過去の記録 ~04/24次回の予定今後の予定 04/25~

担当者 河野俊丈



17:30-18:30   数理科学研究科棟(駒場) 122号室
*The date and room have changed.
Gábor Domokos 氏 (Hungarian Academy of Sciences/Budapest University of Technology and Economics)
'Oumuamua, the Gömböc and the Pebbles of Mars (ENGLISH)
[ 講演概要 ]
In this talk I will concentrate on two examples from planetary science, which made the headlines in recent years to highlight the power and significance of nonlinear geometric partial differential equations (PDEs) explaining puzzles presented by Nature. One key link between PDE theory of shape evolution and natural phenomena is the Gömböc, the first mono-monostatic object whose existence was first conjectured by V.I. Arnold in 1995. I will explain the connection and illustrate the process how mathematical models of Nature may be identified.
[ 講演参考URL ]


15:00-17:20   数理科学研究科棟(駒場) 122号室
J. Scott Carter 氏 (University of South Alabama / Osaka City University)
Part 1 : Categorical analogues of surface singularities
Part 2 : Prismatic Homology (ENGLISH)
[ 講演概要 ]
Part 1 :
Isotopy classes of surfaces that are embedded in 3-space can be described as a free 4-category that has one object and one weakly invertible arrow. That description coincides with a fundamental higher homotopy group. The surface singularities that correspond to cusps and optimal points on folds can be used to develop categorical analogues of swallow-tails and horizontal cusps. In this talk, the 4-category will be constructed from the ground up, and the general structure will be described.

Part 2 :
A qualgebra is a set that has two binary operations whose relationships to each other are similar to the relations between group multiplication and conjugation. The axioms themselves are described in terms of isotopies of knotted trivalent graphs and the handle-body knots that are represented. The moves naturally live in prisms. By using a generalization of the tensor product of chain complexes, a homology theory is presented that encapsulates these axioms and the higher order relations between them. We show how to use this homology theory to give a solution a system of tensor equations related to the Yang-Baxter relation.
[ 講演参考URL ]