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Invited Paper Sessions

Computational Aspects of Algebra, Geometry and Combinatorics

Thursday, August 7 and Friday, August 8, afternoon

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

Tentative List of Speakers

Federico Ardila, San Francisco State University
Dan Romik, University of California Davis
Stephanie van Willigenburg, University of British Columbia
Alexander HolroydMicrosoft Research
Isabella NovikUniversity of Washington
David PerkinsonReed College

Connections between Logic and Arithmetic Geometry

Thursday, August 7, afternoon

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 PoonenMassachusetts Institute of Technology

Confirmed Speakers

Kirsten Eisenträger, The Pennsylvania State University
Russell Miller, Queens College, City University of New York
Alice Medvedev, University of California at Berkeley
Florian PopThe Pennsylvania State University

Mathematical Epidemiology

Thursday, August 7, afternoon

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 CortezTulane University

Confirmed Speakers

Comparing Risk for Chikungunya and Dengue Emergence using Mathematical Models
Carrie Manore, Tulane University

How are Fish Population Dynamics Shaped by a Changing Environment? Insights from a Mathematical Model Driven by Temperature and Dissolved Oxygen Data from Lake Erie
Paul Hurtado, Mathematical Biosciences Institute

Determining Causal Networks in Nonlinear Dynamical Systems: Ecosystem Applications
Bree Cummins, Montana State University

Epidemic Forecasting and Monitoring using Modern Data Assimilation Methods
Kyle Hickmann, Los Alamos and Tulane University

Qualitative Inverse Problems using Bifurcation Analysis in the Recurrent Neural Network Model
Stephen Wirkus, Arizona State University

Mathematics of Planet Earth 2013+: Management of Natural Resources
Abdul-Aziz Yakubu, Howard University

The Mathematics of Biological Fluid Dynamics

Friday, August 8, afternoon

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 CortezTulane University

Confirmed Speakers

Neuromechanics and Fluid Dynamics of an Undulatory Swimmer
Lisa Fauci, Tulane University

Mathematical Modeling of Sperm Motility and Mucociliary Transport
Robert Dillon, Washington State University

Modeling E. Coli Aspartate Chemotaxis in a Stokes Flow
Hoa Nguyen, Trinity University

Modeling Interactions between Tumor Cells, Interstitial Fluid and Drug Particles
Katarzyna A. Rejniak, H. Lee Moffitt Cancer Center & Research Institute and University of South Florida

Sperm Motility and Cooperativity in Epithelial Detachment
Julie Simons, Tulane University

Swimming through Heterogeneous Viscoelastic Media
Jacek Wrobel, Tulane University

Fast Algorithms on Large Graphs (and Matroids)

Saturday, August 9, afternoon

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 ServatiusWorcester Polytechnic Institute
Martin MilaničUniversity of Primorska

Tentative List of Speakers

Gary Gordon, Lafayette College
Randy Paffenroth, Numerica Corporation
Andrzej Proskurowski, University of Oregon
Martin Milanič, University of Primorska
Brigitte Servatius, Worcester Polytechnic Institute

The Eyes Have It: Mathematical Modeling of the Retina

Saturday, August 9, afternoon

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 CamachoMassachusetts Institute of Technology and Arizona State University

Confirmed Speakers

Mechanical Models for Exudative Retinal Detachments
Thomas Chou, Department of Biomathematics, UCLA

Analytical Mechanics and Evolution of a Detaching Retina
William J. Bottega, Department of Mechanical and Aerospace Engineering, Rutgers University

New Paradigms in Retinal Blood Flow Simulation  
Andrea Dziubek, Mathematics Department, SUNY Institute of Technology

Stochastic Modeling of Melanopsin Activation and Deactivation
Christina Hamlet, Center for Computational Science, Tulane University