Abstract: Quantum groups were introduced in the mid 80s by Drinfeld and Jimbo as a systematic means of constructing solvable lattice models in Statistical Mechanics. Algebraically, they are Hopf algebras which deform the enveloping algebras of semisimple Lie algebras, and more generally Kac-Moody algebras. Work of Kohno, Drinfeld, Kazhdan-Lusztig and Etingof-Kazhdan in the 90s clarified how quantum groups arise from, and describe the monodromy of, the Knizhnik-Zamolodchikov equations, a system of integrable first order PDEs with regular singularities. I will describe an alternative, and in some ways more natural construction of quantum groups using differential equations with irregular singularities. This is based in part on joint work with Andrea Appel (a 2013 NEU PhD).
