2 August 2019 
Title: SelfDual Codes over Finite Fields
Dr. Lin SOK Time: 11.00am – 12.00pm
Abstract
In this talk, we study selfdual codes over finite fields using tools from algebraic function field of one variable. An algebraic geometry code is defined with two divisors G and D, where D is the sum of n points on a specified algebraic curve. We characterize selforthogonality of the 0genus code in terms of the divisors G and D and the value of a wellchosen derivative polynomial at points P_i for i from 1 to n. We explore the existence problem of MDS selfdual codes in odd characteristic cases and explicitly construct families of new MDS selfdual codes.
Host: Professor Ling San Division of Mathematical Sciences, School of Physical and Mathematical Sciences

31 July 2019

Title: Seismic tomography, frozen Gaussian approximation and deep learning
Associate Professor Xu Yang Time: 2:00pm – 2:30pm
Abstract
Threedimensional (3D) elastic wave propagation and seismic tomography is computationally challenging in large scales and highfrequency regime. In this talk, we propose the frozen Gaussian approximation (FGA) to compute the 3D elastic wave propagation and use it as the forward modeling tool for seismic tomography with highfrequency data. The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method. With a parallel FGA solver built as a computational platform, we explore various applications in 3D seismic tomography, including seismic travel time tomography and full waveform inversion, respectively. Global minimization for seismic tomography is investigated based on particle swarm algorithm. We also apply the FGA algorithm to train deep neural networks to learn the object of low velocity in the interested areas.
Host: Assistant Professor Tong Ping Division of Mathematical Sciences, School of Physical and Mathematical Sciences

22 July 2019 
Title: CVA Wrong Way Risk: Calibration using a Quanto CDS Basis
Dr. CHUNG TszKin (Bill) Time: 3.00pm – 4.00pm
Abstract
In this article, we discuss the calibration of wrong way risk (WWR) model by using information from the credit default swap (CDS) market. A quanto CDS provides credit protection against the default of a reference entity but is denominated in a nondomestic currency. The payoff of a quanto CDS contract, therefore, reflects the marketimplied interaction of FX risk and a credit event. This in turn, defines the cost of hedging WWR for an FXsensitive portfolio. Our empirical evidence shows that the implied FX jump sizes are significant for a wide range of corporates. For systemic counterparties, the CVA WWR addon could be 40% higher than the standard case, and choosing a proper jumpatdefault WWR model is critical to capture the impact. In contrast, historical correlation gives the incorrect relationship (rightway risk) and cannot calibrate to the market prices in many cases, leading to the mispricing of CVA WWR.
Joint work with Jon Gregory
Host: Assistant Professor Pun Chi Seng Patrick Division of Mathematical Sciences, School of Physical and Mathematical Sciences

21 May 2019 
Title: Algorithms for Wave Scattering of Random Media: Fast multipole method in layered media and a phase shift deep neural network for wideband learning
Professor Wei Cai Time: 3.00pm – 4.00pm
Abstract
In this
talk, we will present two algorithms and numerical results for solving
electromagnetic wave scattering of random metamaterials. Firstly, a fast multipole method for 3D Helmholtz equation for layered media
will be presented based on new multipole
expansion (ME) and multipole to local
translation (M2L) operators for layered media Green's functions. Secondly, a parallel phase shift deep neural network
(PhaseDNN) is proposed for wideband data learning. In order to achieve uniform
convergence for low to high frequency content of data, phase shifts are used to convert high
frequency learning to low frequency learning. Due to the fast learning of many
DNNs in the low frequency range, PhaseDNN is able to learn wideband data
uniformly in all frequencies.
Host: Associate Professor Wang LiLian Division of Mathematical Sciences, School of Physical and Mathematical Sciences

21 May 2019 
Title: Approximation Theory and Regularization for Deep Learning
Assistant Professor Haizhao Yang Time: 4.00pm – 5.00pm
Abstract
This talk introduces new approximation theories for deep learning in parallel computing and high dimensional problems. We will explain the power of function composition in deep neural networks and characterize the approximation capacity of shallow and deep neural networks for various functions on a highdimensional compact domain. Combining parallel computing, our analysis leads to an important point of view, which was not paid attention to in the literature of approximation theory, for choosing network architectures, especially for largescale deep learning training in parallel computing: deep is good but too deep might be less attractive. Our analysis also inspires a new regularization method that achieves stateoftheart performance in most kinds of network architectures
Host: Associate Professor Wang LiLian Division of Mathematical Sciences, School of Physical and Mathematical Sciences

