For more information about this meeting, contact Sergei Tabachnikov.
|Title:||How to Tie Your Unicycle in Knots: An Introduction to Legendrian Knot Theory|
|Speaker:||Josh Sabloff, Haverford College|
|You can describe the configuration of a unicycle on a sidewalk using three coordinates: two
position coordinates x and y for where the wheel comes into contact with the ground and
one angle coordinate t that describes the angle that the direction the wheel makes with
the x axis. At a given point (x,y,t), the instantaneous motions of the unicycle (if we do not
want to scrape the tire by trying to move sideways) are constrained to moving in the
direction the wheel is pointing, turning the wheel without moving forward, or some
combination of the two. As you pedal around, you trace out a path in (x,y,t)-space that
obeys the constraints at every point.
The system of constraints at every point in (x,y,t)-space is an example of a "contact
structure," and a path that obeys the constraints is a "Legendrian curve." If the curve
returns to its starting point, then it is called a "Legendrian knot." A central question in
the theory of Legendrian knots is: how can you tell two Legendrian knots apart? How many
are there? In other words, how many ways are there to parallel park your unicycle?
There will NOT be a practical demonstration.|
Room Reservation Information
|Date:||10 / 30 / 2008|
|Time:||02:30pm - 03:20pm|