| Monday Feb 08 |
| 16:00-16:50 | Number Theory Seminar (MS 6229) |
| Erez Lapid (The Hebrew University of Jerusalem) | Distinction by Unitary Groups |
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. |
| Tuesday Feb 09 |
| 15:00-15:50 | Participating Analysis Seminar (6221) |
| William Meyerson (UCLA) | A highly non-regular map from the cube to the square
|
| Wednesday Feb 10 |
| 15:00-15:50 | Topology Seminar (MS 6221) |
| Peter Oszvath (Columbia University) | Bordered Floer homology |
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. |
| 16:00-16:50 | Functional Analysis Seminar (MS6627) |
| Trond Digernes (Norwegian University of Science and Technology, Trondheim) | Physical models over totally disconnected local fields |
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. |
| 16:00-16:50 | Applied Math Colloquium (MS 6229) |
| Marcus Roper | Fungal Fluid Mechanics |
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. |
| 16:00-16:50 | Algebra Seminar (MS 7608) |
| Bin Zhao (UCLA) | BOI seminar: Discriminant. |
| 16:00-16:50 | Probability Seminar (MS 5137) |
| Nam-Gyu Kang (Caltech) | Gaussian free field, conformal field theory, and
Schramm-Loewner evolution. |
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. |
| Thursday Feb 11 |
| 13:50-14:50 | Combinatorics Seminar (MS 5148) |
| Jozsef Balogh (UCSD) | Almost all cancellative triple systems are tripartite |
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. |
| 15:00-15:50 | Colloquium (MS 6627) |
| Peter Ozsvath (Columbia University) | Heegaard Floer homology |
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. |
| 16:15-17:05 | Colloquium (MS 6627) |
| Kang Tae Kim (POSTECH) | Almost complex but non-complex homogeneous structures |
| Friday Feb 12 |
| 14:00-14:50 | Special Applied Math Talk (MS 6221) |
| Robert Strzodka (Max Planck Institute for Informatics in Saarbruecken, Germany) | Balancing Numerical and Hardware Characteristics of Multigrid Methods |
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. |
| 15:00-15:50 | Analysis and PDE Seminar (6221 MS) |
| Juhi Jang (Courant Institute, NYU) | On the Hilbert expansion of the Boltzmann Equations |
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. |
| 16:00-16:50 | Algebra Seminar (MS 5217) |
| Viraj Navkal (UCLA) | Algebraic surfaces: Intersection theory, 2. |