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UID:0240aab8167d716ee0d64b215d853d35
CATEGORIES:Symplectic Geometry Seminar
CREATED:20250409T160657
SUMMARY:Quantum spectrum and Gamma structure for standard flips
LOCATION:Hill 705
DESCRIPTION:<p style="line-height: 1.6667; text-align: justify; margin-top: 7px;">Abstr
 act: In his 1998 ICM talk, Dubrovin conjectured that a Fano variety X has s
 emisimple quantum cohomology if and only if the derived category D(X) posse
 sses a full exceptional collection. Using Gamma structures, this conjecture
  has been revisited, refined, and generalized to nonsemisimple cases in the
  last decade.&nbsp;</p><p style="line-height: 1.6667; text-align: justify; 
 margin-top: 7px;">In this talk, we investigate the quantum cohomolohy for p
 rojective bundles, blow-ups, and standard flips and its connection to deriv
 ed categories. By restricting the quantum cohomology to a fiber curve direc
 tion, we obtain a decomposition of QH(X) into asymptotic Gamma classes, ind
 exed by the spectrum of quantum multiplication of the first Chern class of 
 X. Using a sequence of reductions and asymptotic expansions of Meijer G-fun
 ctions, we show this decomposition is compatible with the semi-orthogonal d
 ecompositions of projective bundles, blow-ups, and standard flips studied b
 y Orlov and Belmans-Fu-Raedschelders.&nbsp;</p><p style="line-height: 1.666
 7; text-align: justify; margin-top: 7px;">The talk is based on work joint w
 ith Mark Shoemaker. If time permits, I will also talk about our recent prog
 ress on weighted flips.</p>
CONTACT:Yefeng Shen (University of Oregon)
DTSTAMP:20260828T183830
DTSTART;TZID=America/New_York:20250417T140000
DTEND;TZID=America/New_York:20250417T150000
SEQUENCE:0
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