Many problems arising in image processing and signal recovery with multi -regularization and constraints can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function and a nonsmooth function. In this talk, we aim to propose a primal-dual fixed point (PDFP) scheme to solve the above class of problems. The proposed algorithm is a symmetric and fully splitting scheme, only involving explicit gradient, linear transform and the proximity operators which may have closed-form solution. The convergence of the algorithm is established and some numerical examples are performed to show its efficiency. This is a joint work with Peijun Chen and Xiaoqun Zhang from Shanghai Jiao Tong University.
In this talk I will introduce the moduli space of curves, and a class of vector bundles “of conformal blocks” on the moduli space of curves. I’ll give a nonspecialist definition of these bundles, which have connections to algebraic geometry, representation theory and mathematical physics. I’ll talk about how by studying the bundles we can learn about the moduli space of curves, and vice versa, focusing on just a few recent results, and open problems.
Let $X$ be a compact manifold with the boundary $Y$ and $R(k)$ be a
Dirichlet-to-Neumann operator: $R (k):f \to \partial_n u |_Y$ where u solves
$$
(Delta+k^2) u=0, \ u|_Y=f.
$$
We establish asymptotics as $k\to \infty$ of the number of eigenvalues of
$k^{-1}R (k)$ between $a$ and $b$.
We will discuss tools, used to solve this problem: sharp semiclassical spectral
asymptotics and Birman-Schwinger principle.
This is a joint work with Andrew Hassell, Australian National University.
