Seminars this semester


   Series:


Jan 28 Tue Helge Ruddat (Johannes Gutenberg University Mainz)
12:00 J11 Smoothing toroidal crossing varieties
 
  Abstract:
Friedman and Kawamata-Namikawa studied smoothability of normal crossing varieties. I present the proof of a significantly more general smoothing result that also works for toroidal crossing spaces and relates to work on mirror symmetry by Gross-Siebert and Chan-Leung-Ma. The key technologies are the construction of log structures, a proof of a degeneration of the log Hodge to de Rham spectral sequence as well as deformation theory governed by Gerstenhaber algebras. This project is joint with Simon Felten and Matej Filip.
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Feb 18 Tue William Elbaek Mistegaard (IST Vienna)
12:00 F24 Quantum modularity
 
  Abstract:
Lawrence and Zagier have shown that for a Brieskorn homology sphere there exists a power series with integer coefficients and convergent inside the unit disc, such that the Reshetikhin-Turaev invariant of this three-manifold is the radial limit of that power series, as the parameter tends to a certain root of unity. This power series have interesting modularity properties. Subsequent work by Gukov, Putrov, Pei and Vafa aimed at generalizing this phenomena to other three-manifolds, leading them to the invention of a power series invariants of three-manifolds, which is now known as the so-called Zed-hat invariant. These invariants are conjectured to be examples of (higher depth) quantum modular forms, and this is known to be true for some families of three-manifolds. In this talk we present the following result, which is joint with Jørgen E. Andersen: For a Seifert fibered homology sphere, the zed-hat invariant can be computed via Borel-Laplace resummation of the Reshetikhin-Turaev invariant, as proposed (and proven in examples with three singular fibers) by Gukov, Marino and Putrov.
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Mar 20 Fri Mitsuyasu Hashimoto (Osaka City University)
15:00 J11
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Apr 28 Tue Piotr Sulkoski (Warsaw)
12:00 F24
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May 5 Tue Michel van Garrel (Warwick)
12:00 F24
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May 19 Tue Giordano Cotti (Birmingham)
12:00 F24
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