Events for the week of May 23 2016

 Monday May 23 14:00-14:50 Special Seminar (7619C MS) Guy Gilboa (Technion, Israel Inst. of Technology) Spectral TV Abstract. A new framework is proposed for variational analysis and processing. It defines a functional-based nonlinear transform and inverse-transform. The framework is developed in the context of total-variation (TV), but it can be generalized to other functionals. An eigenfunction, with respect to the subdifferential of the functional, such as a disk in the TV case, yields an impulse in the transform domain. This can be viewed as a generalization of known spectral approaches, based on linear algebra, which are extensively used in image-processing, e.g. for segmentation. Following the Fourier intuition, a spectrum can be computed to analyze dominant scales in the image. Moreover, new nonlinear low-pass, high-pass and band-pass filters can be designed with full contrast and edge preservation.Hide 16:00-16:50 Number Theory Seminar (MS 5117) Anne Carter (UCSD) Lubin-Tate Deformation Spaces and $(\phi,\Gamma)$-Modules Abstract. Jean-Marc Fontaine has shown that there exists an equivalence of categories between the category of continuous $\mathbb{Z}_p$-representations of a given Galois group and the category of \'{e}tale $(\phi,\Gamma)$-modules over a certain ring. We are interested in the question of whether there exists a theory of $(\phi,\Gamma)$-modules for the Lubin-Tate tower. We construct this tower via the rings $R_n$ which parametrize deformations of level $n$ of a given formal module. One can choose prime elements $\pi_n$ in each ring $R_n$ in a compatible way, and consider the tower of fields $(K'_n)_n$ obtained by localizing at $\pi_n$, completing, and passing to fraction fields. By taking the compositum $K_n = K_0 K'_n$ of each field with a certain unramified extension $K_0$ of the base field $K'_0$, one obtains a tower of fields $(K_n)_n$ which is strictly deeply ramified in the sense of Anthony Scholl. This is the first step towards showing that there exists a theory of $(\phi,\Gamma)$-modules for this tower. In this talk we will introduce the notions of formal modules and their deformations, strictly deeply ramified towers of fields, and $(\phi,\Gamma)$-modules, and sketch the proof that the Lubin-Tate tower is strictly deeply ramified.Hide Tuesday May 24 14:00-14:50 The Level Set Collective (IPAM 1180) Jun Saito (Method Studios) A Deep Learning Framework for Character Motion Synthesis and Editing Abstract. We present a framework to synthesize character movements based on high level parameters, such that the produced movements respect the manifold of human motion, trained on a large motion capture dataset. The learned motion manifold, which is represented by the hidden units of a convolutional autoencoder, represents motion data in sparse components which can be combined to produce a wide range of complex movements. To map from high level parameters to the motion manifold, we stack a deep feedforward neural network on top of the trained autoencoder. This network is trained to produce realistic motion sequences from parameters such as a curve over the terrain that the character should follow, or a target location for punching and kicking. The feedforward control network and the motion manifold are trained independently, allowing the user to easily switch between feedforward networks according to the desired interface, without re-training the motion manifold. Once motion is generated it can be edited by performing optimization in the space of the motion manifold. This allows for imposing kinematic constraints, or transforming the style of the motion, while ensuring the edited motion remains natural. As a result, the system can produce smooth, high quality motion sequences without any manual pre-processing of the training data.Hide 14:00-14:50 Participating Analysis Seminar (MS 6221) Eden Prywes (UCLA ) Isoperimetric dimension I 15:30-16:20 Participating Analysis Seminar (MS 6221) Misha Hlushchanka (Jacobs University, Bremen) Palindromic subshifts and groups of intermediate growth I Wednesday May 25 11:00-12:50 Algebra Seminar (MS6905) Kevin Carlson (UCLA) Modularity of representations of rational voas Thursday May 26 14:00-14:50 Combinatorics Seminar (MS 7608) Iskander Aliev (Cardiff University) Parametric Polyhedra with at least k Lattice Points Abstract. See here: http://www.math.ucla.edu/~pak/lectures/Iskander-abstract.pdfHide Friday May 27 15:00-15:50 Topology Seminar (MS 5148) Rui Wang (UC Irvine) On Hamiltonian Gromov-Witten theory for symplectic reductions Abstract. Assume $G$ is a connected compact Lie group and $(M,omega)$ is a symplectic manifold which admits a Hamiltonian $G$-action. At each regular value of the moment map, there is a natural reduced symplectic orbifold constructed by the symplectic reduction. In my talk, I will first review some recent results by Chen-Wang on the Hamiltonian Gromov-Witten theory in defining a new quantum deformation for the cohomology ring of a symplectic reduction. Then I will introduce the on-going project with Bohui Chen and Bai-Ling Wang on studying the relation between these invariants and Gromov-Witten invariants.Hide 15:00-15:50 Algebra Seminar (MS 7608) Paolo Aluffi (Florida State University) Chern classes of Schubert varieties Abstract. There is a functorial theory of Chern classes, due to MacPherson, generalizing to singular varieties the notion of total Chern class of nonsingular varieties. The resulting classes can be shown to agree with classes defined earlier by M.-H. Schwartz. In joint work with Leonardo Mihalcea we compute the Chern-Schwartz-MacPherson classes of Schubert varieties in flag manifolds. These classes are obtained by constructing a representation of the Weyl group, by means of certain Demazure-Lusztig type operators. The construction extends to the equivariant setting. Based on explicit computations in low dimension, we conjecture that these classes are Schubert-positive; the analogous conjecture for Schubert varieties was recently proven by June Huh.Hide 16:00-16:50 Analysis and PDE Seminar (MS 6221) Yifeng Yu (UC Irvine) Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model (Joint with Caltech) Abstract. I will talk about some finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis in 90´s. We proved that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Implications on the effective flame front and other related inverse type problems will also be discussed. This is a joint work with Wenjia Jing and Hung Tran.Hide 17:00-17:50 Analysis and PDE Seminar (MS 6221) Joel Tropp (Caltech) TBA (Joint with Caltech) Abstract. TBAHide