Abstract: In this fun, relaxed talk, we will explore the symbiotic relationship between mathematics and juggling by exploring how strings of numbers can represent juggling patterns.
A Voyager from the Fourth Dimension
Speaker: Paul Humke (St. Olaf College and Washington & Lee University)
March 27, 2017 at 7:00 pm in Stackhouse Theater, Elrod Commons
Abstract: When speaking about THE FOURTH DIMENSION I’m invariably asked
How do you know this is what the 4th dimension really looks like?
My answer is
I know because we used the computer to create a 4-dimensional world and then used a monitor as a window to view it.
So there is nothing magical or new in what we did (it is only elementary algebra), but there is a bit of magic in what you’ll see.
Geometry Informs Arithmetic: Rational Points on Curves
Speaker: Rafe Jones (Carleton College)
March 23, 2017 at 4:40 pm in Robinson Hall 105
Refreshments at 4:20 pm in Robinson Hall foyer
Abstract: integer solutions to equations. For instance, x2 + y2 = z2 has infinitely many solutions, some found by the Babylonians, nearly 4000 years ago. On the other hand, x3 + y3 = z3, which is a special case of the renowned "Last Theorem" of Fermat, turns out to have no solutions! What accounts for this radical difference? A beautiful theorem of Faltings from the 1980s links the answer to this question with the geometry of the associated curves. I’ll discuss in detail what this theorem says, give several examples, and mention an application to a problem from dynamics.
Visualizing Four Dimensions
Speaker: Jeff Weeks (Geometer, Educator, MacArthur Fellow)
March 9, 2017 at 4:40 pm in Robinson 105
Refreshments at 4:20 in Robinson foyer
Abstract: This talk will introduce a method for learning to visualize 4‑dimensional space, give participants a chance to work on some 4D visualization exercises in small groups, and then present a few solutions using interactive 4D graphics software. The exercises range from elementary to advanced, so everyone from first-year undergraduates to seasoned professors should find something they like.
The Shape of Space
Speaker: Jeff Weeks (Geometer, Educator, MacArthur Fellow)
March 8, 2017 at 5:00 pm in Stackhouse Auditorium, Elrod Commons
Abstract: When we look out on a clear night, the universe seems infinite. Yet this infinity might be an illusion. During the first half of the presentation, computer games will introduce the concept of a “multi connected universe”. Interactive 3D graphics will then take the viewer on a tour of several possible shapes for space. Finally, we'll see how satellite data provide tantalizing clues to the true shape of our universe. The only prerequisites for this talk are curiosity and imagination. For middle school and high school students, W&L students and faculty, and all members of the greater Lexington community.
Optimal Geometry as Art
Speaker: John Sullivan (Technische Universitat Berlin)
January 26, 2017 at 5:00 pm in Northen Auditorium, Leyburn Library
Refreshments at 4:30 in Robinson Hall foyer
Abstract: Topology studies those properties of curves or surfaces that are unchanged under deformation, while geometry studies properties of particular shapes. For any topological object, we can ask for its optimal geometric shape, minimizing some geometric energy. A classical example is a soap bubble which is round because it minimizes surface area while enclosing a fixed volume. Other examples, at the frontier of current mathematical research, include knots tied tight in thick rope, which minimize their length, and surfaces which minimize elastic bending energy. The resulting shapes are not only mathematically elegant, but often exhibit striking visual beauty.
I will show two computer-generated videos, illustrating optimal shapes for knots and a mathematical way to turn a sphere inside out (controlled by surface bending energy). I will discuss the artistic choices that went into the making these films, and will show other examples of mathematical art arising from optimal geometry, including computer-generated sculpture.
Fall 2016
The Old Made New: Infinitesimals in Calculus
Speaker: Alan McRae (Washington and Lee University)
November 17, 2016 at 4:40 pm in Robinson Hall 105
Refreshments in Robinson Hall foyer at 4:20
Abstract: Amir Alexander wrote
On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.
Come join us as we witness the rebirth of the dangerous infinitesimal and thereby plunge the world into chaos.
A Geometric & Combinatorial Approach to Weighted Voting
Speaker: Jason Parsley (Wake Forest University)
October 6, 2016 at 4:40 pm in Robinson Hall 105
Refreshments in Robinson Hall foyer at 4:20
Abstract: Weighted voting refers to the situation where n players, each with a certain weight, vote on a yes or no motion. For one side to win, the weights of its players must reach a certain fixed quota q. A natural example is a corporation: each stockholder is a player with weight equal to the shares of stock he or she owns. In joint work with Sarah Mason, we describe several combinatorial properties of weighted games. We introduce a geometric approach to weighted voting by constructing a polyhedron for each weighted game. We also form a partially ordered set (a poset) containing all weighted games. Connecting these two perspectives, we prove that the poset is a blueprint for how the polyhedra fit together to form Cn, the configuration region of all weights and quotas for n players. This talk assumes no background information and is suitable for any undergraduate.
What I Did Last Summer (Parents and Family Weekend Event)
Speakers: W&L Math students Holly Paige Chaos, Margaret Kallus, Max Rezek and Saimon Islam.
September 30, 2016 at 4:40 pm in Robinson Hall 105
Refreshments at 4:20 pm in Robinson Hall foyer
Abstract: The students will talk about their summer research.
