Abstract:
In this talk, we will survey some recent progress in
understanding the Gromov-Witten theory of K3 surfaces. In particular, we
will prove and exploit relations with sheaf theory to prove some old
conjectures in the subject (joint with R. Pandharipande and R. Thomas)
Thursday, November 5th
Bohan Fang, Northwestern
"Coherent-constructible correspondence for toric varieties and stacks"
Time: 1:30 PM
Location: SERC 218
Abstract: This is a talk on joint works with Chiu-Chu Liu, David Treumann and Eric Zaslow. I will describe a coherent-constructible correspondence for toric varieties motivated by homological mirror symmetry and T-duality. To each ample line bundle one can assign a polytope-shaped constructible sheaf on a real vector space. This assignment turns out to be a tensorial quasi-equivalence. The correspondence can be extended to toric stacks, using Borisov-Chen-Smith's definition through stacky fans.
Thursday, October 29th
Ron Donagi, U. Penn
"F-theory and its compactifications"
Time: 1:30 PM
Location: SERC 218
Abstract: F-theory is a "12 dimensional variant of string theory" whose study has seen great progress in the past year or two. This will be an introduction for mathematicians to F-theory and its global and local compactifications, including some of the recent progress towards F-theory based phenomenology. I will discuss the issue of local versus global in F-theory (and strings), and explore connections to the geometry of del Pezzo surfaces, Higgs bundles, and Noether-Lefschetz loci. Thursday, 11/5 Bohan Fang, Northwestern
Thursday, October 22nd
Y. Ostrover, IAS
"Algebraic properties of the quantum homology."
Time: 1:30 PM
Location: SERC 218
Abstract: In this talk we discuss certain algebraic properties of the quantum homology algebra of toric Fano manifolds. In particular, we describe an easily-verified sufficient condition for the semi-simplicity of the quantum homology. (This is a joint work with Ilya Tyomkin.)
Thursday, October 8th
Katrin Wehrheim, MIT
"Calculations of Floer homology by reduction"
Time: 1:30 PM
Location: SERC 218
Abstract: I will give some examples of calculating monotone Floer homology from a general strip shrinking isomorphism in quilted Floer homology (for sequences of Lagrangian correspondences). Examples include the Clifford torus in CP^n (previously known by Cho) and nondisplaceable T^{n-k}times S^{2k-1} in CP^ntimes CP^{k-1}. Moreover, the bijection of trajectory moduli spaces can be somewhat generalized to multiply covered compositions of correspondences, yielding e.g. calculations of the Floer homology between Clifford tori and RP^n in CP^n (confirming work by Allston). Finally, "figure eight" bubbling obstructions can be understood explicitly. Work is in progress on overcoming these for the Chekanov/Polterovich torus in S^2times S^2; using symmetries and twisted coefficients.
Thursday, September 24th
Rahul Pandharipande, Princeton University
"New connections between quivers, curve counts, wall-crossing, and symplectomorphisms of C^2. (Joint with String Group Meeting) "
Time: 1:30 PM
Location: SERC 218
Abstract: TBA
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