BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tomoo Yokoyama (Kyoto University of Education) DTSTART:20201009T050000Z DTEND:20201009T060000Z DTSTAMP:20260423T004143Z UID:APATG/8 DESCRIPTION:Title: To pological flow data analysis and its applications to Reeb graphs of Morse functions\nby Tomoo Yokoyama (Kyoto University of Education) as part o f Asia Pacific Seminar on Applied Topology and Geometry\n\n\nAbstract\nIn this talk\, we introduce topological methods to analyze flow data. These m ethods are based on dynamical systems and Morse theory. So\, first\, we re view the results of generic embeddings of closed surfaces in the three-dim ensional Euclidean space and explain the relation between Morse functions and Hamiltonian vector fields on surfaces. In particular\, such embeddings are classified by a finite complement invariant\, call a molecular. Secon d\, we review topological results in flows on surfaces. Third\, we review our complete invariant\, called a COT representation\, of 2D Hamiltonian f lows\, its implementation\, and the list of all generic transitions of 2D Hamiltonian flow. Moreover\, we introduce a complete invariant of 2D flows of finite type and their applications to industrial machines. In addition \, as an application of COT representations\, we list all generic transiti ons of Reeb graphs of Morse functions on a sphere. If time allows\, we sho w higher-dimensional results of flows and describe a topological character ization of Morse-Smale flows and a generic transitions between them.\n LOCATION:https://researchseminars.org/talk/APATG/8/ END:VEVENT END:VCALENDAR