May

29

2019

A chord diagram is a circle with lines going across it. We can make a graph where vertices represent the chords and edges are placed between vertices when the lines intersect inside the circle, called the intersection graph. Different chord diagrams can have the same graph and the question we deal with is when are two chord diagrams sharing the same intersection graph equal in the algebra of chord diagrams, A. This is called the Intersection Graph Conjecture. First, I will use a case where the conjecture is true to find a basis for A in order 5.

May

29

2019

May

30

2019

In this work we consider a mathematical and computational model for biofilm growth and nutrient utilization. In particular, we are interested in a model appropriate at a scale of interface. The model is a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs). One of these PDEs is subject to a constraint, which can be characterized as a parabolic variational inequality (PVI). Solutions to PVI have low regularities which limits the numerical scheme to low order.

May

30

2019

In 2013, Lemke Oliver created a list of all eta-quotients which are theta functions. Then in 2016, Folsom, Garthwaite, Kang, Swisher, and Treneer utilized this list of ``eta-theta'' functions along with Zwegers's construction of mock theta functions to create a set of mock modular forms which are also quantum modular forms. Later in 2016, Diaz, Ellefsen, and Swisher generalized a subset of these quantum modular forms to a single general form of quantum modular forms which included the every element of this subset.

May

30

2019

Consider a polygon lying in the Euclidean plane with labeled edge lengths. The moduli space of polygons is the space of all polygons with the same labeled edge lengths, modulo orientation preserving isometries. It is well known that this space is generically a smooth manifold. For certain combinations of edge lengths, however, singularities can arise. We show these singularities to be isolated, with a neighborhood of each singularity homeomorphic to a cone over a product of spheres. We proceed to explicitly compute the singular topologies that arise as moduli spaces of pentagons.

Naren Vohra was accepted to participate in the Graduate Student Mathematical Modeling Camp to be held at the University of Delaware, and the Mathematical Problems in Industry Workshop to be held at New Jersey Tech June 12-15 and June 17-21, 2019. Naren also received travel and local support to attend. Congratulations, Naren!

The results from the 2019 COMAP Mathematical Contest in Modeling are in. The COMAP contest is an international, team based, undergraduate, mathematical modeling competition. Teams of up to three students write up a thorough solution approach within 4 days. Submissions are judged on the basis of scientific merits as well as clarity and organization of the written report. This year, 14,108 teams representing institutions from seventeen countries/regions participated in the contest.

One of our teams, consisting of Andrea Lanz, Sara Tro and Michael Kupperman, was awarded Meritorious Winner! This...

The National Science Foundation awarded a new grant "Modeling with Constraints and Phase Transitions in Porous Media" DMS-1912938 of $224K for 2019-2022 to Malgorzata Peszynska as Principal Investigator.

With her collaborators and students they will develop new mathematical results as well as continue interdisciplinary modeling efforts. The project is motivated by the multiscale dynamics in the Earth's environment which requires further insights into the coupled processes of energy and mass transport across the several interlinked spatial and temporal scales including the pore-scale. The project will address mathematical and...

Dr. Heidi Schellman will host a workshop titled "Learn How to Negotiate a Tenure Track position," on Tuesday, May 28th from 4 to 5 pm, at the Hallie Ford Center room 115. For more details https://oregonstate.joinhandshake.com/events/304974/share_preview.