## Colloquiums and Public Lectures 2016

Title: | Equiangular line systems and regular graphs |

Speaker: | Dr Gary Greaves |

Date: | 26 October 2016 |

Time: | 4.30pm - 5.30pm |

Venue: | LT 4, (SPMS-03-09), School of Physical and Mathematical Sciences |

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

Abstract: |

Title: | A Personal Perspective and Retrospective on Web Search Technology |

Speaker: | Dr Andrei Broder |

Date: | 21 October 2016 |

Time: | 1.30pm - 2.30pm |

Venue: | LT 4, (SPMS-03-09), School of Physical and Mathematical Sciences |

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

Abstract: | This talk is a review of some Web research and predictions that I co-authored over the last two decades: both what turned out gratifyingly right and what turned out embarrassingly wrong. Topics will include near-duplicates, the Web graph, query intent, inverted indices efficiency, and others. While this seems a completely idiosyncratic collection there are in fact concealed connections that offer good clues to the big question: what will happen next? |

Title: | Introduction to Data Stream Algorithms |

Speaker: | Assistant Professor Li Yi |

Date: | 14 October 2016 |

Time: | 1.30pm - 2.30pm |

Venue: | LT 4, (SPMS-03-09), School of Physical and Mathematical Sciences |

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

Abstract: |

Title: | Robust Stochastic Control and High- Dimensional Statistics with Applications in Finance |

Speaker: | Assistant Professor Pun Chi Seng |

Date: | 21 September 2016 |

Time: | 4.30pm - 5.30pm |

Venue: | LT 4, (SPMS-03-09), School of Physical and Mathematical Sciences |

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

Abstract: | Theoretical results usually assume that the collected data follow a specific model without errors. However, the estimation error associated with the model, especially in a high- dimensional setting, poses practical concerns. Among various applications, I am interested in portfolio optimization problems with estimation errors. The implementation of a theoretical optimal portfolio requires (at least) estimates of the mean vector and the variance- covariance matrix of the asset (stock) returns. Many empirical studies show that the estimation error significantly distorts the performance of the optimized portfolio. This talk investigates several remedies from two perspectives: (1) mathematical formulation of robust dynamic portfolios with respect to model parameters and model risk; and (2) novel statistical approach to resolve the degeneracy caused by the estimation error, particularly when the number of assets is large. In this talk, I shall also briefly introduce my previous and on-going works. |

Title: | Gaussian Concentration |

Speaker: | Associate Professor Nicolas Privault |

Date: | 9 September 2016 |

Time: | 1.30pm - 2.30pm |

Venue: | LT 4, (SPMS-03-09), School of Physical and Mathematical Sciences |

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

Abstract: | This talk will survey some aspects of the Gaussian concentration of measure phenomenon, starting from uniform measures on spheres and then moving on to a global approach to functional inequalities based on stochastic integral representation and stochastic analogues of the fundamental theorem of calculus.. |

Title: | Geometric Numerical Integration and Computational Geometric Mechanics |

Speaker: | Professor Melvin Leok |

Date: | 1 September 2016 |

Time: | 2.00pm - 3.00pm |

Venue: | LT 5, SPMS-03-08, School of Physical and Mathematical Sciences |

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

Abstract: | Symmetry, and the study of invariant and equivariant objects, is a deep and unifying principle underlying a variety of mathematical fields. In particular, geometric mechanics is characterized by the application of symmetry and differential geometric techniques to Lagrangian and Hamiltonian mechanics, and geometric integration is concerned with the construction of numerical methods with geometric invariant and equivariant properties. Computational geometric mechanics blends these fields, and uses a self-consistent discretization of geometry and mechanics to systematically construct geometric structure-preserving numerical schemes. In this talk, we will introduce a systematic method of constructing geometric integrators based on a discrete Hamilton's variational principle. This involves the construction of discrete Lagrangians that approximate Jacobi's solution to the Hamilton- Jacobi equation. Jacobi's solution can be characterized either in terms of a boundary-value problem or variationally, and these lead to shooting-based variational integrators and Galerkin variational integrators, respectively. We prove that the resulting variational integrator is order-optimal, and when spectral basis elements are used in the Galerkin formulation, one obtains geometrically convergent variational integrators. We will also introduce the notion of a boundary Lagrangian, which is analogue of Jacobi's solution in the setting of Lagrangian PDEs. This provides the basis for developing a theory of variational error analysis for multisymplectic discretizations of Lagrangian PDEs. Equivariant approximation spaces will play an important role in the construction of geometric integrators that exhibit multimomentum conservation properties, and we will describe a general construction for group-equivariant interpolants on symmetric spaces with applications to Lorentzian metrics. |

Title: | Market Equilibrium: Algorithms and Complexity |

Speaker: | Nanyang Assistant Professor Bei Xiaohui |

Date: | 24 August 2016 |

Time: | 4.30pm - 5.30pm |

Venue: | LT 4, SPMS-03-09, School of Physical and Mathematical Sciences |

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

Abstract: | The concept of market equilibrium is central in economics. It captures fair, stable, and efficient outcomes in competitive allocation scenarios. The general equilibrium theory in economics studies how to analyze the equilibrium pricing of a given market. However, other than a few isolated results, it is essentially a non-algorithmic theory. With the emergence of new markets on the Internet, the need for developing an algorithmic theory of markets and market equilibria is apparent. In this talk, we will discuss several research issues related to algorithms and complexity for computation of equilibria in markets. In particular, I will present a combinatoric algorithm to compute the market equilibrium in different classes of markets, even if one only has limited knowledge about the market information. |

Title: | Permutations and number theory |

Speaker: | Professor Ben J. Green |

Date: | 16 May 2016 |

Time: | 3.00pm - 4.00pm |

Venue: | LT 5, SPMS-03-08, School of Physical and Mathematical Sciences |

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

Abstract: |

Title: | On the intersection of groups, vector spaces and random variables |

Speaker: | Associate Professor Frederique Elise Oggier |

Date: | 21 April 2016 |

Time: | 3.00pm - 4.00pm |

Venue: | LT 4, SPMS-03-09, School of Physical and Mathematical Sciences |

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

Abstract: | Groups are usually studied in abstract algebra, vector spaces in linear algebra, and random variables in probability. Yet they have several things in common, in particular, they all satisfy fundamental inequalities. In this talk, we will discuss similarities and differences among inequalities for these 3 types of mathematical objects. |