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DTSTART:20240310T070000
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DTSTART:20231105T060000
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UID:69f92eb0a392f
DTSTART;TZID=America/Toronto:20240821T130000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240821T141500
URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-112
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:JACQUES VAN WYK\n\nAn Introduction to Generalised Geometry\n\nG
 eneralised geometry is a field in differential and complex geometry\nin wh
 ich one views the direct sum TM ⊕ T*M instead of TM as the\nbundle assoc
 iated to a manifold M. Generalised geometry has seen great\nsuccess in act
 ing as a unifying framework in which structures defined\non TM and T*M can
  be viewed as specific instances of structures\ndefined on TM ⊕ T*M. For
  example\, almost complex structures and\npre-symplectic structures can bo
 th be viewed as generalised almost\ncomplex structures\, a certain kind of
  automorphism of TM ⊕ T*M.\n\nIn this talk\, I will give an introduction
  to generalised geometry. I\nwill show TM ⊕ T*M comes with an intrinsic 
 non-degenerate bilinear\nform. I will introduce the Dorfman bracket on Γ(
 TM ⊕ T*M)\, an\nanalogue of the Lie bracket\, which together with the af
 orementioned\nbilinear form gives TM ⊕ T*M the structure of a Courant al
 gebroid. I\nwill define generalised almost complex structures in this sett
 ing\, and\nshow how almost complex structures and pre-symplectic structure
 s can\nbe viewed as generalised almost complex structures. I will introduc
 e\ngeneralised metrics and generalised connections\, and if time permits\,
 \nI will discuss integrability of generalised almost complex structures\ni
 n terms of generalised connections\, and/or discuss the analogue of\nthe L
 evi-Civita connection and what complications it comes with.\n\nMC 5417
DTSTAMP:20260504T234136Z
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