Megumi Harada

Department of

Mathematics and Statistics

McMaster University

Photo credit: Jason Krygier-Baum

Office: Hamilton Hall Room 325 (full contact information)

Office hours: Tuesdays 3:00-5:00PM Wedsnesdays 10:30-11:20AM, or by appointment.

E mail: Megumi.Harada at math.mcmaster.ca

Teaching in the Fall term 2009

I will be teaching

  • Math 2R03, Linear Algebra II, and
  • Math 3E03, Abstract Algebra I.
Course webpages can be accessed through the E-Learn at Mac website.

Handouts for 2R03, Linear Algebra II:

Goings-on

Check my Math Activities page for research/math events I'm organizing or am otherwise a part of.

  • I will be spending the Spring (January-May) 2010 semester at MSRI (Mathematical Sciences Research Institute) in Berkeley, taking part in the ``Symplectic and Contact Geometry and Topology'' year-long program.
  • I gave a McMaster Origins Institute Colloquium titled ``Visualizing geometry: the shape of space in higher dimensions'' in March 2009. The video recording is available through McMaster or via iTunes University.
  • My colleague Julianna Tymoczko (U Iowa) and I have received a ``travel grant for research collaboration'' to study the equivariant topology of Hessenberg varieties from the Midwest Topology Network, an NSF-funded organization supporting topologists in the U.S. Midwest.
  • I received the Ontario Early Researcher Award in 2008, a 5-year award given by the Ontario Ministry of Research and Innovation to young researchers in the province.
  • As representatives of the McMaster Department of Math and Stats, one of my former students (Carolyn Junkins) and I participated in the making of an on-line video ``Stories of Science'' series (made by the Science Media lab) for the Faculty of Science at McMaster. See the results at this Science at Mac site.
  • I participated in Dr. George Gadanidis' (Faculty of Education, U Western Ontario) Windows into Elementary Mathematics project (website hosted by the Fields Institute), an on-line resource for elementary-school mathematics teachers, via an exploration of spherical geometry, plus an interview about what it's like to be a mathematician. A current draft of the on-line educational module (not the final cut) is available here.
  • I received the University Faculty Award in 2007, a 5-year research award given by NSERC to young women faculty in mathematics and the sciences.
  • I was one of 10 finalists in TV Ontario's "Best Lecturer in Ontario 2005 " (the "intellectual's Canadian Idol") competition. As part of the competition for the final winner, I gave a televised public lecture on mathematics titled "Symmetry: Nature, Art, and Mathematics," aired October 2005 on TV Ontario's Big Ideas program. You can download the audio (sorry, no video is available) of my lecture here .
  • During the 2005-2006 academic year, I regularly appeared on TV Ontario's "More 2 Life" program with host Mary Ito, discussing mathematics in everyday life.

Research Interests

My research is in symplectic and hyperkahler geometry. More specifically, I compute topological invariants, such as cohomology and K-theory, of spaces with such structure. Symplectic geometry is the mathematical framework of classical physics; hyperkahler manifolds are symplectic manifolds with extra structure, and are of particular recent interest due to their connections to theoretical physics.

I am mainly concerned with the theory of symmetries of manifolds with these structures, as encoded by a Hamiltonian Lie group action, i.e. there exists a moment map on M encoding the action by Hamiltonian flows. Such group actions on symplectic and hyperkahler manifolds arise naturally in the context of physics, representation theory, and algebraic geometry. To a Hamiltonian space, one associates a symplectic (hyperkahler) quotient, which inherits a symplectic (hyperkahler) structure from the original manifold. The main theme of my recent research is the study of the topology and equivariant topology of these quotients.