# Geometry and Topology Seminar 2010

Current contact: Dave Futer or Matthew Stover

The Seminar usually takes place on Wednesdays at 2:45 PM in Room 617 on the sixth floor of Wachman Hall.

• Tuesday January 26, 2010 at 15:30, Wachman 617

Chris Atkinson, Temple University, A combinatorial lower bound on the volume of hyperbolic Coxeter polyhedra

• Tuesday February 2, 2010 at 15:30, Wachman 617

Will Cavendish, Princeton University, On the growth rate of the Weil-Petersson diameter of moduli space

• Tuesday February 9, 2010 at 15:30, Wachman 617

Ara Basmajian, CUNY, Length bounds for self-intersecting geodesics

• Tuesday February 16, 2010 at 15:30, Wachman 617

Moon Duchin, University of Michigan, Measuring the failure of hyperbolicity

• Tuesday February 23, 2010 at 15:30, Wachman 617

Shawn Rafalski, Fairfield University, Small hyperbolic polyhedra

• Tuesday March 2, 2010 at 15:30, Wachman 617

Joseph Maher, CUNY, Generic elements of the mapping class group

• Tuesday March 16, 2010 at 15:30, Wachman 617

Ken Shackleton, University of Tokyo, On the coarse geometry of Teichmuller space

• Tuesday March 23, 2010 at 15:30, Wachman 617

Louis Theran, Temple University, Parallel redrawing, rigidity, and slider-pinning

• Tuesday April 6, 2010 at 15:30, Wachman 617

Ian Biringer, Yale University, Geometric consequences of algebraic rank in hyperbolic 3-manifolds

• Tuesday April 13, 2010 at 15:30, Wachman 617

Karin Melnick, University of Maryland, Normal forms for conformal vector fields

• Monday April 19, 2010 at 15:30, Wachman 447

PATCH seminar, joint with Bryn Mawr & Haverford

John Baldwin, Princeton University, Contact monoids and Stein cobordisms

• Monday April 19, 2010 at 17:00, Wachman 447
GeoTop Seminar

PATCH seminar, joint with Bryn Mawr & Haverford

Josh Sabloff, Haverford College, Lagrangian caps for Legendrian knots via generating families

• Tuesday November 9, 2010 at 15:30, Wachman 617
GeoTop Seminar

John Humphrey, EM Photonics, Using GPUs to Improve Numerical Calculations

GPUs have been a topic of intense research for accelerating numerical processing, due to their high FLOPS/dollar and FLOPS/watt ratios. In particular, the field of numerical linear algebra has been a field of high payoff due to the applicability of the GPU and the widely useful nature of calculations such a system solutions and eigenproblem analysis. We will discuss our experience in this area in light of our CULA package for GPU accelerated linear algebra operations, which Temple University has leveraged in the creation of their PyCULA package.

• Tuesday November 30, 2010 at 15:30, Wachman 617
GeoTop Seminar

Walter Whiteley, York University, When does added symmetry shifts rigid structures to flexible structures?

For finite frameworks with graph $G$ in dimensions $2$ and $3$, we have necessary conditions for rigidity; $|E| = 2|V|-3$ in the plane (Laman's Theorem) and $|E|=3|V|-6$ in 3-space (Maxwell's condition). Recently, work by a group of researchers has given modified necessary counts for orbits of finite symmetric frameworks, whose failure guarantees symmetry generic frameworks are flexible. The most striking case, visible in a number of classical examples, is generically isostatic frameworks in 3-space which become flexible with half-turn symmetry.

Several recent papers have given necessary (and sometimes sufficient) conditions for periodic generic frameworks to be infinitesimally rigid. Building on these two foundations, recent work with Bernd Schulze (TU Berlin) and Elissa Ross (York University) has examined necessary conditions for rigidity of periodic frameworks with added symmetry. Again, there are circumstances, such as inversive symmetry in a crystal which convert the count for generic rigidity into an orbit count which guarantees flexibility.

We will present an overview of these results, with a few animations and tables, as well as the core technique of orbit rigidity matrices. We conclude with an array of unsolved problems. Related papers are on the arXiv.

• Tuesday November 30, 2010 at 17:00, Wachman 617
GeoTop Seminar

Radmila Sazdanović, University of Pennsylvania, Categorification of knot and graph polynomials

We review homology theories of links and graphs, focusing on Khovanov link and chromatic graph homology and relations between them.

• Tuesday December 7, 2010 at 15:30, Wachman 617
GeoTop Seminar

Fred Cohen, University of Rochester, Spaces of particles, their applications and connections.

This talk is an exposition of topological, and geometric properties of the classical configuration space of distinct particles in a manifold.

The main setting is how features of these spaces 'connect' to several phenomena such as linking of circles in three dimensions, knots in three dimensions as well as homotopy groups of spheres. Explanations will be given for how and why these structures fit together.