Events for the week of February 08 2010

Abstract. Given an automorphic representation $\pi$ of the adelic points of a reductive group $G$ over a number field $F$, there is a great interest in knowing whether periods integrals over $H(F)\backslash H(A)$ for some closed subgroup $H$ of $G$, vanish for all functions in the space of $\pi$. I will mostly discuss the case where $G$ is the general linear group over a quadratic extension $E/F$ and $H$ is a unitary group with respect to $E/F$. This case was originally considered by Jacquet and he developed the relative trace formula to attack it. I will also discuss the analogous local question: which representations of $GL_n(E)$ ($E/F$ local) admit a functional invariant under a unitary group and what can be said about these functionals. Joint work with Brooke Feigon and Omer Offen.

Abstract. Bordered Floer homology is an extension of Heegaard Floer homology to three-manifolds with boundary. More precisely, to (parameterized) surface, it associates a differential algebra, and to a three-manifold with (parameterized) boundary, it associates a module over the algebra. The Heegaard Floer homology for a three-manifold split in two along a separating surface can be calculated by a pairing theorem in terms of the modules associated to the two pieces. I will explain this construction. This is joint work with Robert Lipshitz and Dylan Thurston.

Abstract. We discuss some aspects of constructing physical models over totally disconnected local fields. In particular, we will consider a quantum mechanical model with inner symmetries, and obtain a Feynman-Kac formula for the propagator in this setting.

Abstract. To grow and disperse effectively, fungi must solve hard physical problems. I'll show how math modeling can be used to illuminate these problems by connecting events that can happen in less than the blink of an eye with the lengthy evolutionary paths taken to achieve them. I'll focus on two problems of recent interest to me:

#1. The forcibly launched spores of ascomycete fungi must eject through a boundary layer of nearly still air in order to reach dispersive air ï¬~Bows. Because of their microscopic size singly ejected spores are almost immediately brought to rest by fluid drag. However, by coordinating the ejection of thousands or hundreds of thousands of spores, some fungi are able to sculpt a flow of air that carries spores across the boundary layer and around any intervening obstacles.

#2. A growing filamentous fungi may harbor a diverse population of nuclei. There is evidence that this internal diversity makes pathogenic fungi more virulent, and allows fungi in general to better exploit heterogeneous substrates. I'll show that, to maintain stable populations of different nuclei near the growing tips, a fungus must create costly internal flows over the entire of the colony.

Abstract. I will present an elementary introduction to conformal field theory in the context of complex analysis and probability theory. Ward functional is introduced as an insertion operator under which the correlation functions are transformed into their Lie derivatives. This concept leads us to rediscover several formulas in conformal field theory including Ward identities. This presentation will also include relations between conformal field theory and Schramm-Loewner evolutions. This is joint work with Nikolai Makarov.

Abstract. A triple system is cancellative if no three of its distinct edges satisfy A \cup B = A \cup C. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is cancellative.

We prove that almost all triple systems with vertex set $[n]$ are tripartite. This sharpens results of Nagle and Rodl on the number of cancellative triple systems with vertex set [n]. It also extends recent work of Person and Schacht who proved a similar result for triple systems without the Fano configuration.

Our proof uses the strong hypergraph regularity lemma, and stability theorems.

It is joint work with D. Mubayi.

Abstract. Heegaard Floer homology is a tool for studying low-dimensional manifolds, defined using techniques from symplectic geometry. I will outline its construction, describe some of its applications, and discuss some more recent advances. The first form of this invariant was defined in joint work with Zoltan Szabo. I will also describe joint work with other collaborators, including Robert Lipshitz, Ciprian Manolescu, Sucharit Sarkar, and Dylan Thurston.

Abstract. Neither solvers with best numerical convergence nor solvers with best parallel efficiency are the best choice for the fast solution of PDE problems in practice. The fastest solvers require a delicate balance between their numerical and hardware characteristics and the talk will discuss this balance on all levels of current hardware architectures: SIMD vectorization, thread block parallelization, intra-node parallelism and inter-node parallelism in a cluster. Finally, we will look at ways of abstracting the technical complexities for everyday use in computational science.

Bio: Robert Strzodka is the head of the research group Integrative Scientific Computing at the Max Planck Institute for Computer Science in Saarbrücken, Germany since 2007. His research focuses on efficient interactions of mathematic, algorithmic and architectural aspects in heterogeneous high performance computing. Previously, Robert was a visiting assistant professor in computer science at the Stanford University and until 2005 a postdoc at the Center of Advanced European Studies and Research in Bonn. He received his doctorate in numerical mathematics from the University of Duisburg-Essen in 2004.

Abstract. The asymptotic expansions to the Boltzmann equations provide a clue of the connection from kinetic theory to fluid mechanics. The Hilbert expansion turns out to be useful to verify compressible fluid limits. As its applications, we rigorously establish the compressible Euler and acoustic limits from the Boltzmann equation and the Euler-Poisson limit from the Vlasov-Poisson-Boltzmann system. Moreover, we prove a global-in-time convergence for a repulsive Euler-Poisson flow for irrotational monatomic gas.