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T.W.I.G.S.
The "What Is ...?" Graduate Seminar

Room 1634, Lederle Graduate Research Tower
University of Massachusetts, Amherst 		ComplexCubicUnitAction
The Seminar meets on most Wednesdays, 1:30-2:30 in 1634 LGRT.    
Driving Directions   and   Campus Maps
Overview of the Seminar
Maintained by Farshid Hajir.

NOTE Here are the schedules for TWIGS Fall 2002, TWIGS Spring 2003, TWIGS Fall 2003, TWIGS Spring 2004, TWIGS Fall 2004, TWIGS Spring 2005.
Fall Schedule
Wednesday, September 21 Bill Meeks, UMass Amherst.
"What is a minimal surface? What is a lamination? What is a minimal lamination?."
 Abstract: Alternate Title: Embedded minimal surfaces: Applications of the Local Removable Singularity Theorem, the Minimal Lamination Closure Theorem and the Dynamics Theorem A couple of years ago, I gave a survey of the recent progress in the classical theory of minimal surfaces. Since that time, several major structure theorems have appeared that shed light on the general theory of classical minimal surfaces in 3-manifolds. In this talk I will introduce everyone to what a minimal surface is. I will also explain some of the new theory that is providing a much deeper understanding of the local and global structure of complete embedded minimal surfaces in R^3.
Wednesday, October 05 Farshid Hajir, UMass Amherst.
"What is (Place Your Favorite Topic Here)?." .
 Abstract: This is the second annual Stump the Chump Edition of TWIGS. Members of the audience may ask Farshid to define/explain any mathematical topic of their choosing. So come along and have a stab at stumping the chump.
Wednesday, October 12 Michael Sullivan (UMass Amherst).
"What is a Legendrian Knot?."
. Abstract: Contact geometry/topology is the odd-dimensional analog of symplectic geometry/topology, both of which originate from classical mechanics. Legendrian knots are the fundamental objects of study in contact manifolds. I'll introduce them and (try to) describe a recently-developed combinatorial invariant for these knots. This talk will serve as a warm-up to the Oct 14 Valley Geometry Seminar as well as the Oct 20 Colloquium.
Wednesday, October 19 Keith Conrad, UCONN.
"What is a quaternion algebra?."
Abstract: There are two basic examples of 4-dimensional noncommutative rings: the two-by-two real matrices and Hamilton's quaternions. Unlike the ring of matrices, Hamilton's quaternions are a division ring: every nonzero element has a multiplicative inverse. Frobenius proved that Hamilton's quaternions form the only finite-dimensional noncommutative division ring over the reals. However, this does not mean there are no other examples of noncommutative division rings: you just have to use a different field of scalars. Using rational numbers as scalars, we will see how to construct infinitely many new examples of noncommutative division rings, still of dimension 4. We will then look at some features of these rings, which are called quaternion algebras. If time permits, we will sketch how to use Galois theory to construct noncommutative division rings with dimension greater than 4.
Wednesday, October 26 Ivan Soprounov, UMass Amherst.
"What is the Ehrhart polynomial?." .
Abstract: How many monomials of degree t in n variables are there? How many lattice points (points with integer coordinates) are there in the t-dilate of the unit n-dimensional cube? The answer to both questions is a polynomial in t of degree n. In 1960s Eugene Ehrhart discovered that the number of lattice points in the t-dilate of any n-dimensional lattice polytope P (i.e. whose vertices have integer coordinates) is a polynomial in t of degree n. We call it the Ehrhart polynomial of P. We will reprove Ehrhart's result and talk about what's known and what remains open about the Ehrhart polynomial. We will also see how one can find the volume of a lattice polytope by counting lattice points.
Wednesday, November 09 Paul Gunnells, UMass Amherst.
"What is a stratified space?." .
Abstract: A stratified space is a topological space that is built out of manifolds in a nice way. Stratified spaces naturally appear in many different contexts. For example, complex algebraic varieties are stratified spaces, as are quotients of manifolds by finite group actions. In this talk I'll give an overview of these spaces and will try to convince the audience that they're interesting.
Wednesday, November 16 Tom Weston, UMass Amherst.
"What is algebraic geometry?." 1634 LGRT.
Abstract: Algebraic Geometry is a vast and ancient subject. In this talk, I will give an introduction to the part of algebraic geometry that will be discussed in the Spring 2006 course Math 697 G.
Wednesday, November 30 Mike Sullivan, UMass Amherst.
"What is the price of a stock option?."
Abstract: I will give an introduction/overview of the recently-popular field of financial mathematics, while shamelessly plugging Math 697I, a grad class I will teach next semester.
The picture above was created by Paul Gunnells. It visualizes the natural action of the group of units of a complex cubic field on 3-space. Consult Paul for more details.

Last modified: Feb 2004 by Farshid Hajir