Past Events
[Geometry, Topology and Dynamics Seminar] On the nonlocal curvature of surfaces and curves by Dr. Brian Seguin (Loyola University Chicago)
2019-01-29Abstract: Motivated by generalizations of the Ginsburg-Landau energy and the diffusion equation in which derivatives are replaced by fractional derivatives, Caffarelli, Roquejoffre, and Savin studied the minimizers of a fractional perimeter functional on sets involving a parameter between 0 and 1. Such minimizers have to satisfy a pointwise condition on their boundary, which can be used to define a notion of nonlocal mean-curvature. This definition only holds for surfaces which are the boundary of a set. I will describe how to define a nonlocal notion of mean-curvature for any surface by introducing a fractional area functional and considering its minimizers. Moreover, I will describe how these ideas can be extended to curves by defining a fractional length and an associated nonlocal curvature for a curve.
[Geometry, Topology and Dynamics Seminar] Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4) by Dr. Tadayuki Watanabe (Shimane University)
2019-01-24Abstract: The rational homotopy groups of the group Diff(S^4) of self-diffeomorphisms of S^4 with the C^\infty-topology. We present a method to prove that there are many 'exotic' non-trivial elements in the rational homotopy groups of Diff(S^4) parametrized by trivalent graphs. The proof utilizes Kontsevich's characteristic classes for smooth disk bundles and a version of clasper surgery for families. In fact, these are analogues of Chern-Simons perturbation theory in 3-dimension and clasper theory due to Goussarov and Habiro.
[Geometry, Topology and Dynamics Seminar] The General 4 dimensional Light Bulb Theorem by Dr. David Gabai (Princeton University)
2019-01-23[Geometry, Topology and Dynamics Seminar] David Gabai (Princeton University) will talk about the General 4 dimensional Light Bulb Theorem.
[Geometry, Topology and Dynamics Seminar] The Seiberg-Witten equations and topology by Dr. Hirofumi Sasahira (Kyushu University)
2019-01-16Abstract: In this talk, I will explain basics of the Seiberg-Witten equations and applications to topology. I will also mention about recent progress in the Seiberg-Witten Floer theory.
[Seminar] "Exploring Gridworlds with State Complexes" by Tom Burns
2018-12-07Tom Burns, currently a rotation student in the Topology and Geometry of Manifolds (Tsvietkova) Unit, will present a talk on a research project done as part of his lab rotation. The title is "Exploring Gridworlds with State Complexes".
All are welcome.
