Tuesday, April 11, 2017 - 14:05 , Location: Skiles 006 , Dmitri Burago , Penn State , Organizer: Igor Belegradek
Series: Other Talks
Rhythm is a great thing. It therefore follows that several rhythms at once is even greater. Learn 2:3, 3:4, and 4:5, and a little bit about fractions. Polyrhythms when sped up, lead to harmony and scales. Slower polyrhythms happen in celestial mechanics. A little bit of music, a little bit of mathematics.
Monday, April 10, 2017 - 14:00 , Location: Skiles 006 , Peter Lambert-Cole , Indiana University , Organizer: John Etnyre
A foundational result in the study of contact geometry and Legendrian knots is Eliashberg and Fraser's classification of Legendrian unknots They showed that two homotopy-theoretic invariants - the Thurston-Bennequin number and rotation number - completely determine a Legendrian unknot up to isotopy. Legendrian spatial graphs are a natural generalization of Legendrian knots. We prove an analogous result for planar Legendrian graphs. Using convex surface theory, we prove that the rotation invariant and Legendrian ribbon are a complete set of invariants for planar Legendrian graphs. We apply this result to completely classify planar Legendrian embeddings of the Theta graph. Surprisingly, this classification shows that Legendrian graphs violate some proven and conjectured properties of Legendrian knots. This is joint work with Danielle O'Donnol.