Ordinary differential equations as analog computers.
For more information about this meeting, contact Leonid Berlyand.
Speaker: Alessandro Arsie, MIT/PSU
Abstract: In recent years the topic of Analog Computation has become fashionable mainly due to possible applications in Quantum Control and Quantum Computation. The basic idea is to look at (ordinary) differential equations in a new light: not only as a description of natural phenomena, but also as "machines" (or analog computers) that perform certain tasks, which were previously thought to be approachable only via a computer scientist point of view. Surprisingly ODE of special form (for instance in Lax form) can perform typical algorithmic tasks like sorting a list of numbers, diagonalizing matrices, solving inverse eigenvalue problems in linear algebra and linear programming problems. I will discuss some recent result about a system of ODEs that diagonalize a real matrix with simple spectrum and I will point out longstanding open problems in this area which lies at the crossroad of analysis, numerical analysis and geometry.
Room Reservation Information
Room Number: 106 McAllister
Time: 4:00pm - 5:00pm