Confluence for the Ktheoretic Jfunction
 Date
 November 12 (Fri) at 16:00  18:00, 2021 (JST)
 Speaker

 Todor Milanov (Associate Professor, Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo)
 Venue
 via Zoom
 Language
 English
I am planning to talk about my recent paper (1) written in collaboration with Alexis Roquefeuil. In the first part of the talk I would like to explain the background of our project: quantum differential equations and Ktheoretic quantum qdifference equations in genus0 GromovWitten theory. In the second part of the talk, I would like to explain our main result with an interesting application. Namely, under the assumption that the first Chern class of the tangent bundle is positive, we proved that the small Jfunction in quantum cohomology can be obtained as a limit q >1 of the small Jfunction in quantum Ktheory. In the case of a Fano toric manifold of Picard rank 2, we proved the Ktheoretic version of an identity due to Iritani that relates the Ifunction of the toric manifold and the oscillatory integral of the toric mirror. In particular, our confluence result yields a new proof of Iritani's identity in the case of a Fano toric manifold of Picard rank 2.
*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
Reference
 Todor Milanov, Alexis Roquefeuil, Confluence in quantum Ktheory of weak Fano manifolds and qoscillatory integrals for toric manifolds, (2021), arXiv: 2108.08620