Research
Our Faculty's Recent Work
Oscar Fernandez spent the summer working on several research projects and presenting his work at conferences. Prof. Fernandez supervised the research of Ana Plascencia-Casillas ('14) on ``The Quantum Mechanics of a Nanocar,'' and their work yielded results that will be submitted for publication later this year. In July he presented some of his prior work at the 9th AIMS Conference in Orlando, FL, where he also continued his work with collaborators on existing projects, including the extension of the topological conclusions of the Arnold-Liouville theorem of Hamiltonian mechanics to the nonholonomic context. He presented his preliminary work on this topic at a conference on Geometry, Mechanics, and Control in Salamanca, Spain in late August. Prof. Fernandez also relocated to Newton Center, buying a condo within walking distance of the local J.P. Licks. He and his wife are now trying to cope with the late-night frozen yogurt cravings.
In July, Megan Kerr traveled to Marburg, Germany to participate in a Workshop on Geometric Structures on Manifolds and their Applications, at the Castle Rauischholzhausen. Along with co-author Andreas Kollross of the Universität Stuttgart, she recently submitted two papers, one of which will will appear in the Annals of Global Analysis and Geometry soon. In addition, she has been working on a project with Kristopher Tapp, of Saint Joseph's University, Philadelphia, which they intend to submit for publication soon. Outside of mathematics, she enjoyed a summer of traveling, gardening, and spending time with family.
Karen Lange enjoyed celebrating the 100th anniversary of the birth of Alan Turing with other computability theorists in Oberwolfach, Germany, Cambridge, England, and Washington DC. She had two papers accepted this past year including her paper with Peter Cholak and Peter Gerdes ``On n-tardy sets", which appeared in Annals of Pure and Applied Logic. This past summer she worked with collaborators at the University of Konstanz and taught a class on randomness at MathCamp, a summer program for highly talented high school students hosted this summer at the University of Puget Sound.
Andrew Schultz continued his work on Galois cohomology during the summer by investigating the appearance and interconnections between the nonabelian groups of order p3 as Galois groups. This work generalizes some of the classic results about these groups and provides a new framework for understanding questions of this type. He and his coauthors anticipate submitting this work for publication later in the fall. He also started a new line of research which studies certain deformations of Weyl denominator formulae from a statistical mechanical interpretation of alternating sign matrices. Building on this work, Prof. Schultz will be guiding Ran Ji ('13) through a senior thesis in which she counts alternating sign matrices which are associated to particular classical Lie groups. He is also working with Farrah Yhee ('14) on a sharpness result related to a q-binomial congruence he proved in the summer of 2010.
Ann Trenk travelled to Halifax, Nova Scotia in June 2012 to attend the SIAM Conference on Discrete Mathematics. She presented the talk ``Unit Interval Graphs of Mixed Intervals’’ based on joint work with Alan Shuchat, Randy Shull and Lee West ’11. In the spring she finished a project with coauthor Karen Collins of Wesleyan University and they submitted the paper, ``A Nordhaus-Gaddum Theorem for the Distinguishing Chromatic Number’’ for publication. She also collaborated with students from her classes to develop hands-on exhibits in mathematics that they brought to the Hardy Elementary School’s ``Science Rocks’’ night.
Ismar Volic is returning from a productive summer during which he traveled to Bosnia and Tunisia to deliver talks at conferences and meet with coauthors. The paper he coauthored with Pascal Lambrechts, "Formality of the little N-discs operad" was accepted for publication in the Memoirs of the American Mathematical Society and the paper he coauthored with Brian Munson, "Configuration space integrals and the cohomology of the space of homotopy string links" was submitted for publication. He also continues to work on the book "Cubical homotopy theory", also a joint project with Brian Munson, which will be published by Cambridge University Press in 2014. He looks forward to several upcoming trips to conferences, including a visit to the University of Tokyo.
