Alex Nita (CU Boulder) Pseudodifferential Operators

Wed, Feb. 12 4pm (MATH 350)

Grad Student Seminar

Connor Mccranie (CU Boulder)

X

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)

MathClub

Nat Thiem (CU Boulder)

X

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.