BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benedikt Kolbe (INRIA\, Nancy) DTSTART:20210416T050000Z DTEND:20210416T060000Z DTSTAMP:20260423T024448Z UID:APATG/22 DESCRIPTION:Title: T he mapping class group\, hyperbolic tilings\, and structures in three-dime nsional Euclidean space\nby Benedikt Kolbe (INRIA\, Nancy) as part of Asia Pacific Seminar on Applied Topology and Geometry\n\n\nAbstract\nWe di scuss some recent breakthroughs concerning an inherently interdisciplinary project between mathematicians\, physicists\, chemists\, and computer sci entists that attempts to produce structures in three-dimensional Euclidean space from graph embeddings on triply-periodic minimal surfaces. The mapp ing class group (MCG) of a surface is the group of homeomorphisms of the s urface modulo isotopies of the surface. It has a long history in topology and represents an active area of research. We present in this talk a recen t new application of MCGs relevant for crystallography\, materials science \, structure formation\, and knot theory. We first explain the necessary s et-up for the construction of candidates for new crystalline structures fr om graph embeddings on surfaces\, where intrinsically hyperbolic triply-pe riodic minimal surfaces in three-dimensional Euclidean space are used as a scaffold for promising three-periodic structures. We then give an overvie w of new results on MCGs that facilitates an enumeration of isotopy classe s of graph embeddings with a given group of symmetries. Lastly\, we presen t a catalogue of three-dimensional structures that have resulted from this project and explain some of the difficulties involved as well as future d irections.\n LOCATION:https://researchseminars.org/talk/APATG/22/ END:VEVENT END:VCALENDAR