## Seminars 2016

Title: | Computable and Convergent Bounding Functions for Expectation and Boundary Value Problems |

Speaker: | Dr Ray Kawai |

Date: | 5 June 2016 |

Time: | 10.00am - 11.00am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Associate Professor Nicolas Privault |

Abstract: | The computation of expectations involving stochastic processes has long been one of the central issues, in one form or another, in various fields of natural and social sciences, such as the Fokker-Planck equation, financial derivatives pricing, the assessment of ruin probabilities of an insurance company, to mention just a few. It is often the case that expectations are easy to compute for a simple model (such as Black-Scholes model and compound Poisson surplus processes for insurance), while small perturbations (such as additional jumps to Black-Scholes model and diffusion to compound Poisson surplus processes) make the computation of expectation surprisingly more difficult or even almost prohibitive. To address this issue, we propose a novel method for measuring the impact of such small perturbations in expectations without significant computing effort, for instance, without simulating their sample paths for Monte Carlo estimation from scratch. The proposed method constructs deterministic upper and lower bounding functions for the expectation by making full use of a similar structure in the infinitesimal generator of underlying stochastic processes. Our hard bounding functions have the form of Markov-type inequalities, parametrized by the perturbation parameter, so that the upper and lower bounds converge to each other when the perturbation tends to vanish. The proposed method requires only well-developed numerical methods for boundary value problems for partial differential equations and elementary numerical integration of smooth functions. Numerical results are presented throughout in the context of mathematical finance and insurance mathematics to support our theoretical developments and to illustrate the effectiveness of the proposed approach. |

Title: | Algorithmic mechanism design on cloud computing and facility location |

Speaker: | Professor Minming Li |

Date: | 9 May 2016 |

Time: | 3.30pm - 4.30pm |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Nanyang Assistant Professor Bei Xiao Hui |

Abstract: | Algorithmic mechanism design is now widely studied for various scenarios. In this talk, we discuss two applications: CPU time auction and facility location problem. In CPU time auction, we designed two greedy frameworks which can achieve truthfulness (approximate-truthfulness) from the bidders while at the same time a certain global objective is optimized or nearly optimized. In facility location problem, we introduce weight to the traditional study and prove that those mechanisms that ignore weight are the best we can have. Furthermore, we also propose a new threshold based model where the solution that optimizes the social welfare is incentive compatible. |

Title: | Hyperbolization of certain 3-manifolds |

Speaker: | Professor John H. Hubbard |

Date: | 27 April 2016 |

Time: | 1.00pm - 3.00pm |

Venue: | SPMS-TR12 (SPMS-05-06) |

Host: | Associate Professor Andrew James Kricker |

Abstract: | Thurston's geometrization programme, which culminated in the proof of the Poincare conjecture, studies the topology of 3-manifolds by equipping them with geometric structures. We will sketch a key development in this program: how to give a hyperbolic structure to a 3-manifold that fibers over the circle with pseudo-Anosov holonomy. |

Title: | Theta correspondence and Moment maps |

Speaker: | Dr Ma Jiajun |

Date: | 29 March 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Initialed by Roger Howe four decades ago, Theta correspondence has become one of the major tools in the theory of representations and automorphic forms. "Theta'' relates representations of different (classical) groups which is considered as an explicit realization of Langlands functorality. However, precise statements are often highly nontrivial to establish. In this talk, I will first give a brief introduction of Theta correspondence. Then I will summarize my contributions on the subject: (1) the description of the correspondence of associated cycles and (2) the description of the correspondence between supercuspidal representations. Both of the works show that moment maps play essential roles in theta correspondences. |

Title: | Uncertainty Quantification in Earth and Environmental Systems Modeling |

