Alex Nita (CU Boulder) Pseudodifferential Operators
Wed, Feb. 12 4pm (MATH 350)
Grad Student Seminar
Connor Mccranie (CU Boulder)
Of all mathematical definitions, perhaps one of the most pervasive is that of the continuous function, where a small change in input results in a small change in output. But there is an abundance of natural phenomena that aren't like this: water suddenly freezes with a continuous change in temperature, a star suddenly goes supernova, a camel's back breaks with N+1 straws. Catastrophic behavior is the antithesis of continuity, where a small perturbation of input induces a fundamentally different output.
In this talk, we will examine how catastrophes are connected to critical points of functions, and we will state a classification theorem for catastrophes of low dimension. There will be lots of desmos examples and 3D pictures.
Catastrophe Theory: Are continuous functions overrated?
Wed, Feb. 12 5pm (Math 350)
Nat Thiem (CU Boulder)
Matrices are everywhere, but they can also be cumbersome to work with. A standard strategy therefore is to replace complicated matrices with simpler matrices while preserving all the desired properties of the original. This talk explores the basic ground rules for such a simplification, and presents some families of answers. These can vary widely from simple generalizations of row-reduced echelon form to rich combinatorial structures. In some key cases we even find that there is provably no solution.