20 November 2019 
Title: BernsteinBezier
Polynomials for High Order Finite Element Approximation
Speaker: Professor
Mark Ainsworth Time: 10.30am
– 11.30am
Abstract: We explore the use of Bernstein polynomials as a basis for finite element approximation on simplices in any spatial dimension. The Bernstein polynomials have a number of interesting properties that have led to their being the industry standard for visualisation and CAGD. It is shown that the basis enables the element matrices for the standard finite element space, consisting of continuous piecewise polynomials of degree n on simplicial elements in Rd, to be computed in optimal complexity O(p^2d). The algorithms take into account numerical quadrature; are applicable to nonlinear problems; and do not rely on precomputed arrays containing values of onedimensional basis functions at quadrature points (although these can be used if desired). The standard tools for the evaluation of Bezier curves and surfaces is the de Casteljau algorithm. The archetypal pyramid algorithm is the de Casteljau algorithm. Pyramid algorithms replace an operation on a single high order polynomial by a recursive sequence of selfsimilar affine combinations and, as such, offer significant advantages for high order finite element approximation. We develop and analyze pyramid algorithms for the efficient handling of all of the basic finite element building blocks, including the assembly of the element load vectors and element stiffness matrices. The complexity of the algorithm for generating the element stiffness matrix is optimal. A new, nonuniform order, variant of the de Casteljau algorithm is developed that is applicable to the variable polynomial order case but incurs no additional complexity compared with the original algorithm. The work provides the methodology that enables the efficient use of a completely general distribution of polynomial degrees without any restriction in changes between adjacent cells, in any number of spatial dimensions.
Host: Associate Professor Wang LiLian 
11 November 2019 
NUS meets NTU Miniworkshop in Mathematical Finance
Title: Portfolio diversification and model uncertainty: a robust dynamic meanvariance approach
Speaker: Assistant
Professor Chao Zhou Time: 2.00pm – 2.45pm
Abstract
This talk is concerned with multiasset meanvariance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected rate of return and correlation matrix of stocks, and for studying the effects on portfolio diversification.
We prove a separation principle for the associated robust control problem formulated as a meanfield type differential game, which allows to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function.
Our results provide a justification for underdiversification, as documented in empirical studies, and that we explicitly quantify in terms of correlation and Sharpe ratio ambiguity parameters. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. This extends to the continuoustime setting the results obtained by Garlappi, Uppal and Wang (2007), and Liu and Zeng (2017) in a oneperiod model.
Based on joint work with Huyên Pham (Paris Diderot University) and Xiaoli Wei (University of California, Berkeley).
Title: Systemic Portfolio Diversification Speaker: Professor Marko Weber Time: 2.55pm –3.40pm
Abstract
We study the implications of firesale externalities on balance sheet composition. Banks choose their asset holdings accounting for the liquidation costs incurred when they sell assets to manage their leverage. Our analysis highlights the fundamental tradeoff between diversification at the bank and at the systemic level. While sacrificing diversification benefits to reduce portfolio commonality may increase the bank's idiosyncratic probability of liquidation, it also lowers the endogenous probability of a costly widespread selloff. We show that higher heterogeneity in banks' leverage is socially beneficial because it gives banks stronger incentives in achieving systemic diversification. The socially optimal level of systemic diversification can be attained by taxing banks for creating interlinked balance sheets with high concentration on illiquid assets.
Title: Mean Field LeaderFollower Games with Terminal State Constraint Speaker: Research Fellow Dr FU Guanxing Tme: 4.00pm –4.30pm
Abstract
We analyze linear McKeanVlasov forwardbackward SDEs arising in leaderfollower games with meanfield type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in timeweighted spaces as well as a convergence result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel singleplayer model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players.
Title: Deep Learning Algorithm to solve Portfolio management with Proportional Transaction Cost Speaker: PhD Student Zhang Weiwei Time: 4.30pm –5.00pm
Abstract
We propose a deep learning based numerical scheme to solve transaction cost problems, compare its effectiveness with a penalty partial differential equation (PDE) method, and further extend it to multiasset cases which existing numerical methods can not be applied to due to the curse of dimensionality. Deep learning algorithm directly approximates the optimal trading strategies by a feedforward neural network at each discrete time. It is observed that deep learning approach can achieve satisfying performance to characterize optimal buy and sell boundaries and thus value function.
Host: Nanyang Assistant Professor Ariel Neufeld
Division of Mathematical Sciences, School of Physical and Mathematical Sciences

