## Mathematical Epidemiology

*Thursday, August 7, 1:00 p.m. - 3:50 p.m., Hilton Portland, Plaza Level, Pavilion East*

Mathematical Epidemiology has grown at an accelerated pace over the last two decades through the integration of mathematical models, available data, computational methods and fieldwork. Successful epidemiological models are validated using parameters from particular epidemics, can predict likely outcomes of an epidemic, and can be used to propose specific interventions strategies.

Modern epidemiological models involve temporal and spatial features, age structure, transmission across networks or patches, deterministic and stochastic elements, seasonality, ecological factors, and more. The inclusion of these features also calls for new mathematical analysis of the models. This session features expository presentations covering a variety of aspects of modern Mathematical Epidemiology.

**Ricardo Cortez**, *Tulane University*

Abstracts

### Comparing Risk for Chikungunya and Dengue Emergence Using Mathematical Models

*1:00 p.m. - 1:20 p.m.*

**Carrie Manore**, *Tulane University*

### How are Fish Population Dynamics Shared by a Changing Environment? Insights from a Mathematical Model Driven by Temperature and Dissolved Oxygen Data from Lake Erie

*1:30 p.m. - 1:50 p.m. *

**Paul Hurtado**, *Mathematical Biosciences Institute*

### Determining Causal Networks in Nonlinear Dynamical Systems: Ecosystem Applications

*2:00 p.m. - 2:20 p.m.*

**Bree Cummins**, *Montana State University*

### Epidemic Forecasting and Monitoring using Modern Data Assimilation Methods

*2:30 p.m. - 2:50 p.m.*

**Kyle Hickmann**,* Los Alamos and Tulane University*

### Qualitative Inverse Problems using Bifurcation Analysis in the Recurrent Neutral Network Model

*3:00 p.m. - 3:20 p.m.*

**Stephen Wirkus**, *Arizona State University*

### Mathematics of Planet Earth 2013+: Management of Natural Resources

*3:30 p.m. - 3:50 p.m.*

**Abdul-Aziz Yakubu**, *Howard University*

## Connections between Logic and Arithmetic Geometry

*Thursday, August 7, 1:45 p.m. - 3:45 p.m., Hilton Portland, Ballroom Level, Grand Ballroom II*

In the past few years, ideas from model theory and computability theory, branches of logic, have led to proofs of new results in arithmetic geometry. Sometimes these ideas from logic serve as inspiration by analogy; other times they are directly used in the proofs. The proposed session will consist of survey talks by experts, suitable for a broad audience.

**Bjorn Poonen**, *Massachusetts Institute of Technology*

Abstracts

### Computability Theory at Work: Factoring Polynomials and Finding Roots

*1:45 p.m. - 2:15 p.m.*

**Russell Miller**,* Queens College, City University of New York*

### The Zilber Trichotomy Principle for Algebraic Dynamics: Hands-On Examples of Deep Notions from Model Theory

*2:30 p.m. - 3:00 p.m.*

**Alice Medvedev**, *University of California at Berkeley*

### On the Elementary Theory of Finitely Generated Fields

*3:15 p.m. - 3:45 p.m.*

**Florian Pop**, *The Pennsylvania State University*

## Computational Aspects of Algebra, Geometry and Combinatorics

*Friday, August 8, 1:00 p.m. - 5:15 p.m., Hilton Portland, Plaza Level, Pavilion West*

This session will highlight recent advances in mathematics inspired by experimental and computational aspects of research. The talks will be in areas of combinatorics and probability related to algebra and geometry. This is a highly active area of research, which often lends itself to interesting talks accessible to a wide audience.

**Sara Billey**, *University of Washington*

**Benjamin Young**, *University of Oregon*

Abstracts

### The Combinatorics of CAT(0) Cubical Complexes and Robotic Motion Planning

*1:00 p.m. - 1:30 p.m.*

**Federico Ardila**, *San Francisco State University*

### A Borsuk-Ulam Equivalent that Directly Implies Sperner's Lemma

*1:45 p.m. - 2:15 p.m.*

**Kathryn Nyman**, *Willamette University*

### The Combinatorics of Fully Packed Loops and Razumov-Stroganov Conjectures

*2:30 p.m. - 3:00 p.m.*

**Dan Romik**, *University of California, Davis*

### Parking Functions and Tree Inversions

*3:15 p.m. - 3:45 p.m.*

**David Perkinson**, *Reed College*

### Expanding Hall-Littlewood Polynomials into Schur Functions

*4:00 p.m. - 4:30 p.m.*

**Austin Roberts**, *University of Washington*

### Self-Organizing Cellular Automata

*4:45 p.m. - 5:15 p.m.*

**Alexander E. Holroyd**, *Microsoft Research*

## The Mathematics of Biological Fluid Dynamics

*Friday, August 8, 2:00 p.m. - 4:50 p.m., Hilton Portland, Plaza Level, Pavilion East*

One exciting area of mathematical research within Mathematical Biology is “biological fluid dynamics,” which consists of explaining and understanding the interaction of fluids and living organisms. This includes the motion of microorganisms such as bacteria and algae, cell motion, the fluid flow in the respiratory and cardiovascular systems, flying and swimming, and much more. The research problems are inspired by the need to understand basic functions of life, such as reproduction, growth, feeding, and locomotion.

