Our Faculty's Recent Work
Stanley Chang returns to the classroom after a semester exclusively doing research on the Wellesley Brachman-Hoffman Fellowship. This past summer, he completed two articles "Positive scalar curvature and a new index theorem for noncompact manifolds" and "Modular symbols and the topological nonrigidity of arithmetic manifolds." He is currently working to complete his textbook (with coauthor Shmuel Weinbeger) titled "A course in surgery theory," under contract with Princeton University Press. Stanley is the current holder of the Whitehead Associate Chair of Critical Thought.
Oscar Fernandez spent the summer toiling over what color to paint the baby room, what crib to buy, and what to name the baby (girl) he and his wife are expecting in early December. When he wasn't deciphering pages long building instructions, Oscar was busy continuing his research in geometric and nonholonomic mechanics. He submitted a grant to the NSF's applied mathematics division to study the quantum mechanics of nonholonomic systems. Some results have already emerged from his work in this direction, including possible implications for the quantum mechanics of "nanocars," which he is studying with Prof. Radhakrishnan (chemistry department). Oscar also spent time putting the finishing touches on his book, titled "Everyday Calculus," that will be published by Princeton press in May. Finally, he took a break from painting and attended the Applied Math, Modeling, and Computational Science conference in August, where he gave a talk on the application of the Poincare-Hopf theorem to questions of integrability in nonholonomic mechanics.
Megan Kerr had two research papers in global Riemannian geometry appear this year (in March and September). Both were on nonnegatively curved homogeneous metrics, joint work with Andreas Kollross (Universität Stuttgart, Germany). She also submitted a paper, joint with Kris Tapp (Saint Joseph's University), on quasi-positive curvature conditions. In June, Megan traveled to Cabo Frio, Brazil for a workshop entitled Encounters in Geometry. In July, she submitted a paper on new examples of non-symmetric Einstein solvmanifolds of negative Ricci curvature, and started a joint project with Tracy Payne (Idaho State University). She looks forward to trips in October, first to Union College, where she will be speaking at a conference session on Special Geometric Structures, and then to Dartmouth College, to their Geometry and Topology Seminar.
Karen Lange spent the past year working on projects in computable structure theory and classical computability theory. Her papers "Degrees of orders on torsion-free abelian groups" (with Asher Kach and Reed Solomon) and "Real closed exponential fields" (with Paola D'Aquino, Julia Knight, and Salma Kuhlmann) were published in the Annals of Pure and Applied Logic and Fundamenta Mathematicae respectively. She also co-organized the fall and spring meetings of the Northeastern Recursion and Definability Seminar. This summer she visited collaborators at the University of Konstanz and the Second University of Naples, and worked on a summer undergraduate research project with Abigail Raz ('14) and Rebecca Scanlon ('15). She also spoke at the annual meeting of the Association for Symbolic Logic and at a workshop on computable stability theory at the American Institute of Mathematics (AIM).
Martin Magid continued his work in differential geometry this summer. He worked with Oscar Palmas (UNAM) and Martha Dussan (University of São Paulo) on timelike surfaces in product manifolds. He also began a project with Erhan Güler (Bartin University) studying minimal surfaces in four space. Finally, his article “The Björling problem for timelike surfaces in R42" was published in the Journal of Geometry and Physics.
Andrew Schultz had two papers accepted for publication last year: p-groups have unbounded realization multiplicity (with Jen Berg) and A generalization of the Gaussian formula and a q-analog of Fleck's congruence (with Robert Walker). He divided his summer research time between two projects. One of them is a continuation of the work he has previously done on Galois modules. One component of this project (which is slotted for submission for publication this fall) discusses how some known results on the appearance of non-abelian Galois groups of order p3 can be generalized to infinite families of p-groups. The second family of projects that he is working on deals with realizations of some classical Weyl denominator formulas using the combinatorial machinery of ice models. This projects extends some work already completed for the family An to the families Bn, Cn and Dn, and is connected to the thesis project he supervised with Ran Ji last year.
Fred Shultz visited the University of Guelph and the Institute of Quantum Computing in Waterloo during August 2012, where he gave talks on "Finding decompositions of separable states" (joint work with Prof. Erik Alfsen). The visit to Guelph led to a collaboration with some mathematicians there, and then to a paper "Uniqueness of quantum states compatible with given measurement results," which appeared in summer 2013 in Physical Review. In January he visited the University of Oslo, continuing his collaboration with Prof. Erik Alfsen. In May he gave a talk on "Complete positivity of the map from a basis to its dual basis" at the annual GPOTS (Great Plains Operator Theory Symposium), held this year in Berkeley. (The Great Plains is interpreted liberally!) The material in this talk was based on a paper of Prof. Shultz and Prof. Vern Paulsen (U. Houston) which appeared in the Journal of Mathematical Physics in July, 2013. When not involved in mathematics, Prof. Shultz can often be found either on the golf course or playing tennis.
Ann Trenk continued work in characterizing the class of Unit Mixed Interval Graphs, together with Alan Shuchat and Randy Shull, and gave a talk on this subject at the AMS Sectional Meeting at Rochester Institute of Technology. Together with coauthor Karen Collins of Wesleyan University, she revised the paper, "A Nordhaus-Gaddum Theorem for the Distinguishing Chromatic Number," which will appear in the Electronic Journal of Combinatorics, and began work on a new project with Karen Collins. Ann served as an outside reviewer for the mathematics department at Bates College where she can report that it was quite cold in February 2012. In the world of teaching, Ann taught Math 205 for the first time ever in Fall 2012 and learned to appreciate Green’s Theorem. 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 Night.
Ismar Volic is returning from a productive summer during which he traveled to Poland to deliver a talk at a conference and meet with coauthors. The paper he coauthored with Brian Munson, "Cosimplicial models for spaces of links" was accepted for publication in the Journal of Homotopy and Related Structures and the paper he coauthored with Robin Koytcheff and Brian Munson, "Configuration space integrals and the cohomology of the space of homotopy string links" was accepted for publication in Journal of Knot Theory and Its Ramifications. He 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 2015 and looks forward to several upcoming trips, including to Dubrovnik, Croatia, where he is coorganizing a conference on "K-theory, manifolds, and related topics".