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Martin Guest (Waseda University) 
2026-04-28  13:00 - 14:30
Room 202, Astronomy and Mathematics Building

Since the discoveries and predictions by physicists, and the foundational work of mathematicians in the 1990's, it has become well known that differential equations and integrable systems play a (surprisingly) effective role in the theories of quantum cohomology and Gromov-Witten invariants.  A basic example of this is the interaction between the quantum cohomology of a Fano manifold X with H^2(X) of rank 1, and the monodromy data of the quantum differential equation (an o.d.e. in the complex plane). There is then a (still more surprising) phenomenon: the monodromy data (Stokes and connection matrices) of the o.d.e. has been observed to match certain algebraic/topological data in the derived category of vector bundles over X (Euler form and exceptional sequences) - at least, in a number of examples. This was the origin of the Dubrovin Conjecture, announced by him at the 1998 ICM.  A key role in this correspondence is played by the "gamma class". In the first lecture we shall try to build up some intuition behind this geometric phenomenon, together with some (mainly classical) foundations.