Mathematical Sciences

School of Natural Sciences & Mathematics

Geometry, Topology, Dynamical Systems Seminar, AY 12-13

Feb. 22 Dr. Rachinskiy Mathematical Sciences, UTD A mechanism of mode locking in slow-fast delayed systems

Feb. 15 M. Dabkowski Mathematical Sciences, UTD Kauffman Bracket Skein Module of a 3-manifold

Feb. 8 Zelenko Texas A&M Geometry of nonholonomic distributions with given Jacobi symbol
This talk is devoted to a novel approach to geometry of vector
distribution, based on the ideas from Optimal Control (the colloquium talk
can be considered as an introductory and motivating for this talk but I
will try to make the presentation here independent of the colloquium
talk). This procedure allows one to reduced the problem to the (extrinsic)
differential geometry of curves of flags of isotropic and coisotropic
subspaces in a linear symplectic space. The extrinsic geometry of such
curves is simpler in many respects than the original equivalence problem,
because symbols of curves in flag varieties are simpler algebraic objects
than the classical Tanaka symbols of distributions.

In this way we define another basic invariant of distribution , the Jacobi
symbol which is much coarser than the Tanaka symbol and, more importantly,
discrete and classifiable. Then we describe the unified construction of
the canonical frame for all distributions with given Jacobi symbol in
terms of natural algebraic operations with this symbol.

Dec. 7 A. Phung The number of intersections of plane algebraic curves

Nov. 30 T. Hagge Mathematical Sciences, UTD What is a 3-Manifold?

Nov. 9 M. Dabkowski Mathematical Sciences, UTD Polynomial Knot Invariants

Nov. 2 M. Dabkowski Mathematical Sciences, UTD Why knot?

Oct. 26 V. Dragovic Mathematical Sciences, UTD Siebeck-Marden Theorem