Stanford Applied Math Seminar

Wednesdays at 4:30 PM in 384H.

Winter 2017 Schedule

January 17
Li-Cheng Tsai, Columbia University
KPZ equation limit for the six vertex model

The Six Vertex (6V) model, initially introduced as a model for ice, is an integrable model for tiling in two dimensions. In this talk we consider symmetric and stochastic 6V models, and show that, under certain scaling into the ferroelectric/disordered phase critical point, fluctuations described by the Kardar--Parisi--Zhang (KPZ) equation arises. Our approach utilizes the one- and two-point Markov duality enjoyed by the stochastic 6V model. One-point duality gives the (so-called) microscopic Hopf--Cole transform, and thereby exposes the connection to the KPZ equation. On the other hand, two-point duality provides exact, analyzable formulas that help to establish certain self-averaging, which is the key step in the proof given the aforementioned transform. Joint work with Ivan Corwin, Promit Ghosal, and Hao Shen

January 24
Houman Owhadi, Caltech
A game theoretic approach to numerical approximation and algorithm design

This talk will cover interplays between Game Theory, Numerical Approximation and Gaussian Process Regression. We will illustrate this interface between statistical inference and numerical analysis through problems related to numerical homogenization, operator adapted wavelets, fast solvers, and computation with dense kernel matrices. This talk will cover joint work with F. Schäfer, C. Scovel, T. Sullivan and L. Zhang.

January 31
Yuwei Fan Stanford University
On the moment model reduction for kinetic equation

Model reduction of kinetic equation turns a high dimensional problem to a low dimensional quasi-linear system, which not only provides further understanding of the problem, but also essentially improves the efficiency of the numerical simulation. As a quasi-linear system with Cauchy data, the well-posedness of the model deduced is required to be hyperbolic. In the existed models, some of them are hyperbolic, and some of them may be regularized to be hyperbolic, while there are seldom progress on the else models. In this talk, I will start from Grad's moment method, and point out that all Grad's moment system are not hyperbolic even around the thermodynamic equilbrium, and then proposed a globally hyperbolic regularization for Grad's moment system to obtain the globally hyperbolic moment system. By exploring the essential of the regularization, we extend the regularization to a generic framework to moment model reduction for kinetic equation. The fascinating point is, with only routine calculation, symmetric hyperbolic models can always be deduced with any ansatz for generic kinetic equation by the framework we proposed. By this framework, existing models are re-presented and brand new models are discovered.

February 7
Jonathan Luk, Stanford
Multi-dimensional shock formation for hyperbolic systems

Shock formation for hyperbolic systems in one spatial dimension has been well-understood since the 70s. More recently, there has been much progress in understanding shock formation in more than one dimensions in the special case of quasilinear scalar wave equations. The problem for general hyperbolic systems, especially for those featuring more than one characteristic speeds, still remains widely open.
In this talk, I will discuss some of the recent progress and present a joint result with Speck (MIT) in which we exhibit a solution regime of stable shock formation for the full 3D compressible Euler equations with non-trivial vorticity and variable entropy. This is the first multi-dimensional shock formation result featuring multiple characteristic speeds. I will emphasis and discuss the geometric methods used in the proof.

February 23, Friday, 3pm in 384I
David Loaiza, Aperio
Inventing the Future of Finance, Alternative Data and Aperio

Times are changing. Traditionally, Corporate access and financial modeling were paramount to the investing process. Today, we are surrounded by alternative data from credit cards, smart devices and sensors. That means that there are radical ways to gain deeper understanding of a company’s revenue performance and trends leveraging big data. Aperio models terabytes of raw data, delivering powerful insights to our Long/Short Equity teams.
Dr. David Loaiza is a Managing Director and the Chief Data Scientist for Aperio. He is responsible for Point72’s big data research team. Prior to joining Point72, David was the Chief Data Scientist and Global Head for Compliance Analytics at JP Morgan Chase. He led teams overseeing Anti-Money Laundering, Trade Surveillance, Know Your Customer risk scoring, Sanction List and Fair Lending analytics.
Dr. Loaiza was also a White House Fellow working as a special assistant to the White House Office of Management and Budget. Before the White House, he was the technical advisor and a technical team leader for the U.S. Delegations monitoring the denuclearization activities in North Korea. He has fifteen years of experience leading research programs at Los Alamos National Laboratory. Dr. Loaiza has a Ph.D. in nuclear physics and an MBA.

February 28,
Chrysoula Tsogka, Stanford

March 7,
Charles-Albert Lehalle, Paris
From Empirical Behaviour of High Frequency Traders to Optimal High Frequency Interactions with a Limit Orderbook

As a motivation, I will start by a quick summary of [1], that gives empirical evidences on the behaviour of HFT around news and gives some statistics about their activity in Europe. After a short discussion on the way they provide less liquidity on expected news than usual, even once corrected from volatility variations, I will take evidences from [3] and [4] to show that HFT do use the imbalance of orderbooks to take decisions at the finest level. Since imbalance of orderbook is known to play a role in orderbook dynamics [5], I will then present the stochastic control framework of [2] dedicated to take decisions at this level. Then we will see how to obtain results in this framework and conclude by comparing them to previous empirical evidences. This will suggest HFT are using control frameworks that are probably close to ours.

March 14,
Domokos Szasz, Budapest University of Technology and Economics
Fourier law from Hamiltonian dynamics

It is a classical and fundamental quest of mathemat- ical statistical physics to rigorously understand the heat trans- fer equation of Laplace from Hamiltonian dynamics. In 2008 the physicists Gaspard and Gilbert came up with a billiard model and suggested a two step approach for it: 1. for the energies of the par- ticles derive – in the rare interaction limit – a Markov jump pro- cess (dynamical part); 2. take the hydrodynamic limit of the ob- tained jump process; this is expected to lead to the Laplace equa- tion (stochastic part). Since their model was still unsuitable for mathematics, we first introduced its tractable variant: the disk- piston model. For it we can show that its rare interaction limit is, indeed, a Markov jump process. The talk is based on joint works with P. Balint, Th. Gilbert, P. Nandori and I.P. Toth

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