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Explore the mathematical connections between Steinberg symbols and tau functions in this 50-minute conference talk delivered at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the concept of Steinberg symbols as multiplicative bicharacters of rings that satisfy additional Steinberg relations, and examine Beilinson's 1982 proposal for an explicit expression of a canonical symbol for ring functions on a circle. Discover how this symbol functions as both a multiplicative analogue of a residue and as a cocycle that defines the Heisenberg group. Learn about the construction of boson-fermion correspondence using the symbol, and understand how finite-gap tau-functions can be interpreted as automorphic forms. Gain insights into advanced topics in algebraic geometry, representation theory, and mathematical physics through the expertise of Vladimir Fock from IRMA Strasbourg, as he presents these sophisticated mathematical concepts and their interconnections.