The mathematics of biological fluid dynamics involves developing theory, creating models, and designing computational methods for numerical simulations of the systems being investigated. This is typically done in collaboration with experimentalists and other scientists. This expository session highlights a variety of applications of the mathematics behind biological fluid dynamics and identifies current research questions in this area.

**Ricardo Cortez**, *Tulane University*

Abstracts

### Neuromechanics and Fluid Dynamics of an Undulatory Swimmer

*2:00 p.m. - 2:20 p.m.*

**Lisa Fauci**, *Tulane University*

### Mathematical Modeling of Sperm Motility and Mucociliary Transport

*2:30 p.m. - 2:50 p.m. *

**Robert Dillon**, *Washington State University*

### Modeling E. Coli Aspartate Chemotaxis in a Stokes Flow

*3:00 p.m. - 3:20 p.m.*

**Hoa Nguyen**, *Trinity University*

### Modeling Interactions between Tumor Cells, Interstitial Fluid and Drug Particles

*3:30 p.m. - 3:50 p.m.*

**Katarzyna A. Rejniak**, *H. Lee Moffitt Cancer Center & Research Institute and University of South Florida*

### Sperm Motility and Cooperativity in Epithelial Detachment

*4:00 p.m. - 4:20 p.m.*

**Julie Simons**, *Tulane University*

### Swimming through Heterogeneous Viscoelastic Media

*4:30 p.m. - 4:50 p.m.*

**Jacek Wrobel**, *Tulane University*

## The Eyes Have It: Mathematical Modeling of the Retina

*Saturday, August 9, 1:00 p.m. - 2:50 p.m., Hilton Portland, Plaza Level, Pavilion West*

Models of the retina are crucial in understanding various retinal diseases and abnormalities that contribute to blindness such as myopia, glaucoma, retinitis pigmentosa, and others. In this session speakers will present mathematical models of retinal detachment, retinal blood flow, and melanopsin activation and inactivation. Utilizing a diverse set of mathematical techniques, analysis, and computer simulations from dynamical systems, numerical analysis, and stochastic processes these models investigate complex retinal process including elevated ocular pressure and forces from retinal adhesion, retinal pigment epithelium pumps, and retinal elasticity leading to retinal detachment, alterations in ocular curvature caused by a reduction retinal blood flow, and the chemical reaction associated with non-image forming process in the retina.

**Erika Camacho**, *Massachusetts Institute of Technology and Arizona State University*

Abstracts

### Mechanical Models for Exudative Retinal Detachments

*1:00 p.m. - 1:20 p.m.*

**Thomas Chou**, *Department of Biomathematics, UCLA*

### New Paradigms in Retinal Blood Flow Simulation

*1:30 p.m. - 1:50 p.m.*

**Andrea Dziubek**, *Mathematics Department, SUNY Institute of Technology*

### Analytical Mechanics and Evolution of a Detaching Retina

*2:00 p.m. - 2:20 p.m.*

**William J. Bottega**, *Department of Mechanical and Aerospace Engineering, Rutgers University*

### Stochastic Modeling of Melanopsin Activation and Deactivation

*2:30 p.m. - 2:50 p.m.*

**Christina Hamlet**, *Center for Computational Science, Tulane University*

## Fast Algorithms on Large Graphs (and Matroids)

*Saturday, August 9, 1:00 p.m. - 3:45 p.m., Hilton Portland, Plaza Level, Pavilion East*

Very large graphs, such as the internet, have become part of our daily routine. Quite naturally they pose new challenges for the mathematician. What are the methods and tools to find out something about a structure so large that we cannot know all of it? Being greedy seems a successful real life strategy familiar to most of us.

Matroids are the most general structures on which the greedy algorithm finds a basis. Communications networks, such as the internet, organic molecules, quasicrystals, etc. are modeled by large graphs. The coarsest analysis uses the matroid structure only. However, in a general geometric setting many problems become hard. For example connectivity augmentation can be solved efficiently on matroids, but becomes NP-hard for geometric planar graphs, even on trees. The purpose of this session is to identify graph properties relevant to current applications and their complexity behaviour as the setting is changed from matroid to graphs and geometric graphs. Speakers will direct their talks on this rapidly developing topic to a general audience.

**Brigitte Servatius**, *Worcester Polytechnic Institute*

**Martin Milanič**, *University of Primorska*

Abstracts

### Pick a Tree, Any Tree

*1:00 p.m. - 1:30 p.m.*

**Gary Gordon**, *Lafayette College*

### Multi-Source Spanning Trees of Graphs

*1:45 p.m. - 2:15 p.m.*

**Andrzej Proskurowski**, *University of Oregon*

### Large Graphs in Internet Tomography and Cyber Defense

*2:30 p.m. - 3:00 p.m.*

**Randy Paffenroth**, *Numerica Corporation*

### Large and Sparse Graphs

*3:15 p.m. - 3:45 p.m.*

**Brigitte Servatius**, *Worcester Polytechnic Institute*