A weekly seminar on topics in discrete geometry with a combinatorial
flavor.
We meet on Wednesdays 2:003:00pm in South Hall, 4607B.
For
more information, contact the organizers: Gordon
Kirby,
Michael
Dougherty, and Jon McCammond.
Past schedules:
Distribution of Descents in Matchings
Gene Kim  January 17

The distribution of descents in certain conjugacy classes of $S_n$ have been previously studied, and it is shown that its moments have interesting properties. This paper provides a bijective proof of the symmetry of the descents and major indices of matchings (also known as fixed point free involutions) and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.
On the Topology of Braid Factorizations
Michael Dougherty  January 31

"How can an ncycle permutation be factored into transpositions?" The answer to this question yields a simplicial complex with high levels of symmetry and close ties to the braid group. In this talk we will discuss new results on interesting subcomplexes and their connections with braids. This is joint work with Jon McCammond.
The Configuration Space of the Canfield Joint
Christian Bueno  February 7

This past summer I interned at NASA Glenn Research Center where I worked with other interns on better understanding the suitability of a pretty neat robotic linkage known as the Canfield Joint. To this end, we decided to investigate the Canfield joint's configuration and moduli spaces. The mathematics involved ended up being quite fun and pretty so I thought I'd share what we found.
Limits of Algebraic varieties: towards a continuous Nullstellansatz
Daryl Cooper  February 14

The set of common zeroes of finitely many polynomials involving n variables is called an affine variety. If a sequence of varieties converges to some subset of Euclidean space when is the limit a variety? For example a sequence of ellipses (varieties) can converge to a line segment (not a variety) and if it is, which polynomials define it? Oddly enough this appears to be unknown .... until now.
Subgroups of lattices
Darren Long  March 14
 I'll give a gentle introduction to some problems associated
with subgroups of lattices.