Seminars

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2019

Date Information
​2 August 2019 ​Title: Self-Dual Codes over Finite Fields​

Dr. Lin SOK
Time: 11.00am – 12.00pm

Abstract

In this talk, we study self-dual 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 self-orthogonality of the 0-genus code in terms of the divisors G and D and the value of a well-chosen derivative polynomial at points P_i for i from 1 to n. We explore the existence problem of MDS self-dual codes in odd characteristic cases and explicitly construct families of new MDS self-dual 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

Three-dimensional (3-D) elastic wave propagation and seismic tomography is computationally challenging in large scales and high-frequency regime. In this talk, we propose the frozen Gaussian approximation (FGA) to compute the 3-D elastic wave propagation and use it as the forward modeling tool for seismic tomography with high-frequency 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 3-D 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 Tsz-Kin (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 non-domestic currency. The payoff of a quanto CDS contract, therefore, reflects the market-implied interaction of FX risk and a credit event. This in turn, defines the cost of hedging WWR for an FX-sensitive 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 add-on could be 40% higher than the standard case, and choosing a proper jump-at-default WWR model is critical to capture the impact. In contrast, historical correlation gives the incorrect relationship (right-way 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 meta-materials.  Firstly, a fast multipole method for 3-D 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 Li-Lian
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 high-dimensional 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 large-scale 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 state-of-the-art performance in most kinds of network architectures

Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
​15 May 2019  ​Title: A general approach to non-Markovian time-inconsistent stochastic control for sophisticated players​

 Assistant Professor​ Dylan Possamai​
Time: 4.00pm – 5.00pm

Abstract

This paper is the first attempt at a general non-Markovian theory of time-inconsistent stochastic control problems in continuous-time. We consider sophisticated agents who are aware of their time-inconsistency and take into account in future decisions. We prove here that equilibria in such a problem can be chara​cterised through a new type of multi-dimensional system of backward SDEs, for which we obtain wellposedness. Unlike the existing literature, we can treat the case of non-Markovian 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 set-valued solution concept for zero-sum games called weak saddle. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based 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 required---I 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 well-posedness 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. Menoukeu-Pamen

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 non-smooth 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 Large-Dimensional 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
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