# Seminar talk, 13 May 2015

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Speaker: Sergey Tychkov

Title: Invariants of solutions of associativity equation

Abstract:

The talk will discuss the associativity equation [math]\displaystyle{ u_{yyy} + u_{xxx}u_{xyy} - u_{xxy}^2 = 0 }[/math].

We found the Lie algebras of symmetries of this equation, proved that its action is algebraic, and described the algebra of differential invariants of solutions of the associativity equation. Using the Lie-Bianchi theorem we found some solutions of the associativity equation.