# Graduate Seminar 2021

Current contact: Brandi Henry and Ruth Meadow-MacLeod

The seminar takes place on Fridays from 3:00 to 4:00pm on Zoom, and there will be a social time from 2:00 to 3:00pm in lieu of the refreshments usually offered.

• Friday January 22, 2021 at 15:00,

For the first graduate seminar of the semester, we thought it would be helpful to run an advanced Canvas workshop. Our very own Delaney Aydel will begin the workshop by demonstrating:

• how to organize your Canvas site & make your Canvas site navigable without sacrificing aesthetics
• how to implement mastery paths
• how to use the "Commons" to share materials across courses
• surveys on Canvas
• various features within Canvas quizzes
• how to access analytics.

We hope to also have discussions on good resources for students and how to best encourage our students to engage with them, on using the discussion board feature in a math course, and on how to utilize active learning in virtual education. We also invite and encourage questions, other discussion topics, and any other useful demonstrations or tips!

• Friday January 29, 2021 at 15:00,
Quaternion Algebras in Geometry

Rebekah Palmer, Temple University

Abstract: Quaternion algebras are a generalization of Hamilton's quaternions which are applied in the mechanics of three-dimensional space. These algebras provide a firm link between number theory and geometry. In this talk, we'll discuss how to construct these algebras, to associate them with matrices, and to harness their structure to make strong conclusions about hyperbolic 2- and 3-manifolds.

• Friday February 5, 2021 at 15:00,
Macroscopic Interpretation of Microscopic Models with Traffic Waves

Nour Khoudari, Temple University

Abstract: Real traffic flow develops instabilities and traffic waves. Traffic waves are traveling disturbances in the distribution of vehicles on a highway. They travel backwards relative to the vehicles themselves. Low density autonomous vehicles, acting as Lagrangian flow actuators, have the potential to dampen and prevent these undesirable non-equilibrium phenomena. By connecting traffic models from micro to macro scales, we outline some of the key macroscopic flow consequences of microscopic traffic waves and AV-based flow smoothing.

• Friday February 12, 2021 at 15:00,
The Mapping Class Group and the k-Curve Graph

Rob Oakley, Temple University

Abstract: One of the most common ways to understand a group is to understand how it acts on spaces. The mapping class group is no different! In this talk I hope to illustrate one 'flavor' of space that the mapping class group acts on rather nicely. I will focus on a specific example, the k-curve graph to explore the mapping class group action on it.

• Friday February 19, 2021 at 15:00,
Navier-Stokes equations in 3D

Elie Abdo, Temple University

Abstract: The Navier-Stokes (NS) equations are partial differential equations describing the flow of incompressible fluids. It has been shown that global smooth solutions exist in the two-dimensional case. In this talk, we study the NS equations in three-dimensional bounded smooth domains: we prove existence of global weak solutions and unique local strong solutions.

• Friday February 26, 2021 at 15:00,
Longest Common Subsequences

Apo Demirelli, Temple University

Abstract: The theory of longest common subsequences is one of the most well-studied problems of probability theory. It has lots of applications from computer science to computational biology. In recent years, this problem has become more popular than ever with the improvements on the gene matchings and the similarity problems. In this talk, we will investigate some properties of the longest common subsequences in random words, examine upper and lower bounds for the expected value of the longest common subsequences in this setting, and discuss the behavior of the asymptotic order of the longest common subsequences’s variance. We will also study the relationship between longest common subsequences and longest increasing subsequences in random permutations and discuss some properties of the matrix L(n) that is generated by the length of the longest common subsequences of permutations.

• Friday March 5, 2021 at 15:00,

Brandi Henry, Temple University

Abstract: Biofilms are communities of microorganisms that form when these microorganisms attach to surfaces, secrete a sticky substance, and reproduce within this sticky extracellular matrix. Biofilms enable interactions between the microorganisms, such as the exchange of genetic material. We are interested in how the structure of the biofilms within the human gastrointestinal tract affects these interactions, and specifically how structural changes relate to antibiotic resistance. Structural changes can occur when biofilms are stressed. Hydrogen peroxide is one such stressor that causes rigid, dense towers to grow within the biofilm, resulting in a highly heterogeneous structure. We will discuss our recent work in reconstructing the biofilm environments from microscopy data and modeling and simulating movement of antibiotics through the biofilm environments when put under flow.

• Friday April 9, 2021 at 15:00,
Random Walks on Weakly Hyperbolic Groups

Leah Leiner, Temple University

Abstract: Let G be a countable group of isometries acting on a Gromov hyperbolic space. Then G is called weakly hyperbolic if it contains a pair of independent hyperbolic isometries— one wide studied example of such a group is the mapping class group acting on its curve complex. In this talk, we will discuss random walks on these groups, and show they almost surely converge to the Gromov boundary.

• Friday April 16, 2021 at 15:00,
Links in Thickened Surfaces

Rosie Kaplan-Kelly, Temple University

Abstract: A link is alternating if it has a diagram with an orientation such that, if we travel along the link according to this orientation, we will alternate between over- and under-crossings. Traditionally, alternating links have been studied with alternating diagrams on $S^2$ in $S^3$. In this talk we will consider links which are alternating on higher genus surfaces in $S_g \times I$. We will sketch Howie and Purcell's theorem giving conditions for when such links are hyperbolic. We will then define what it means for the complements of these generalized alternating links to be right-angled and discuss work towards proving which links will have this property.

• Friday April 23, 2021 at 13:00,
Transshipment Problem, its conversion into a transportation problem and its applications

Irem Altiner, Temple University

Abstract: Transshipment problem involves sending products from sources/warehouses to the determined destinations/sinks via some middle centers we call transshipment points. Using these transshipment points may reduce the total cost of transportation significantly. In this talk we will talk about how we treat this problem as a transportation problem and we will talk about a couple of its numerous applications including Brazilian soybean exportation based on real needs and statistics and vaccine distribution, if time allows.