Monday, February 2 2015

10:00am - 11:00am

10:00am - 11:00am

Computational & Applied Mathematics Seminar

CCM &Discrete Joint Seminar :: Clayton Shonkwiler :: Geometry of random polygons, knots, and biopolymers

Please join us for the first CCM Seminar of the Spring 2015 semester. The seminar room has moved to Room 4119 in the Student Commmons Building (still shown as Academic Building 1, AB1, on the campus maps). This CCM Seminar is joint with the Discrete Seminar.

Our speaker for February 2, 2015, is Dr. Clayton Shonkwiler from Colorado State University who is an expert on using geometry to solve topological and physical problems (www.math.colostate.edu/~clayton/research/). He will present his recent work with applications to biopolymers.

Title: Geometry of random polygons, knots, and biopolymers

Abstract:

In 1884, Lewis Carroll asked the question: what is the probability that a random triangle is obtuse? Of course, the key word in this question is "random", and the answer depends entirely on what one means by a "random triangle". This quickly leads to rather deep and interesting mathematical questions: how should we assign a probability measure to the space of polygons? How could we sample that measure by computer? What is the probability that a random hexagon in space is knotted?

These sorts of questions also arise in the study of biopolymers: loops of DNA can be modeled by polygons in space consisting of hundreds or thousands of edges, so it is very natural to study the statistics of shape of these very complicated objects.

This talk will survey an approach to these questions informed by the study of polygon spaces in algebraic and symplectic geometry. For example, using the complex squaring map there is an identification between the space of n-gons in the plane and the Grassmannian of 2-planes in R^n. Using these geometric connections, we can draw samples by computer for experimental work and also make some exact computations of probabilities over the space of random polygons...including the probability that a triangle is obtuse.

The talk covers joint work with Jason Cantarella and his students (University of Georgia), Alexander Grosberg (NYU), Rob Kusner (UMass), and Tetsuo Deguchi and Erica Uehara (Ochanomizu University, Tokyo).

Our speaker for February 2, 2015, is Dr. Clayton Shonkwiler from Colorado State University who is an expert on using geometry to solve topological and physical problems (www.math.colostate.edu/~clayton/research/). He will present his recent work with applications to biopolymers.

Title: Geometry of random polygons, knots, and biopolymers

Abstract:

In 1884, Lewis Carroll asked the question: what is the probability that a random triangle is obtuse? Of course, the key word in this question is "random", and the answer depends entirely on what one means by a "random triangle". This quickly leads to rather deep and interesting mathematical questions: how should we assign a probability measure to the space of polygons? How could we sample that measure by computer? What is the probability that a random hexagon in space is knotted?

These sorts of questions also arise in the study of biopolymers: loops of DNA can be modeled by polygons in space consisting of hundreds or thousands of edges, so it is very natural to study the statistics of shape of these very complicated objects.

This talk will survey an approach to these questions informed by the study of polygon spaces in algebraic and symplectic geometry. For example, using the complex squaring map there is an identification between the space of n-gons in the plane and the Grassmannian of 2-planes in R^n. Using these geometric connections, we can draw samples by computer for experimental work and also make some exact computations of probabilities over the space of random polygons...including the probability that a triangle is obtuse.

The talk covers joint work with Jason Cantarella and his students (University of Georgia), Alexander Grosberg (NYU), Rob Kusner (UMass), and Tetsuo Deguchi and Erica Uehara (Ochanomizu University, Tokyo).

Speaker: | Clayton Shonkwiler |

Affiliation: | Dept. of Mathematics, Colorado State University |

Location: | AB1-4119 |