For more information about the Seminar, to suggest speakers, or to volunteer to speak, contact Bahar Acu, Dave Bachman, Sam Nelson, Vin de Silva, or Helen Wong
| Date | Speaker | Title and Abstract |
| Tuesday
September 22 |
Sam Nelson Claremont McKenna College (CMC)
|
Title: Permutation Jones Polynomials
Abstract: The Jones Polynomial is an important invariant of knots with applications in physics, quantum computation and more. In this talk I will introduce a family of generalizations of the Jones polynomial associated to permutations of finite sets and discuss their properties. |
| Tuesday
September 29 |
Helen Wong CMC
|
Title: Introduction to the colored Jones polynomial
Abstract: This is a learning seminar. We will present an accessible definition of the colored Jones polynomial for knots and links and discuss the Volume Conjecture, which relates the colored Jones polynomial of K with the volume of its complement S^3 \K. |
| Tuesday
October 6 |
Puttipong Pongtanapaisan Pitzer College
|
Title: Introduction to Quantum Invariants of 3-Manifolds
Abstract: The previous speakers showed us how to distinguish knots and links using techniques involving quantum groups. I will start by explaining briefly why 3-manifolds, much like the universe we live in, can actually be represented as knots and links with numbers assigned to each component. Furthermore, diagrams of equivalent 3-manifolds differ by a sequence of moves that are highly similar to Reidemeister moves. To study 3-manifolds, we will adapt the techniques discussed by previous speakers to come up with a quantity unchanged by these new moves. I will compute the invariant for some classic examples and draw lots of pictures. |
| Tuesday
October 13 |
Jim Hoste Pitzer College
|
Title: Enumeration of Rational Knots, A New Proof of an Old Theorem
Abstract: I will begin with a quick review of rational knots, an interesting and well-studied class of knots. (Also known as 2-bridge knots.) In 1985, C. Ernst and D.W. Sumners gave an explicit formula for the number of rational knots with a given crossing number c. The formula is exponential in c, thus giving the first proof of the (widely believed) fact that the number of all prime knots grows exponentially with crossing number. In this talk I will give a new proof of their theorem which is diagrammatic in nature and which not only counts the number of rational knots with crossing number c, but also provides a fast and efficient way to tabulate these knots. These methods can also be used to calculate various invariants of rational knots and in some cases, the average value of a given invariant for a given crossing number. This is joint work with Patrick D. Shanahan, Loyola Marymount University. |
| Tuesday
October 20 |
No Meeting | Fall Break |
| Tuesday
October 27 |
Robert Cass CMC
|
Title: An introduction to quantum mechanics
Abstract: We will give an introduction to quantum mechanics from a mathematical perspective. We will start with a quick survey of classical Lagrangian and Hamiltonian mechanics. Then we will explain the basic axioms of quantum mechanics, such as how observables and measurable quantities are encoded by operators on Hilbert spaces and their eigenvalues. We will focus on the example of a single particle in one dimension, where the Hilbert space is L^2(R). |
| Tuesday
November 3 |
Chris Soteros University of Saskatchewan
|
Title: Knot and Link Statistics for Lattice Models of Polymers
Abstract: Lattice models such as self-avoiding polygons on the simple cubic lattice (with vertices in Z^3) have proved useful for studying the entanglement complexity of polymers. I will begin by reviewing what's known and believed regarding the knot and link statistics for cubic lattice self-avoiding polygons. Then recent results that combine novel knot theory, lattice combinatorics and Monte Carlo computer simulations will be presented regarding the knot and link statistics for self-avoiding polygons in tubular sub lattices of the simple cubic lattice. The lattice tube results have potential applications to experiments involving polymers (such as DNA) in nano channels. |
| Tuesday
November 10 |
Vin de Silva Pomona College
|
Title: TBA
Abstract: TBA |
| Tuesday
November 17 |
Bahar Acu Pitzer College
|
Title: TBA
Abstract: TBA |
| Tuesday
November 24 |
No Meeting | Thanksgiving Week |
| Tuesday
December 1 |
Giuseppe Martone Sam Houston State University
|
Title: TBA
Abstract: TBA |
| Tuesday
December 8 |
Dave Bachman Pitzer College
|
Title: TBA
Abstract: TBA |