比利时vs摩洛哥足彩
,
university of california san diego
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algebraic geometry seminar
martijn kool
utrecht university
new directions in vafa-witten theory
abstract:
in the 1990's, vafa-witten tested s-duality of n=4 susy yang-mills theory on a complex algebraic surface x by studying modularity of a certain partition function. in 2017, tanaka-thomas defined vafa-witten invariants by constructing a symmetric perfect obstruction theory on the moduli space of higgs pairs (e,$\phi$) on x. the instanton contribution ($\phi=0$) to these invariants is the virtual euler number of moduli space of sheaves. i outline a method to calculate this contribution, when x is of general type, by reducing to descendent donaldson invariants. for rank 2, this leads to verifications of a formula from vafa-witten. the method can be ``refined'' to virtual $\chi_y$ genus, elliptic genus, and cobordism class, which involves weak jacobi forms and borcherds lifts thereof. i also give a new formula for rank 3 vw invariants on general type surfaces, correcting an error in the physics literature. joint with g$\ddot{\text{o}}$ ttsche.
host: dragos oprea
may 18, 2018
2:30 pm
ap&m 5829
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