WIMIN

Plenary Talks

 

Lisa Traynor, Bryn Mawr College.

An Unknotting Number in the World of Contact Topology

Mathematical knots can be modeled by tangled, closed loops of string in 3D-space. Legendrian and transverse knots are smooth knots that satisfy an extra geometric condition imposed by a contact structure. Many ideas for invariants for smooth knots can be transported to the setting of contact manifolds to study Legendrian and transverse knots.  For example, the unknotting number is a classic and basic measure of complexity for smooth knots. I will introduce an unknotting number for transverse knots and explain how an ancestor-descendent relationship for smooth knots can be modified to define transverse family trees.   Portions of this work was done with an undergraduate student Blossom Jeong (BMC 2020).  

Lisa Traynor is Professor of Mathematics and the Class of 1897 Professor of Science at Bryn Mawr College.  Her research focuses on contact and symplectic topology, which concern the flexibility and rigidity of knotted objects under particular geometric constraints.  After completing her PhD at Stony Brook, she was a postdoc at the Mathematical Sciences Research Institute (MSRI), Stanford, and at the Institut Henri Poincaré, and has been a research visitor at MSRI, the Institute for Advanced Study (IAS), and the American Institute of Mathematics.  She has also been involved in many programs supporting women in the mathematical sciences, including the Women in Mathematics Program at the IAS, the Women in Geometry Workshops, and the WiSCon (Women in Symplectic and Contact Topology) Workshop.
 

 

Lidia Mrad, Mount Holyoke College.

A Spatial Agent-Based Model for Mosquito Dispersal

Mosquito-borne diseases pose an increasing health threat, not only in tropical regions, but also in new areas such as North America and Europe. Aedes aegypti is a mosquito that transmits dangerous viruses, including dengue and zika. Understanding the local spatial dispersal of Aedes aegypti can lead to better intervention strategies for disease control. I will present a diffusive agent-based model for mosquito dispersal, focusing on methods that accurately determine the associated diffusion coefficient. I will highlight some mathematical tools needed for designing the computational code, as well as techniques for analyzing data resulting from simulations that closely mimic field experiments. Our results refine the interpretation of field data and suggest improvements in their measurement.

Lidia Mrad is an Assistant Professor of Mathematics at Mount Holyoke College.  Her research spans theoretical and applied mathematics, and draws on techniques from partial differential equations, calculus of variations, and agent-based modeling, to study applied questions from the structure of liquid crystals and population dynamics.  She received her PhD from Purdue University, and held a postdoctoral position at the University of Arizona, before joining the faculty at Mount Holyoke. She is active in many outreach programs, particularly related to K12 education and women in math,  and has taught courses for Jumpstart, MathPath, and was a facilitator for the Tucson Math Teachers’ Circle.