In the numerical simulation for fluid-structure problems, many different possible combinations of coordinate systems can be used for fluid and structure problems.   While Eulerian coordinate is almost always used for fluid problems,  either Eulerian or Lagrangian coordinate can be used for structure problems.   In this talk, I will discuss some mathematical and numerical issues for these different choices of coordinate systems.  In particular, I will report some convergence analysis for eXtended Finite Element Methods (XFEM) for Eulerian-Eulerian coordinates and the study of the well-posedness and preconditioning for finite element discretization based Arbitrary Lagrangian-Elerian (ALE) coordinates.  I will also present some numerical results for some practical applications such as hydroelectric power generator and abdominal aortic aneurysm.

Just as we study varieties by utilizing vector bundles over them, we
often study symplectic manifolds by utilizing holomorphic curves.
While holomorphic curves are by far the most useful tool in
symplectic geometry, the analytical details can often be a
bottleneck. In this talk, we'll talk about how the most computable
cases of holomorphic curve theory may conjecturally be recovered by
purely topological (i.e., non-analytical) means---namely, through the
algebraic structure inherent in cobordisms. As an example theorem, we
will show that if two exact closed Lagrangians submanifolds are
related by an exact Lagrangian cobordism, then their Floer theories
are identical in a very strong sense.

Consider a stochastic heat equation (SHE) driven by multiplicative space-time white noise. It is known that if the initial function had compact support, then the solution is bounded almost surely for all time t. On the other hand, if the initial function is constant, then the solution is not bounded for all time t>0. A natural question is that "is there some decay rate of the initial function at infinity which tells us that the solution is bounded or unbounded for some or even all t”? A short answer is “Yes” and, in this talk, we describe precisely the decay rate of the initial function at infinity which tells us boundedness and unboundedness for some or all time t. This is based on ongoing work with Le Chen and Davar Khoshnevisan.

 Schedule:

 9:00-10:00    Stanislaw Jarecki (UCI), Secure Computation and Oblivious Random Memory

Abstract: We will give an overview of the central cryptographic concept of secure multi-party computation, i.e., of protocols that allow participating parties to perform any computation on their joint data in a way which outputs only the final computation result and hides everything else about the input data.  We will explain the role of Oblivious Random Memory protocols in enabling secure computation on large data, and we will show some recent work and research problems in this area.

10:00-10:30   Refreshments

10:30-11:30   Stanislaw Jarecki (UCI), Covert Computation

Abstract: A notion of covert computation is a variant of secure computation whose goal is to assure that the participants in the computation not only do not learn anything about each other's data except for the final output, but also, unless this final computation output is "favorable" in some way, protocol participants cannot distinguish each other from random noise beacons. In this way no party can even tell if anyone else participates in the computation, except when the final computation output reveals it to them.  For example, covert authentication allows participants to authenticate each other without letting anyone else know that an authentication has taken place.  We will explain the challenges covert computation poses and show some recent work in this area.

 1:00-2:00     Amit Sahai (UCLA), Tutorial on Indistinguishability Obfuscation, Part 1

 2:00-3:00     Refreshments

 3:00-4:00    Amit Sahai (UCLA), Tutorial on Indistinguishability Obfuscation, Part 2

We will recall the standard notions of perfect and scattered subsets of 2^{\omega} and give several equivalent characterizations, make some observations, and record some facts. We will then discuss how some natural analogues to these characterizations diverge from one another in the generalized 2^{\kappa} setting. We will make some observations and give some open questions/directions.