Graduate/faculty Seminar
Monday, February 1, 2016, 12:00pm, 119 Physics
Joshua Cruz (Duke University)
An Introduction to the Riemann-Hilbert Correspondence
Abstract:- Early in the history of complex analysis, it was realized that there are
no continuous versions of the square root or the logarithm on the entire
complex plane; instead, analysts invented multi-valued functions to deal
with these strange behaviors. The "graphs" of these multi-valued
functions can get very interesting, and can be interpreted
topologically. In general, the space of solutions to a "nice" system of
holomorphic ordinary differential equations on the non-zero complex
numbers will not be made up of functions, but of multi-functions.
Studying these spaces of solutions have led to several ideas in
algebraic topology, especially monodromy, and the relationship between
systems of ODE and possible monodromies is called the Riemann-Hilbert
Correspondence. [video]
Generated at 9:46pm Wednesday, April 24, 2024 by Mcal. Top
* Reload
* Login