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Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-CrossingLin, Yu-Shen 08 October 2013 (has links)
We defined a new type of open Gromov-Witten invariants on hyperK\"aher manifolds with holomorphic / Mathematics
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Wall-crossing Behavior of Strange Duality Morphisms for K3 SurfacesChen, Huachen 13 August 2015 (has links)
No description available.
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Moduli of Bridgeland-Stable objectsMeachan, Ciaran January 2012 (has links)
In this thesis we investigate wall-crossing phenomena in the stability manifold of an irreducible principally polarized abelian surface for objects with the same invariants as (twists of) ideal sheaves of points. In particular, we construct a sequence of fine moduli spaces which are related by Mukai flops and observe that the stability of these objects is completely determined by the configuration of points. Finally, we use Fourier-Mukai theory to show that these moduli are projective.
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4d Spectra from BPS Quiver DualitiesEspahbodi, Sam 26 September 2013 (has links)
We attack the question of BPS occupancy in a wide class of 4d N = 2 quantum field theories. We first review the Seiberg-Witten approach to finding the low energy Wilsonian effective action actions of such theories. In particular, we analyze the case of Gaiotto theories, which provide a large number of non-trivial examples in a unified framework. We then turn to understanding the massive BPS spectrum of such theories, and in particular their relation to BPS quivers. We present a purely 4d characterization of BPS quivers, and explain how a quiver's representation theory encodes the solution to the BPS occupancy problem. Next, we derive a so called mutation method, based on exploiting quiver dualities, to solve the quiver's representation theory. This method makes previously intractable calculations nearly trivial in many examples. As a particular highlight, we apply our methods to understand strongly coupled chambers in ADE SYM gauge theories with matter. Following this, we turn to the general story of quivers for theories of the Gaiotto class. We present a geometric approach to attaining quivers for the rank 2 theories, leading to a very elegant solution which includes a specification of quiver superpotentials. Finally, we solve these theories by an unrelated method based on gauging flavor symmetries in their various dual weakly coupled Lagrangian descriptions. After seeing that this method agrees in the rank 2 case, we will apply our new approach to the case of rank n. / Physics
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A Quantum Lefschetz Theorem without ConvexityWang, Jun 01 October 2020 (has links)
No description available.
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