Speaker: | Dr Shuo Wang |

Date: | 22 March 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Mathematical models are recognized as a powerful tool to solve complex environmental problems. When models that consist of mathematical equations are used to mimic the behavior of real-world systems, a variety of uncertainties exist due to the simplification of complex natural processes, the scarcity of acquirable data, the estimation of parameter values, data errors, and incorrect assumptions. It is thus necessary to quantify inherent uncertainties in Earth and environmental systems modeling, enhancing the credibility of model results. In this seminar, I will introduce a series of computational methods for quantifying uncertainties and associated interactions in hydrologic simulation and water resources optimization. In addition, real-world case studies will be provided to demonstrate how these uncertainty quantification methods can be used to advance the understanding of physical mechanisms that govern the hydrologic cycle, as well as to help water managers make sound technical and policy decisions in an uncertain and changing environment. I will also talk about potential extensions for my future research in the challenging area of uncertainty quantification. |

Title: | Intersecting Families of Permutations and Set Partitions |

Speaker: | Dr Ku Cheng Yeaw |

Date: | 10 March 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | The simplest version of the Erdos-Ko-Rado theorem asserts that if a family A of subsets of size k from a set of size n, where k < n/2, such that any two k-subsets have at least one point in common, and A is as large as possible, then it consists of all k-subsets that contain a given point from the underlying set. While the original proof of this theorem uses the idea of shifting, other combinatorial and algebraic proofs are now known. In recent years, a number of analogs of this theorem have been proved for permutations and set partitions. In the case of permutations, this is related to the eigenvalues of some Cayley graphs on the symmetric group. In this talk, I will present some new ideas and progress in the area. |

Title: | Topological modeling and analysis of complex data in biomolecules |

Speaker: | Dr Xia Kelin |

Date: | 8 March 2016 |

Time: | 9.15am – 10.15am |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics, and transport is one of the mostchallenging tasks in biological science. We have introduced persistent homology for extracting molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification, and classification. The multidimensional persistent homology isproposed and further used to quantitatively predict the stability of protein folding configurations generated by steered molecular dynamics. An excellentconsistence between my persistent homology prediction and molecular dynamics simulation is found. Further, we introduce multiresolution persistent homology to handle complex biomolecular data. The essential idea is to match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. By appropriately tuning the resolution of a density function, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks and graphs. Finally, we offerpersistent homology based new strategies for topological denoising and for resolving ill-posed inverse problems. |

Title: | Stability of Ensemble Kalman Filters |

Speaker: | Dr Xin Tong, Thomas |

Date: | 25 February 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Ensemble Kalman filters are data assimilation methods for high dimensional, nonlinear dynamical models. Despite their widespread usage in weather forecast, very little is known about their long-time dynamical behavior. In this talk, we discuss the criterions that guarantee the filter ensemble to be time uniformly bounded and geometrically ergodic. Contradiction to these criterions may lead to catastrophic filter divergence, which can be demonstrated by a simple example. Finally, we show that a simple adaptive covariance inflation scheme can guarantee filter stability. |

Title: | Probing the Earth's interior with Mathematical Tools |

Speaker: | Dr Ping Tong |

Date: | 23 February 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Mathematical methods are the core components of seismic imaging that uses waves generated by earthquakes or artificial explosions to produce images of the Earth's interior. The obtained images can help us understand how the Earth works and provide critical information to modern oil-and-gas exploration/production companies and contractors. In this seminar I will first give a brief introduction to the mathematical foundations of seismic imaging, which mainly include partial differential equations, numerical methods, and optimization. Then I will show the results of our recent studies in seismic numerical modeling and seismic imaging. After that, I will talk about the most advanced wave-equation-based earthquake location method that directly inverts the full waveform content for the precise earthquake location. Finally, research plans for generating higher-resolution subsurface images by using modern mathematical tools will be mentioned. |

