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.
After the seminar we will take the speaker to lunch.
See the Algebra Seminar web page for information about other seminars in the series.
Anthony Henderson firstname.lastname@example.org.