Alexander Chervov (Institute for Theoretical and Experimental Physics, Moscow)

Friday 10th August, 12.05-12.55pm, Carslaw 373

Quantum integrable systems and the Langlands correspondence

After a brief introduction to integrable systems and their quantization, we will present a construction of the "quantum spectral curve" which originates from the work of D. Talalaev. Spectral curves play an essential role in classical integrable systems. We will show that "quantum spectral curves" play the same key role in quantum integrable systems. In particular, they allow to construct quantum commuting Hamiltonians explicitly and to find their spectra and eigenfunctions of the respective quantum model. Moreover, the quantum spectral curves provide explicit and simple construction of the geometric Langlands correspondence and they have many other applications in representation theory.