I will speak about the solution of an old open problem in complex hypercontractivity theory on the Hamming cube (1979). The question is  to obtain necessary and sufficient conditions for boundedness of "Hermite operator" on the Hamming cube.  If time permits I will discuss some applications and open problems.  The talk is based on my recent joint work with Fedor Nazarov. 

No background is required for this talk except the knowlegde of complex numbers. Undegraduate and graduate students are especially welcome.