### Mon Jan 22, 2018

**Nam Trang**- (UCI)

Models of the axiom of determinacy and their generic extensions

Forcing and elementary embeddings are central topics in set theory. Most of what set theorists have focused on are the study of forcing and elementary embeddings over models of ZFC. In this talk, we focus on forcing and elementary embeddings over models of the Axiom of Determinacy (AD). In particular, we focus on answering the following questions: work in V which models AD. Let P be a forcing poset and g ⊆ P be V -generic.

1) Does V [g] model AD?

2) Is there an elementary embedding from V to V [g]?

Regarding question 1, we want to classify what forcings preserve AD. We show that forcings that add Cohen reals, random reals, and many other well-known forcings do not preserve AD. Regarding question 2, an analogous statement to the famous Kunen’s theorem for models of ZFC, can be shown: suppose V = L(X) for some set X and V models AD, then there is no elementary embedding from V to itself. We conjecture that there are no elementary embeddings from V to itself. We present some of the results discussed above. There is still much work to do to completely answer questions 1 and 2. This is an ongoing joint work with D. Ikegami.

**SCGAS**- (Winter School)

2018 SCGAS Winter School

**Winter School Website:** https://sites.google.com/a/uci.edu/2018-scgas-winter-school/

**Jianxian Qiu**- (Xiamen University)

A simple and efficient WENO method for hyperbolic conservation laws

In this presentation, we present a simple high order weighted essentially non- oscillatory (WENO) schemes to solve hyperbolic conservation laws. The main advantages of these schemes presented in the paper are their compactness, robustness and could maintain good convergence property for solving steady state problems. Comparing with the classical WENO schemes by {G.-S. Jiang and C.-W. Shu, J. Comput. Phys., 126 (1996), 202-228}, there are two major advantages of the new WENO schemes. The first, the associated optimal linear weights are inde- pendent on topological structure of meshes, can be any positive numbers with only requirement that their summation equals to one, and the second is that the new scheme is more compact and efficient than the scheme by Jiang and Shu. Extensive numerical results are provided to illustrate the good performance of these new WENO schemes.

**Gabriel Drummond-Cole**- (POSTECH IBS-CGP)

Subdivisional spaces and configuration spaces of graphs

Configuration spaces of manifolds are often studied using the local model of configurations of Euclidean space. Configuration spaces of graphs have been studied as rigid combinatorial objects. I will describe a model for configuration spaces of cell complexes which combines the best features of both of these traditions, along with some applications in the homology of the configuration spaces of graphs. This is joint work with Byunghee An and Ben Knudsen.

### Tue Jan 23, 2018

**Andrew Seth Raich**- (University of Arkansas )

The Global Behavior of the Fourier and FBI transforms

In this talk, I will discuss the strengths and shortcomings of the Fourier transform as a tool to investigate the global analysis of PDEs. As part of this discussion, I will give various applications to problems in several complex variables and introduce a FBI transform as a more broadly applicable tool.

### Thu Jan 25, 2018

**Roman Vershynin**- (UCI)

Deviations of random matrices and applications

Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This talk will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

**Bianca Thompson**- (Harvey Mudd)

Uniform Bounds of Families of Twists

The study of discrete dynamical systems boomed in the age of computing. The Mandelbrot set, created by iterating 0 in the function z^2+c and allowing c to vary, gives us a wealth of questions to explore. We can ask about the number of rational preperiodic points (points whose iterates end in a cycle) for z^2+c. Can this number be uniform as we allow c to vary? It turns out this is a hard question to answer. Instead we will explore places where this question can be answered; twists of rational functions.

**Hongzi Cong**- (UCI and Dalian University of Technology (China))

The stability of full dimensional KAM tori for nonlinear Schrödinger equation

In this talk, we will show that the full dimensional invariant tori obtained by Bourgain [J. Funct. Anal., 229 (2005), no. 1, 62–94] is stable in a very long time for 1D nonlinear Schrödinger equation with periodic boundary conditions.

### Fri Jan 26, 2018

**Xiaowen Zhu**- (UC Irvine)

Proof of localization for Anderson Model in d dimension II

I will continue the talk and give the details of the proof.

**Alexander Figotin**- (UC Irvine)

Neoclassical Theory of Electromagnetic Interactions

The theory of electromagnetic (EM) phenomena known as electrodynamics is one of the major theories in science. At macroscopic scales the interaction of the EM field with matter is described by the classical electrodynamics based on the Maxwell-Lorentz theory. Many of electromagnetic phenomena at microscopic scales are covered by the so-called semiclassical theory that treats the matter according to the quantum mechanics, whereas the EM field is treated classically. The subject of this presentation is a recently advanced by us neoclassical electromagnetic theory that describes EM phenomena at all spatial scales –microscopic and macroscopic. This theory modifies the classical electrodynamics into a theory that applies to all spatial scales including atomic and nanoscales. The neoclassical theory is conceived as one theory for all spatial scales in which the classical and quantum aspects are naturally unified and emerge as approximations. It is a classical Lagrangian field theory, and consequently it is a local and deterministic theory. Probabilistic aspects of the theory may arise in it effectively through complex nonlinear dynamical evolution. This presentation is to provide an introduction to our theory including a concise historical review.

(Joint work with Anatoli Babin)