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(11.01.) Cancelled: Towards Fay identities and an analogue of the Kronecker function at genus two
Johannes Broedel (ETH Zurich)
11.01.2024 at 16:15
Polylogarithms -- defined as iterated integrals on Riemann surfaces of various genera -- have proven a versatile language for observables in quantum field theory. Polylogarithms on Riemann surfaces of genus zero and one are rather well understood, which is partly due to the so-called Kronecker function: while almost trivial at genus zero, the genus-one Kronecker function generates a set of differentials for building genus-one polylogarithms.
In my talk, I will consider the defining properties of the Kronecker function at genus one and discuss, how those can be modified and extended to lead to a genus-two function for Riemann surfaces at genus two. This will heavily constrain possible functional forms of the Kronecker function. I will discuss possible representations as well as connections to the well-known Fay trisecant identities at higher-genus Riemann surfaces.
Arnold Sommerfeld Center Theresienstrasse 37
Room 348 via ZOOM