BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gian Michele Graf (ETH Zurich) DTSTART:20260605T190000Z DTEND:20260605T200000Z DTSTAMP:20260525T025051Z UID:MathPic/151 DESCRIPTION:Title: An elementary derivation of the periodic table of topological matter \nby Gian Michele Graf (ETH Zurich) as part of Mathematical Picture Langua ge Seminar\n\nInteractive livestream: https://harvard.zoom.us/j/779283357\ nView-only livestream: https://www.youtube.com/channel/UCrlS3CuPlahBp_M46f DaWVw/videos\nLecture held in Jefferson 356.\n\nAbstract\nBand insulators and superconductors are of topological interest\, depending on the dimensi on of physical space and on their symmetry classes. Within the context of the independent particle approximation\, their topological content is summ arized by a periodic table (due to Kitaev and precursors) that lists the i ndex groups for each dimension and each of 10 classes. Various derivations of the table have been provided. The talk is about one more\, prompted by the striking feature that groups are constant along the diagonals of the table. That observation calls for a corresponding proof\, which will be pr ovided by an isomorphism between groups that are diagonal neighbors. The d etails of the isomorphisms depend on the pair of classes involved. For ins tance\, if the domain of that map relates to a non-chiral class (and hence the target to a chiral class in the next lower dimension)\, the map itsel f can be understood quite simply by way of an analogy: A real bundle on a circle can be pictured as a strip\, either as a Möbius strip or an ordina ry one. The isomorphism is the one mapping the bundle to the clutching map that comes from cutting the circle. (Joint work with F. Santi).\n LOCATION:https://researchseminars.org/talk/MathPic/151/ URL:https://harvard.zoom.us/j/779283357 URL:https://www.youtube.com/channel/UCrlS3CuPlahBp_M46fDaWVw/videos END:VEVENT END:VCALENDAR