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UID:c55b840425348aab1131ee85cc0401b4
CATEGORIES:Symplectic Geometry Seminar
CREATED:20250114T130206
SUMMARY:Renato Vianna (Open-string Quantum Lefschetz formula)
LOCATION:Hill 705
DESCRIPTION:<p>Abstract:&nbsp;&nbsp;<span style="font-family: 'Times New Roman', serif;
  color: #313131;">Let Y be a symplectic divisor of X, omega. In the Kahler 
 setting, Givental's&nbsp;Quantum&nbsp;Lefschetz&nbsp;formula relates certai
 n Gromov-Witten invariants (encoded by the G function) of X and Y.&nbsp;Giv
 en an Lagrangian L in (Y, omega|Y), we can lift it to a Lagrangian L' in ne
 ighbourhood NY subset X. We will introduce the notion of the potential of a
  Lagrangian, which encodes information of Maslov index 2 J-holomorphic disk
 s with boundary on it. We will discuss the conditions in which the potentia
 l for L' relates with the potential for L according to a lifting&nbsp;formu
 la. In particular, this&nbsp;formula&nbsp;involves counts J-holomorphic sph
 eres with certain tangency on Y (part of relative Gromov-Witten invariants)
 . It generalizes a&nbsp;formula&nbsp;that can be extracted from Biran-Khane
 vski, under some more restrictive assumptions on Y. As applications, we rec
 over some&nbsp;Lefschetz&nbsp;formulas&nbsp;appearing in the work of Coates
 -Corti-Galkin-Kasprczyk and show the existence of infinitely many Lagrangia
 n tori in CP^n, Quadrics, Cubics, among other symplectic manifolds. This is
  joint work with Luis Diogo, Dmitry Tonkonog and Weiwei Wu.&nbsp;</span></p
 >
CONTACT:Renato Vianna
DTSTAMP:20260826T072453
DTSTART;TZID=America/New_York:20250123T140000
DTEND;TZID=America/New_York:20250123T150000
SEQUENCE:0
TRANSP:OPAQUE
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