Valerio Toledano Laredo

Sponsor: NSF

Transcendental fiber functors, shift of argument algebras and Riemann-Hilbert correspondence for q-difference equations

This project stems from the recent discovery that quantum groups naturally arise from the Stokes data of differential equations associated to classical symmetries. The main goals are to further explore this bridge between classical and quantum symmetries. Of particular interest is the extension to difference equations, which are natural discretisations of differential equations, and whose Stokes data are not well-understood beyond the one-variable case. Another important direction will the study of the integrable systems, or constants of motion, corresponding to these differential and difference equations. The project will provide research training opportunities for graduate students.