Talks (unless otherwise indicated) are in Davis 301 from 3:30–4:30 PM on Fridays. Refreshments begin at 4:30 on the second floor of Davis.
You can see next semester’s schedule.
It’s often said that in mathematics things are either correct or incorrect. That is true, but it still happens quite often that even a bad mistake hides inside it an important idea. Kurt Hensel was particularly talented at making interesting mistakes. This talk introduces Hensel and some of his mathematical life, then focuses on a spectacular mistake he made in 1905 and what eventually came of it.
Summer Student Researchers
Knots and Neuroscience
Colby students who did research in the Mathematics department over the summer will discuss their projects.
Tuesday, October 12 (Runnals Dinner)
Realizing Convex Codes in d-Dimensional Space
Every collection of sets in R^d divides space up into a number of regions, with each region labeled by the sets that contain it (think of a Venn diagram in R^2, for example). Motivated by neuroscientific phenomena, Curto, Itskov, Veliz-Cuba, and Youngs posed the following question in 2013: Which collections of labels can arise in R^d from collections of convex open sets? A complete answer has remained elusive, but this question has motivated a great deal of interesting combinatorics and geometry. We will discuss some recent progress on this question and the geometric ingredients that make this progress possible.
The Riddle of Projective Planes
A projective plane is an enlargement of the usual plane where parallel lines intersect. Some projective planes are finite, having only finitely many points and lines. Finite projective planes, which are interesting on their own right, find uses in many areas; such as designing experiments in statistics, as well as answering some game questions like how many different types of solutions to Sudoku! Constructing projective planes with different orders can be very mysterious and challenging. We will talk about the journey of solving the riddle of projective planes of small order, and learn about the still-unsolved riddle of larger projective planes.
Visual Taylor Series
I will describe what the foundation of a second Calculus course might look like in a parallel universe.
The talk should be accessible to students in a first Calculus course.