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SUMMARY:Ignacio Barros-Reyes (Paris-Saclay University)
DTSTART:20210923T185000Z
DTEND:20210923T195000Z
DTSTAMP:20260423T022916Z
UID:GPRTatNU/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/30/
 ">Irrationality of moduli spaces</a>\nby Ignacio Barros-Reyes (Paris-Sacla
 y University) as part of Geometry\, Physics\, and Representation Theory Se
 minar\n\n\nAbstract\nI will talk about the problem of determining the bira
 tional complexity of moduli spaces of curves and K3 surfaces. I will recal
 l some recently introduced invariants that measure irrationality and talk 
 about what is known for these moduli spaces. In the second half I will rep
 ort on joint work with D. Agostini and K.-W. Lai\, where we study how the 
 degrees of irrationality of the moduli spaces of polarized K3 surfaces gro
 w with respect to the genus g. We provide polynomial bounds. The proof rel
 ies on Kudla's modularity conjecture for Shimura varieties of orthogonal t
 ype. For special genera we exploit the deep Hodge theoretic relation betwe
 en K3 surfaces and special hyperkähler fourfolds to obtain much sharper b
 ounds.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/30/
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