Georgia Institute of Technology College of Sciences

Why do parasites cause disease? Theory has shown that natural selection could select for virulent parasites if virulence is correlated with between-host parasite transmission. Because ecological conditions may affect virulence and transmission, theory further predicts that adaptive levels of virulence depend on the specific environment in which hosts and parasites interact. To test these predictions in a natural system, we study monarch butterflies (Danaus plexippus) and their protozoan parasite (Ophryocystis elektroscirrha). Our studies have shown that more virulent parasites obtain greater between-host transmission, and that parasites with intermediate levels of virulence obtain highest fitness. The average virulence of wild parasite isolates falls closely to this optimum level, providing additional support that virulence can evolve as a consequence of natural selection operating on parasite transmission. Our studies have also shown that parasites from geographically separated populations differ in their virulence, suggesting that population-specific ecological factors shape adaptive levels of virulence. One important ecological factor is the monarch larval host plants in the milkweed family. Monarch populations differ in the milkweed species they harbor, and experiments have shown that milkweeds can alter parasite virulence. Our running hypothesis is that plant availability shapes adaptive levels of parasite virulence in natural monarch populations. Testing this hypothesis will improve our understanding of why some parasites are more harmful than others, and will help with predicting the consequences of human actions on the evolution of disease.

We are going to continue explaining the proof of Seip's Interpolation Theorem for the Bergman Space. We are going to demonstrate the sufficiency of these conditions for a certain example. We then will show how to deduce the full theorem with appropriate modifications of the example.

We present a new theory on Hamiltonian PDE. The linear theory solves an old spectral problem on boundedness of L infinity norm of the eigenfunctions of the Schroedinger operator on the 2-torus. The nonlinear theory develops Fourier geometry, eliminates the convexity condition on the (infinite dimension) Hamiltonian and is natural for PDE.

Gibbs free energy plays an important role in thermodynamics and has strong connection with PDE, Dynamical system. The results about Gibbsfree energy in 2-Wasserstein metric space are known recently.First I will introduce some basic things, so the background knowledge isnot required. I will begin from the classic definition of Gibbs freeenergy functional and then move to the connection between Gibbs freeenergy and the Fokker-Planck equation, random perturbation of gradientsystems. Second, I will go reversely: from a dynamical system to thegeneralized Gibbs free energy functional. I will also talk about animportant property of the Gibbs free energy functional: TheFokker-Planck equation is the gradient flux of Gibbs free energyfunctional in 2-Wasserstein metric.So it is natural to consider a question: In topological dynamical systemand lattice dynamical system, could we give the similar definition ofGibbs free energy, Fokker-Planck equation and so on? If time allowed, Iwill basicly introduce some of my results in these topics.