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UID:86d78cabed14f3f781337a2a937af5f8
CATEGORIES:Colloquia
CREATED:20260127T114133
SUMMARY:Holonomy in Geometry: History and Current Developments
LOCATION:Hill 705
DESCRIPTION:<p>The concept of ‘holonomy’ originally arose in the late 19th century in m
 echanics as a way to describe motion subject to constraints, such as a ball
  rolling on a table without slipping or twisting.&nbsp; However, its profou
 nd connection with the notion of curvature in differential geometry and gen
 eralizations of ‘conserved quantities’ under parallel translation was reali
 zed quite early in the 20th century, with fundamental contributions by É. C
 artan, J. Schouten, E. Kähler and others in the decades 1910-30.&nbsp; A mo
 re systematic exploration in the 1950s by M. Berger and S.-s. Chern clarifi
 ed its foundations and inspired conjectures such as Calabi’s conjecture abo
 ut compact Kähler manifolds with trivial canonical bundle, famously solved 
 by S.-T. Yau in the 1970s.<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; In
  the last 40 years, there have been many important advances in the so-calle
 d ‘exceptional’ cases, inspired by the desire to extend the ideas and resul
 ts in Calabi–Yau geometry to these cases, with the ultimate goal of applyin
 g such results to physical theories going beyond string theory.<br>&nbsp;&n
 bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The current state of the subject still p
 resents enormous challenges in geometric analysis, topology, and theoretica
 l physics, and I hope to give the audience a sense of this rapidly developi
 ng frontier.</p>
CONTACT:Robert Bryant
DTSTAMP:20260827T005640
DTSTART;TZID=America/New_York:20260304T153000
DTEND;TZID=America/New_York:20260304T163000
SEQUENCE:0
TRANSP:OPAQUE
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