23–26 May 2014
Buehler Alumni Center
US/Pacific timezone

Quantum curves and the infinite-dimensional Grassmannian

24 May 2014, 11:15
45m
Alpha Gamma Rho Room (Buehler Alumni Center)

Alpha Gamma Rho Room

Buehler Alumni Center

University of California, Davis, CA 95616. USA

Speaker

Prof. Albert Schwarz (UC Davis)

Description

One says that a pair $(P,Q)$ of ordinary differential operators specify a quantum curve if $[P,Q]=\hbar$. If a pair of difference operators $(K,L)$ obey the relation $KL=\lambda LK$ where $\lambda =e^{\hbar}$ we say that they specify a discrete quantum curve. This terminology is prompted by well known results about commuting differential and difference operators , relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions. Our methods are based on the interpretation of quantum curves in terms of infinite-dimensional Grassmannian; in particular, it follows from this interpretation that (discrete) KP-hierarchy can be used to deform a (discrete) quantum curve. The main goal is to study the moduli spaces of quantum curves. We will relate the moduli spaces for different $\hbar$. We will show how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve)

Primary author

Prof. Albert Schwarz (UC Davis)

Presentation materials

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