# Graduate Seminar

Current contact: Rebekah Palmer and Timothy Morris

The seminar takes place on Fridays (from 2:30-3:30pm) in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.

• Friday February 22, 2019 at 14:30, Wachman Hall 617
Classifying Actions of $T_n \otimes T_n$ on Path Algebras of Quivers

Delany Aydel, Temple University

Abstract: Let $T_n$ denote the $n$th Taft algebra. We fully classify inner-faithful actions of $T_n \otimes T_n$ on four-vertex Schurian quivers as extensions of the actions of $\mathbb{Z}_n \times \mathbb{Z}_n$. One example will be presented in full, with the remaining results briefly given.

• Friday February 15, 2019 , Wachman Hall 617
Bead Movement in Biofilms: Effects of Curli Amyloids and Analysis of Density Dependence

Brandi Henry, Temple University

Abstract: Microbial cells form communities, called biofilms, by producing an extracellular adhesive. By tracking the movement of 1µm glyoxylate beads in biofilms through the use of laser-scanning confocal microscopy and image-processing software, we can study the properties of the biofilm that may affect interactions of other cells with the microbiota. We developed a tool that can analyze the distance the beads travel, the volume of the region within which the beads travel, the time for which the bead is associated with the biofilm, the velocity with which the bead travels, and density of the region within which the bead travelled. Bead movement was studied for Enterococcus faecalis, Salmonella Typhimurium, Escherichia coli biofilms, and their isogenic curli mutants. Consistent with visual observations, our statistical analysis showed that the presence of curli in biofilms introduces a rigidity to the biofilm structure. Conversely, the lack thereof correlates to more bead movement suggesting less rigidity. In biofilms lacking curli where more free movement occurred, we analyzed the dependency of bead movement on the local density. While greater movement occurred in less dense environments, bead movement is not strictly dependent on density, suggesting other material properties of the biofilm influence bead movement.

• Friday February 8, 2019 , Wachman Hall 617
Resolution of singularities

Rebekah Palmer, Temple University

Abstract: To study structures that are not quite smooth, it is convenient to transform them so that we can apply the many tools developed for smooth structures. Given a variety with singularities, we ask if there is a consistent method of transformation into a non-singular variety. In this talk, we will introduce ourselves to some varieties with singularities, demonstrate how to uniquely resolve algebraic curves, and further discuss approaches to resolving higher-dimensional varieties.

• Friday February 1, 2019 at 14:30, Wachman Hall 617
Cannon's conjecture

Thomas Ng, Temple University

Abstract: The class of all groups (even finitely generated ones) are known to have wildly inefficient, in fact often unsolvable, algorithmic properties. It is thus helpful to specialize to well-behaved subclasses. In the early 1900s Dehn studied groups as geometric objects and showed that finitely generated groups arising as the fundamental group of manifolds in dimensions less that 4 are often very algorithmically efficient. Given the existence of these well-behaved groups, one is naturally led to ask how unique they are or under what conditions are they uniquely determined. Following Gromov's notion of boundary for a hyperbolic group introduced in 1987, Cannon conjectured that for hyperbolic groups the condition that its boundary is a 2-sphere uniquely determines 3-manifold fundamental groups. In this talk we will briefly review the notions of Cayley graph, hyperbolicity, and boundary of a group. We will then survey some of the recent results that inspired and attempt to solve the Cannon conjecture.