Wall-crossing structures


Soibelman, Y. (2013). Wall-crossing structures. Perimeter Institute. https://pirsa.org/13100119


Soibelman, Yan. Wall-crossing structures. Perimeter Institute, Oct. 23, 2013, https://pirsa.org/13100119


          @misc{ pirsa_13100119,
            doi = {10.48660/13100119},
            url = {https://pirsa.org/13100119},
            author = {Soibelman, Yan},
            keywords = {},
            language = {en},
            title = {Wall-crossing structures},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {oct},
            note = {PIRSA:13100119 see, \url{https://pirsa.org}}

Yan Soibelman Kansas State University


The concept of wall-crossing structure (WCS for short) was introduced recently in my joint work with Maxim Kontsevich. WCS appear in different disguises in the theory of Donaldson-Thomas invariants of Calabi-Yau 3-folds, quiver representations,integrable systems of Hitchin type, cluster algebras, Mirror Symmetry, etc.
I plan to discuss the definition of WCS and illustrate it in several well-known examples. If time permits I will speak about a special class of WCS called rational WCS. It gives rise to wall-crossing formulas with factors which are algebraic functions. Conjecturally such WCS appear in Hitchin integrable systems with singularities.