31 October 2019 
Title: Stability of (F)BSDEs under Mémin's framework
Postdoctoral Assistant Professor Alexandros Saplaouras Time: 5.00pm – 6.00pm
Abstract: Backward
Stochastic Differential Equations, in short BSDE, have become a particularly
active field of research, due to their numerous potential applications to
mathematical finance, partial differential equations, game theory, economics,
and more generally in stochastic calculus and analysis. In this talk we will
discuss initially the stability property of special semimartingales, where we
refine the result obtained by Mémin (2003). Then we focus on the special case
where the sequence of semimartingales consists of solutions of Backward
Stochastic Differential Equations with Jumps, in short BSDEJ, and we provide a
suitable framework for obtaining the stability property of BSDEJ. Afterwards,
we will proceed on some ongoing research and present some ideas on the
stability property of ForwardBackward Stochastic Differential Equations with
Jumps (FBSDEJ).
Host: Nanyang Assistant Professor Ariel Neufeld Division of Mathematical Sciences, School of Physical and Mathematical Sciences

31 October 2019 
Title: Improved FréchetHoeffding bounds, optimal transport and modelfree finance
Assistant Professor Antonis Papapantoleon Time: 04.00pm – 5.00pm
Abstract: This talk considers modelfree bounds for multiasset option prices in a setting where the marginals are known and the dependence structure is partially known. We will first present methods to sharpen the classical FréchetHoeffding bounds on copulas using additional information on the dependence structure, and discuss their application in option pricing, portfolio ValueatRisk and the detection of arbitrage. Then, we will consider modelfree hedging of multiasset option prices in the presence of additional information on the dependence structure. An extension of the classical optimal transport superhedging duality will allow us to provide new insights in modelfree hedging, and show (non) sharpness of the improved FréchetHoeffding bounds.
Host: Nanyang Assistant Professor Ariel Neufeld Division of Mathematical Sciences, School of Physical and Mathematical Sciences

4 October 2019 
Title: On the Artificial Boundary Conditions and PML Methods for Schrödinger Equations
Professor Xavier Antoine Time: 3.00pm – 4.00pm
Abstract: In this talk, I will introduce some mathematical methods to build artificial boundary conditions for Schrödinger equations. The derivation of stable discretization schemes will also be developed. In addition, I will provide shortly some recent results on the implementation of the Perfectly Matched Layer for the Schrödinger equation approximated by pseudospectral methods.
Host: Associate Professor Wang LiLian Division of Mathematical Sciences, School of Physical and Mathematical Sciences

27 September 2019 
FinTech Seminar Series
Title: ASEAN FinTech Landscape & Women In FinTech
Neha Mehta (Founder of FemTech Partners)
Time: 10:30 AM  12:30 PM Venue: SPMS LT2, SPMS 0303
Abstract:
Is Singapore the best FinTech Hub? Is 50% female
representation in FinTech a far fetched dream? This workshop will answer some
of these burning questions and broadly cover ASEAN FinTech landscape and Women
in FinTech.
ASEAN FinTech landscape will give a bird's eyeview on
every jurisdiction within ASEAN key FinTech markets, the soft/light
regulation, regulators managing the thin line between promoting FinTech
Innovation and market protection. It will give participants an understanding of
the regulatory sandbox, Initial Coin Offerings (ICO), Future Trends of FinTech,
Blockchain, RegTech, InsurTech and AI. The workshop will also focus on API’s,
Open Banking and throw some light on project Ubin of the Monetary Authority
Bank of Singapore (MAS)  clearing and settlement of payments and securities
using Blockchain. LASTLY, makes sense of the buzz around Data Privacy and
General Data Protection Regulation (GDPR).
The other part of the workshop will focus on "Women
in FinTech"; only 2% of Venture Capital funding goes to women
entrepreneurs. Women need to step UP and break into the old boys club to shine
in this domain. Learn the art of selling yourself and be market ready for a
great career in the FinTech industry. The much needed "soft" and
"hard" skills to launch yourself into the ever evolving world of
FinTech will be the focus of this session.
Host: Asst Prof Pun Chi Seng (Director of MSc in FinTech) Division of Mathematical Sciences, School of Physical and Mathematical Sciences