15 May 2019 
Title: A general approach to nonMarkovian timeinconsistent stochastic control for sophisticated players
Assistant Professor Dylan Possamai Time: 4.00pm – 5.00pm
Abstract
This paper is the first attempt at a general nonMarkovian theory of timeinconsistent stochastic control problems in continuoustime. We consider sophisticated agents who are aware of their timeinconsistency and take into account in future decisions. We prove here that equilibria in such a problem can be characterised through a new type of multidimensional system of backward SDEs, for which we obtain wellposedness. Unlike the existing literature, we can treat the case of nonMarkovian dynamics, and our results go beyond verification type theorems, in the sense that we prove that any (strict) equilibrium must necessarily arise from our system of BSDEs. This is a joint work with Camilo Hernández, Columbia University.
Host: Nanyang Assistant Professor Ariel Neufeld Division of Mathematical Sciences, School of Physical and Mathematical Sciences

29 April 2019 
Title: Finite element methods with discontinuous approximations
Professor Xiu Ye Time: 10.30am – 11.30am
Abstract
In this presentation, different
finite element methods with discontinuous approximations will be discussed
including IPDG, HDG and specially WG finite element methods as well as the
relations between them. In addition, a new conforming DG finite element method
will be introduced which combines the features of both conforming finite
element method and discontinuous Galerkin method.
Host: Assistant Professor Kelin Xia Division of Mathematical Sciences, School of Physical and Mathematical Sciences

4 April 2019 
Title: Fair Allocation of Combinations of Indivisible Goods and Chores
Ayumi Igarashi Time: 3.30pm – 4.30pm
Abstract
We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are “goods” i.e., they yield positive utility for the agents. There is also some work where the items are “chores” that yield negative utility for the agents. In this work, we consider more general scenarios where for any item, an agent may have negative or positive utility for it. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new algorithms for finding fair allocations in the general setting. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties and further study the complexity of computing such allocations. This is a joint work with Haris Aziz, Ioannis Caragiannis, and Toby Walsh.
Host: Nanyang Assistant Professor Bei Xiaohui Division of Mathematical Sciences, School of Physical and Mathematical Sciences

4 April 2019 
Title: An Ordinal Minimax Theorem
Warut Suksompong Time: 2.30pm – 3.30pm
Abstract
In the early 1950s Lloyd Shapley proposed an ordinal and setvalued solution concept for zerosum games called weak saddle. We show that all weak saddles of a given zerosum game are interchangeable and equivalent. As a consequence, every such game possesses a unique setbased value. Our result can be seen as an ordinal version of the celebrated minimax theorem of John von Neumann. No prior knowledge of game theory or economics is requiredI will explain all the necessary concepts in the talk.
Host: Nanyang Assistant Professor Bei Xiaohui Division of Mathematical Sciences, School of Physical and Mathematical Sciences

21 March 2019 
Title: FBSDEs with discontinuous coefficients
Assistant Professor Ludovic Tangpi Time: 4.00pm – 5.00pm
Abstract
In this talk we consider wellposedness of systems of forward and backward stochastic differential equations when (at least some of) the coefficients are merely assumed to be measurable. Since such systems cannot be tackled with classical fixed point theory, we device new methods based on "domination arguments" and Malliavin calculus techniques.
The talk is based on joint works with K. Bahlali and O. MenoukeuPamen
Host: Nanyang Assistant Professor Ariel Neufeld Division of Mathematical Sciences, School of Physical and Mathematical Sciences

12 February 2019 
Title: Virtual element methods for elliptic variational inequalities of the second kind
Professor Huang Jianguo Time: 4.00pm – 5.00pm
Abstract
In this talk, we are concerned with virtual element methods for solving elliptic variational inequalities (EVIs) of the second kind. First, a general framework is provided for the numerical solution of the EVIs and for its error analysis. Then, two virtual element methods are applied to solve two representative EVIs: a simplified friction problem and a frictional contact problem, respectively. Optimal order error estimates are derived for the virtual element solutions of the two EVIs, including the effects of numerical integration for the nonsmooth term in the EVIs. A fast solver is introduced to solve the discrete problems. Several numerical examples are included to show the numerical performance of the proposed methods. This is a joint with Fang Feng from Shanghai Jiao Tong University and Weimin Han from University of Iowa.
Host: Assistant Professor Tong Ping Division of Mathematical Sciences, School of Physical and Mathematical Sciences

30 January 2019 
Title: Analytical Nonlinear Shrinkage of LargeDimensional Covariance Matrices
Professor Michael Wolf Time: 3.30pm – 4.30pm
Abstract
We have proposed an analytical method for nonlinear shrinkage of covariance matrices based on kernel estimation in large dimensions. It enjoys the following merits:
1) Performs as well as existing methods
2) Easy to implement
3) Computationally cheap
4) More potential to accommodate future variations and extensions
Host: Associate Professor Pan Guangming Division of Mathematical Sciences, School of Physical and Mathematical Sciences 