A second order energy stable numerical scheme is presented for the two and three dimensional Cahn-Hilliard equation, with Fourier pseudo-spectral approximation in space. The convex splitting nature assures its unique solvability and unconditional energy stability. Meanwhile, the implicit treatment of the nonlinear term makes a direct nonlinear solver not available, due to the global nature of the pseudo-spectral spatial discretization. In turn, a linear iteration algorithm is proposed 
to overcome this difficulty, in which a Douglas-Dupont-type regularization term is introduced. As a consequence, the numerical efficiency has been greatly improved, since the highly nonlinear system can be decomposed as an iteration of purely linear solvers. Moreover, a careful nonlinear analysis shows a contraction mapping property of this linear iteration, In addition, a maximum norm bound of numerical solution is also derived at a theoretical level. A few numerical examples 
are also presented in this talk.

9:30-10     Welcome and refreshments
10-10:45    Hovav Shacham (UCSD) will speak on 
                 "Elliptic curves in kleptography: 
                  The case of the Dual EC random number generator"
10:45-11    Refreshments
11-12         GENERAL AUDIENCE TALK: Hovav Shacham (UCSD) will speak on 
                  "Why making elections trustworthy is a computer science problem"
2-2:45        Hovav Shacham (UCSD) will speak on 
                  "Subnormal floating point and abnormal timing"
2:45-3        Refreshments
3-4             Rafail Ostrovsky (UCLA) will speak on 
                  "Delegation of computation into the cloud" Part 1
4-4:30        Refreshments
4:30-5:30   Rafail Ostrovsky (UCLA) will speak on 
                  "Delegation of computation into the cloud" Part 2

Website: http://www.math.uci.edu/~asilverb/CryptoDayApril2016.html

The Toda lattice is the prototypical discrete-space, continuous-time completely integrable Hamiltonian system.  It was introduced by Morikazu Toda in 1967 and analyzed in detail by Flaschka in 1974.  The bi-infinite Toda lattice can be solved with its associated inverse scattering transform (IST).  The IST is closely tied to the interpretation of the flow as an isospectral deformation of a bi-infinite tridiagonal matrix.  The Toda lattice has a completely integrable counterpart for finite symmetric and Hermitian (dense) matrices.  And due the the isospectral nature of the flow, it can be used as an eigenvalue algorithm. This talk has two parts. First, I will discuss the numerical computation of the IST for the Toda lattice by solving Riemann--Hilbert problems numerically.  Second, I will show that the time, called the halting time, it takes for the Toda lattice to compute the largest eigenvalue of a random matrix is universal --- the rescaled halting time converges to a universal distribution.

We study random permutations of the vertices of a hypercube  given by products of (uniform, independent) random transpositions on edges.  We establish the existence of a phase transition accompanied by emergence of cycles of diverging lengths. The problem is motivated by phase transitions in quantum spin models. (Joint work with Piotr Miłoś and Daniel Ueltschi.)

For singular operators of the form (H_{\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+ \frac{g(\theta+n\alpha)}{f(\theta+n\alpha)} u_n, we prove such operators have purely singular spectrum on the set {E: \delta{(\alpha,\theta)}>L(E)\}, where f and g are both analytic functions.