On solutions modulo p of geometric differential equations
Speaker:
Alexander Varchenko, University of North Carolina at Chapel Hill
Date and Time:
Thursday, June 6, 2024 - 4:00pm to 5:00pm
Location:
Fields Institute, Room 230
Abstract:
The KZ differential equations were defined by physicists in 1984 as equations for conformal blocks in conformal field theory. Now the KZ equations are a key structure in representation theory, enumerative geometry, … The KZ equations can be realized geometrically as the equations satisfied by periods of algebraic differential forms. I will explain an elementary construction of polynomial solutions of the KZ equations modulo a prime number $p$. These solutions are obtained as $p$-approximations of hypergeometric integrals.