advisor: Paul Melvin.
The Chaotic Dynamics of the Three-Obstacle Billiard Map, Theresa Y. Kim, 2001. Advisor: Victor Donnay.
Groundwater Flow: A Mathematical Model. A look at groundwater flow in the Canal Creek Aquifer of the Aberdeen Proving Ground, Maryland, Marisha Kirtane, 2001. Advisor: Rob Manning.