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Discrete quantum curves

QMAP Seminar

Speaker: Albert Schwarz, UC Davis
Location: 2112 MSB
Start time: Thu, Oct 10 2013, 4:10PM

Quantum curves can be defined as solutions to the equation [P,Q]=const where P and Q are ordinary differential operators. We define discrete quantum curves as solutions to the equation KL=const LK where K and L are difference operators. We give a description of discrete quantum curves in terms of flags in infinite-dimensional Grassmannian; we use this description to show how to obtain a discrete quantum curve by means of quantization of classical curve. One can show that discrete curves are related to B-model of topological string theory and to gauge theories (to Seiberg-Witten curve), but I'll keep the exposition at more elementary level.