During Fall 2019, ICERM held a special semester on Illustrating Mathematics, including computer visualization, 3d printing, and virtual reality, among other media, with an eye toward advancing research, as well as art, outreach and teaching. We will give a brief overview of the program and then present a few highlight projects. Mathematical topics will include algebraic number fields, Fuchsian groups, Thurston geometries and elliptic curves.

Illustrating Mathematics

Tue, Jan. 28 3pm (MATH 350)

Algebraic Geometry

Srimathy Srinivasan (University of Colorado)

X

We will discuss the notion of good reduction of reductive groups, it’s implications and what is known so far. I will also give an outline involving main ideas on the proof of a conjecture of Chernousov, Rapinchuk, Rapinchuk for good reduction of unitary groups of quaternionic skew-hermitian forms.

Good reduction of unitary groups of quaternionic skew-hermitian forms

Tue, Jan. 28 4pm (MATH 350)

Topology

Bob Gompf (University of Texas at Austin)

X

One of the most surprising discoveries in 4-manifold topology was the existence of smooth manifolds homeomorphic, but not diffeomorphic, to Euclidean 4-space. For fundamental reasons, this phenomenon can only occur in 4 dimensions. We will survey the subject, from its origin to recent developments regarding symmetries of such manifolds. This talk should be accessible to a broad audience.