# 2012-2013 Mathematics Colloquia

### Schedule for Winter 2013

#### The Elephant is a Rope: Metaphor and Mathematics

##### Public Mathematics Lecture - John McCleary (Vassar College)

Time: Thursday, February 28 at 3:30pm

Place: Northern Auditorium, Leyburn Library

Abstract**: **George Lakoff and Rafael Nunez have sketched a linguistic/cognitive science description of the origins of elementary notions of mathematics through the mechanism of metaphor. Extending their idea to higher mathematics, a story emerges when we consider how metaphor changes over time. The talk will focus on these notions as a lens through which to view the history and development of mathematics.

John McCleary is Professor of Mathematics on the Elizabeth Stillman Williams Chair of Mathematics at Vassar College. His areas of research include topology and geometry and their histories.

### Diophantine equations with generalized Fibonacci numbers

#### Florian Luca (Universidad Autonoma de Mexico)

Time: Thursday, March 21 at 4:40pm

Place: Robinson Hall, Room 6

*Refreshments in Robinson Hall 2 at 4:20pm

### Geometry of Graph Braid Groups

#### Praphat Fernandes (Emory University)

Time: Thursday, March 28 at 4:40pm

Place: Robinson Hall, Room 6

*Refreshments in Robinson Hall 2 at 4:20pm

Abstract: Given a set number of robots on a fixed system of rails, one can consider the set of all their possible configurations on the system of rails. Additionally one can consider their set of configurations geometrically, so that configurations which are geometrically close, correspond to configurations which are intuitively close on the system of rails. We will then use this space of configurations to define the graph braid groups, and use the geometry of these spaces to study the geometry of the group.

### How far can you see in the woods?

#### Pi Mu Epsilon Speaker - Aaron Abrams (W&L Math Dept)

An introduction to the geometry of numbers.

Time: Wednesday, April 3 at 4:40pm

Place: Robinson Hall, Room 6

Refreshments in Robinson Hall 2 at 4:20pm

### Schedule for Fall 2012

### On the factorization of the trinomials x^n+cx^{n-1}+d

#### Josh Harrington

Time: 4:40-5:35, Thursday, September 20

Place: Robinson Hall, Room 6

Refreshments at 4:20 in Robinson Hall 2

Abstract: In this talk we investigate the factorization of trinomials of the form x^n+cx^{n-1}+ d in Z[x]. We then use these results about trinomials to prove results about the factorization of polynomials of the form x^n+c(x^{n-1}+...+x+1) in Z[x].

### The Roanoke Crochet Coral Reef

#### Jan Minton (Roanoke College) and Caren Diefenderfer (Hollins University)

Time: 4:40 - 5:35, Tuesday, September 25

Place: Robinson Hall, Room 6

Refreshments at 4:20 in Robinson Hall 2

Abstract:

The Roanoke Valley Reef is a satellite reef of the Hyperbolic Crochet Coral Reef, a project of the Institute for Figuring in Los Angeles. The Hyperbolic Crochet Coral Reef has been exhibited in museums and art galleries around the world, including the Natural History Museum of the Smithsonian. The project combines mathematics, the arts, environmental science and other disciplines in an exciting way. The Roanoke Valley Reef is sponsored by Roanoke College and will open for exhibition in Olin Gallery in January 2013. Everyone is welcome to contribute to this unique community art project. This talk will explain the reef project, including an introduction to the mathematics involved.

### Mercer Consulting

#### Presentation by Colin Bracis (‘03) representative of Mercer, Inc.

Time: 4:40 pm, Monday, October 15

Place: Robinson Hall, Room 6

Refreshments at 4:20 in Robinson Hall 2

### Radford Professor of Mathematics Inaugural Address

#### Nathan Feldman

Time: 4:30pm, Thursday, November 1

Place: Northern Auditorium, Leyburn Library

### Student Summer Research Presentations

Time: 3:35 pm, Friday November 2

Place: Robinson Hall, Room 6

Refreshments at 3:15 in Robinson Hall 2

### Shortest Paths, Soap Films, and Mathematics

#### Michael Dorff, BYU, currently at the MAA Headquarters in Washington DC

Time: 4:40 pm, Wednesday, November 14

Place: Robinson Hall, Room 6

Refreshments at 4:20 in Robinson 2

Abstract: In high school geometry we learn that the shortest path between two points is a line. In this talk we explore this idea in several different settings. First, we apply this idea to finding the shortest path connecting four points. Then we move this idea up a dimension and look at a few equivalent ideas in terms of surfaces in 3-dimensional space. Surprisingly, these first two settings are connected through soap films that result when a wire frame is dipped into soap solution. We use a hands-on approach to look at the geometry of some specific soap films or "minimal surfaces".

### The Abel Prize in Mathematics: Discrete Mathematics, theoretical computer science, additive number theory and ergodic theory

#### Carrie Finch, W&L Mathematics Professor

Time: 12:40pm , Thursday, November 15

Place: Hillel Multipurpose Room