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Geneva's Chalk Talks - Andras Szenes
The blackboard displays some famous formulas linking Theoretical Physics and Enumerative Geometry. They mark some of the first in a remarkable series of contacts between the two subjects. While in enumerative geometry these numbers count geometric objects satisfying certain conditions, in physics, they characterize and classify physical systems.
The first blackboard represents this connection, linking quantum gauge theories on a surface with g holes to certain enumerative quantities.
The second blackboard displays the elegant and mysterious Verlinde formula (cases r=2,3), which was the subject of my thesis. Remarkably, this remarkable sum represents an integer for all positive values of the parameters.
On the third blackboard, there is a method to calculate these sums using iterated residues, along with some more complex enumerative formulas (remotely) related to the Higgs boson discovered at CERN. Finally, the formula on the last blackboard represents noncommutative deformations of spaces, and the associated enumerative formulas, which are the subject of my current research.
Images: Jaime Benicio Neto (UNIGE)
30 avr. 2025