26 September 2019 
Title: Computation of Free Energy at ab initio QM/MM Level Made Orders of Magnitude Faster via the ReferencePotential Approach
Professsor Ye Mei Time: 02.00pm – 3.30pm
Abstract:
Multiscale simulation methods are now playing a more and more important role for the study of complex chemical systems. However, application of these methods is often limited by its computational expense, especially when ab initio quantum mechanical methods are inevitable for the description of the processes, for instance chemical reactions. Referencepotential methods can be a cure for this difficulty, in which the phasespace sampling and ensemble average calculations are separated using different Hamiltonians. In the latter, the weight for each sample should be properly considered, if a nonBoltzmann statistical ensemble is used. In this lecture, I will introduce the development of referencepotential methods for the calculations of differences in state free energies and free energy profiles for specific chemical processes with samples extracted from single and mixed ensembles.
Host: Assistant Professor Kelin Xia Division of Mathematical Sciences, School of Physical and Mathematical Sciences

18 September 2019 
Title: Bayesoptimal filtering in the tensortrain format
Professor Colin Fox Time: 04.00pm – 5.00pm
Abstract: Optimal sequential Bayesian inference, or filtering, for the state of a dynamical system requires solving a partial differential equation. For lowdimensional, smooth systems the finitevolume method is an effective solver that converges to the optimal continuoustime solution and estimates. For higherdimensional systems the curse of dimensionality may be overcome by representing density functions by an interpolated tensor train decomposition.
We give examples of filtering for
continuoustime and discretetime systems to demonstrate that the resulting
Bayesoptimal filter is able to handle nonlinear systems and multimodal
filtering distributions.
Host: Associate Professor Hoang Viet Ha Division of Mathematical Sciences, School of Physical and Mathematical Sciences

13 September 2019 
Title: P1–nonconforming polyhedral finite elements in high dimensions
Professor Dongwoo Sheen Time: 11.00am – 12.00pm
Abstract: We consider the lowest–degree nonconforming finite element methods for the approximation of elliptic problems in high dimensions. The P1–nonconforming polyhedral finite element is introduced for any high dimension. Our finite element is simple and cheap as it is based on the triangulation of domains into polytopes, which are combinatorially equivalent to the d–dimensional unit cube, rather than the triangulation of domains into simplices. Our nonconforming element is nonparametric, and on each polytope it contains only linear polynomials, but it is sufficient to give optimal order convergence for second–order elliptic problems.
Host: Associate Professor Hoang Viet Ha Division of Mathematical Sciences, School of Physical and Mathematical Sciences

15 August 2019 
Title: Tight Bounds for L1 Oblivious Subspace Embeddings
Associate Professor David Woodruff Time: 3.00pm to 4.00pm
Abstract
Oblivious subspace embeddings have proven to be an essential ingredient for approximately solving numerical linear algebra problems, such as regression and lowrank approximation. While for p = 2 there are nearly optimal tradeoffs in terms of the dimension, distortion, and sparsity, for the important case of p = 1, much less was known. In this talk I will present our results on l1 oblivious subspace embeddings, including (i) nearly optimal lower bounds and (ii) new constructions for sparse l1 oblivious subspace embeddings. Oblivious subspace embeddings are crucial for distributed and streaming environments, as well as entrywise lp low rank approximation. Our results give improved algorithms for these applications. Based on joint work with Ruosong Wang.
Host: Dr Li Yi, Division of Mathematical Sciences School of Physical and Mathematical Sciences 
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 