Oct

07

2022

The complexity of eco-evolutionary dynamics has challenged researchers to classify patterns in rapidly evolving ecosystems, for example in HIV infection, where the virus undergoes frequent mutations to escape several immune responses. Here, we develop a framework to connect evolutionary genetics with population dynamics by analyzing a resource-prey-predator network differential equation model with binary sequence representations of prey fitness and susceptibility to predation.

Oct

07

2022

Many partial differential equations (PDEs) can be formulated as the gradient descent of an energy functional in an appropriate function space. The heat equation, biharmonic heat equation, Allen-Cahn equation, and Cahn-Hilliard equation are all examples of this. In this talk, we will discuss how to formulate these PDEs as gradient descents and how to use this energy functional to our advantage when solving the Cahn-Hilliard equation. The result is effectively a parameter-free adaptive time stepping method that works with any temporal discretization method.

Oct

10

2022

Lagrangian submanifolds of symplectic 2n-manifolds are n-dimensional submanifolds on which the symplectic form vanishes. Lagrangians have been extensively studied and are often an important source of symplectic invariants. One approach to studying symplectic manifolds with contact boundary is to consider its Lagrangian submanifolds with Legendrian boundary, where Legendrians are submanifolds of the boundary whose tangent space lies in the contact structure. We will consider exact Lagrangian fillings in the standard symplectic 4-ball of Legendrian links in the standard contact 3-sphere.

Oct

10

2022

All smooth Manifolds have a CW-complex structure, that is they can be built topologically from disks D^{k} of dimension k ≤n if dimension of M is n. A handlebody description of a manifold M is a recipe for M with thickened disks, also called handles, D^{k}×D^{n-k}. For many 4-manifolds, these handlebody descriptions can be encoded by smooth links in S^{3} or #^{n}(S^{1}×S^{2}). Many important 4-manifolds are in fact symplectic, that is they have a nondegenerate closed 2-form associated to them.

Oct

11

2022

This talk will discuss the application of Abelian differentials of the first kind (i.e., holomorphic one form) on both compact Riemann surfaces of finite genus and infinite type Riemann surfaces with singularities to problems in coastal and ocean engineering, and physical oceanography. I will start by discussing how each Abelian differential on a compact Riemann surface determines a translation structure on the compact Riemann surface because the Abelian differentials on the compact Riemann surface generate flat cone metrics on the surface.

The conference is a two-day event hosted at Oregon State University on Nov 4-5, 2022. This will be a hybrid event with in-person participants and live streamed talks. Additionally, there will be a series of corresponding background talks in departmental seminars that will be available on the website before the conference so that participants may be more prepared for the talks at the conference. Lunch will be provided to registered participants. Please see https://sites.google.com/view/pnw-ip for more details

The PNGS will take place at Seattle University, Nov 5-6. There will be travel support for graduate students and faculty from OSU. Please contact Christine Escher if you are interested in going and would like travel support. Please see https://sites.math.washington.edu/~lee/PNGS/2022-fall/ for more details.