| Colloquia Spontaneous symmetry breaking-a view from derived geometry Owen Gwilliam Department of Mathematics, University of Massachusetts Amherst |
This Colloquium is held in conjunction with the Current Advances in Mathematics seminar group, and is a collaborative work with Dr. Chris Elliott.
Please virtually attend Dr. Gwilliam's Colloquium at 4 PM CDT (UTC-5) via this zoom link
| Colloquia Ropelength Criticality for Knots and Links John Sullivan Institut für Mathematik, Technische Universität Berlin |
In terms of the core curve, the thickness constraint has two parts: an upper bound on curvature and a self-contact condition. The curvature bound is especially difficult to handle, as the curve may fail to be twice differentiable. In the end, we express thickness as the minimum of a compact family of smooth functions in order to apply Clarke's theorem on the derivative of such a minimum.
Using our balance criterion, we can give explicit descriptions of several tight links. The tight configuration of the Borromean rings, for instance, is piecewise smooth with 42 pieces. Even two simply clasped ropes surprising geometric behavior: there is a slight gap between them when they are pulled tight.
Finally, we will consider analogous problems for triply periodic knots and links, and for knot diagrams in the plane.
Please virtually attend Dr. Sullivan's colloquium via this zoom link on Wednesday the 31st at 2:00 PM, CDT (UTC-5).