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.
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:
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.
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.
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.
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.
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.
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.
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.
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.
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.