Title:  Limits, Colimits, and Homotopy . . . Oh, my!

Abstract:  Given maps f: X --> Y and g: X --> Z of topological spaces, we obtain a unique map h: X --> Y x Z that respects the appropriate projections.  This property corresponds more generally to the limit of a diagram of spaces.  In this talk, we will define the limit, colimit, and their homotopy analogs and discuss their universal properties and relative merits/uses.  No prior topological knowledge is assumed.

Title:  Modeling Foot and Mouth Disease in cattle in northern Cameroon

Abstract:  Foot and Mouth Disease (FMD) is endemic in cattle in the Far North Region of Cameroon. While many cattle herds remain in a fixed location throughout the year, there are a small number of mobile herds that migrate depending on the season. These mobile herds share grazing space with many other cattle throughout the year, leading to increased disease transmission. In this talk I will present a multi-scale agent-based simulation model of FMD in northern Cameroon, focusing on the mathematical SIRS epidemic model running both inter- and intra-herd. Various parameters are determined by data from researchers on the ground while others are determined via in silico experimentation. The goal of the first phase of the project is to determine how each herd type contributes to the overall number of secondary infections. This model is a work in progress and the talk is meant to stimulate discussion about means of incorporating epidemic models in a multi-scale setting.

Title:  Tropical plane quartics

Abstract:  I will begin with a brief introduction to tropical geometry, and explain how algebraic curves give rise to tropical curves. I will then show that every tropical plane quartic admits 7 families of bitangent lines. This is analogous to the remarkable fact in classical geometry that a smooth plane quartic has exactly 28 bitangent lines. While the proof is purely combinatorial, I will discuss recent developments which suggest that the classical and tropical results are closely related. This is joint work with Matt Baker, Ralph Morrison, Nathan Pflueger, and Qingchun Ren.

Abstract:
We now believe that every large galaxy hosts a supermassive black
hole at its core, with masses ranging from millions to billions of
times that of our Sun. At times, these black holes are actively
accreting, causing the nuclei of the galaxies to shine brightly
across the electromagnetic spectrum. However, in many, perhaps
most quasars, obscuring material along the line of sight shields
us from directly viewing the inner nucleus. This obscuring material
is heated, and emits strongly in the mid-infrared. The Wide-field
Infrared Survey Explorer, or WISE, has recently mapped the entire
sky in mid-infrared light with exquisite depth and clarity. WISE
has allowed us to find luminous quasars across the whole sky due
to this heated material, more than tripling the number of quasars
known. I will discuss several surprising new insights into quasars
that have come out of this work. In brief, the dominant paradigms
do not match our observations, with potentially important implications
for the role of quasars in the growth of galaxies. I will conclude
by discussing how these studies will be further enabled by the
Euclid and WFIRST satellites.