Benedict Morrissey

In fall 2017 there is a seminar happening on Wall Crossing. Notes available on request.

Talk Schedule:

To appear Shortly.

Reference List:

Fundamental Mathematics of (refined) DT invariants and Wall Crossing Formula:

• M. Kontsevich, Y. Soibelman Lectures on motivic Donaldson-Thomas invariants and wall-crossing formulas, (Lectures providing an overview of some of the below papers)
• M. Kontsevich, Y. Soibelman Motivic Donaldson-Thomas invariants: summary of results, (Summary of below paper)
• M. Kontsevich, Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations.
• M. Kontsevich, Y. Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• D. Joyce, Y. Song A theory of generalized Donaldson-Thomas invariants
• T. Bridgeland, An Introduction To Motivic Hall Algebras.
• T. Bridgeland Hall algebras and Donaldson-Thomas invariants

The Links to Integrable systems, and to physics:

• M. Kontsevich, Y. Soibelman Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry.
• D. Gaiotto, G. Moore, A. Neitzke Four-dimensional wall-crossing via three-dimensional field theory.
• D. Gaiotto, G. Moore, A. Neitzke Wall-crossing, Hitchin Systems, and the WKB Approximation.
• M. Caorsi, S. CecottiCategorical Webs and S-duality in 4d N=2 QFT

2d Wall Crossing and 2d/4d Wall Crossing

• S. Cecotti, C. Vafa On Classification of N=2 Supersymmetric Theories.
• D. Gaiotto, G. Moore, A. Neitzke, Wall-Crossing in Coupled 2d-4d Systems

Spectral Networks and WKB analysis

• D. Gaiotto, G. Moore, A. Neitzke, Spectral networks
• T. Bridgeland, I. SmithQuadratic Differentials as Stability Conditions
• K. Iwaki, T. Nakanishi Exact WKB analysis and cluster algebras.

Categorified Wall Crossing:

• M. Kapranov, M. Kontsevich, Y. Soibelman Algebra of the infrared and secondary polytopes