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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20250730T090000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defence-38
SUMMARY:PhD Thesis Defence
CLASS:PUBLIC
DESCRIPTION:ROBERT HARRIS\, UNIVERSITY OF WATERLOO\n\n_Exotic constructions
  on covers branched over hyperplane arrangements_\n\nAs a consequence of e
 mbedded surfaces and codimension two submanifolds\ncoinciding in dimension
  four\, many of the tools that are used in\nhigher dimensions fail or are 
 underwhelming when applied to\n4-manifolds. For this reason\, the developm
 ent and advancement of\ntechniques that are applicable to 4-manifolds are 
 of particular\ninterest and importance to low dimensional topologists. The
  general\ntechniques of interest are those that either construct a 4-manif
 old in\na novel way or those that provide ample control over the geometric
 \ndata of the resulting 4-manifold.\n\nIn this talk\, I will discuss my th
 esis\, in which we investigate ways\nto construct 4-manifolds with positiv
 e signature. We also describe a\nconstruction that can guarantee the exist
 ence of algebraically\ninteresting embedded symplectic submanifolds. \n\nS
 pecifically\, we discuss how the combinatorial data of line\narrangements 
 and the algebraic data of their complements in rational\ncomplex surfaces 
 can be utilized to construct symplectic 4-manifolds\nwith arbitrarily larg
 e signatures through the method of branched\ncoverings. In general\, we no
 t only show that these line arrangements\ncan be used to provide asymptoti
 c bounds for the existence of\nsymplectic 4-manifolds but we also show tha
 t for any line arrangement\,\nthere exists symplectic branched covers with
  sufficiently nice\ngeometric and topological properties. Namely\, we show
  they contain\nembedded symplectic Riemann surfaces which carry their fund
 amental\ngroup.\n\nOnline presentation: contact r26harri@uwaterloo.ca for 
 details on how\nto attend
DTSTAMP:20260504T211836Z
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