Title: | Leveraging Large-Scale and Heterogeneous Computing Systems |

Speaker: | Dr Colin Glass |

Date: | 16 February 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Computing has become a new frontier of knowledge. The enormous computing power at our disposal today, sheds light on questions hitherto beyond our reach and changes what we know and how we think about the world. However, leveraging these resources is far from trivial: the available hardware is constantly evolving, necessitating new algorithms and new software design strategies. At the same time, models need to be developed, allowing to gather meaningful data on matters of interest in silico. In this seminar, a cross section of research in the field of high performance computing is presented. |

Title: | Mathematical modelling of limit order |

Speaker: | Dr Frederic Abergel |

Date: | 12 February 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | The limit order book is the at the core of any modern, electronic financial markets. In this talk, I will present some results pertaining to their statistical properties, mathematical modelling and numerical simulation. Questions such as ergodicity and stationarity, induced price dynamics, dependencies, relation betwen time scales... will be addressed and sometimes answered to, and on-going research projects will be presented |

Title: | Deformation Quantization, Genesis And Avatars: An Elementary Introduction For Mathematicians |

Speaker: | Professor Daniel Sternheimer |

Date: | 29 January 2016 |

Time: | 10.00am - 11.00am |

Venue: | MAS Executive Classroom 2, MAS-03-0 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | In 1963/64 appeared both index theorems for (elliptic) pseudodifferential operators and Gerstenhaber's theory of deformations of algebras. I participated then in the first and used the second for physics. In the mid-seventies the two converged to explain quantum mechanics as a deformation of classical mechanics, using symplectic (or Poisson) geometry, what is now called "deformation quantization". Quantum groups and noncommutative geometry (which appeared in the early 80s in different contexts) can be considered as avatars of that approach. I shall explain in general terms what are these notions and describe some results. The talk should be accessible to graduate students and researchers from all fields of mathematics. |

Title: | Data Intensive Scientific Computing |

Speaker: | Professor Scott Klasky |

Date: | 15 January 2016 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Scientific discovery at the exascale will not be possible without significant new research in the management, storage and retrieval over the long lifespan of the extreme amounts of data that will be produced. In this presentation I discuss my vision, plan and implementation of creating a software ecosystem to handle some of these challenges. In particular I discuss the path I went down 25 years ago in order to create the ADIOS framework which is used all over the world by application scientist and computer science researchers. I will discuss the plan, implementation and research ideas which went into this vision, and the new research challenges we face as we proceed further down the path to create a next generation multi-tiered storage and I/O system for scientific data. |

Title: | Six Lectures on Supercomputing |

Speaker: | Professor Deng Yuefan |

Date: | 11, 13, 15, 18, 20, 22 January 2016 |

Time: | 3.00pm - 4.30pm |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

Abstract: | Six 1.5-hour public lectures on supercomputing focusing on the latest development trends of supercomputer architectures and applications will be offered at the School of Physical and Mathematical Sciences at NTU on Mondays, Wednesdays and Fridays starting on January 11, 2016. Graduate students, postdocs and junior faculty in computer science, computer engineering, physical and mathematical sciences are the targeted audience. The expected outcome of the six lectures includes (1) knowledge of supercomputer architectures; (2) mastery of software architecture and MPI protocols; (3) understanding of performance measurements; (4) mastery of parallel algorithms and parallel programming; (5) mastery of applications of parallel computers for solving representative engineering and scientific problems. |

Title: | A Note on Non-ordinary Primes |

Speaker: | Dr SeokHo Jin |

Date: | 11 January 2016 |

Time: | 10.00am - 11.00am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Host: | Associate Professor Chan Song Heng |

Abstract: | Suppose that O_L is the ring of integers of a number field L, and suppose that f(z) is a normalized Hecke eigenform for SL(2,Z) . We say that f is non-ordinary at a prime p if there is a prime ideal p?O_L above p for which a_f(p)=0 (mod p). For any finite set of primes S , we prove that there are normalized Hecke eigenforms which are non-ordinary for each p?S . The proof is elementary and follows from a generalization of work of Choie, Kohnen and Ono. |