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3 July 2020 | Title: Random and deterministic dimension reduction in state-space systems. A geometric explanation of the reservoir computing phenomenon. Prof Juan-Pablo Ortega Time: 3.00 pm – 4.00 pm
Venue: Join Zoom Meeting: https://ntu-sg.zoom.us/j/95550890075
Abstract The last years have seen the emergence of significant interplays between machine learning, control theory, dynamical systems, and stochastic processes, with interesting applications in time series analysis and forecasting. The resulting techniques are based on the use of randomly generated state-space systems with cheap-to-estimate parameters and have revolutionized the way in which we learn and path-continue complex and high-dimensional dynamic processes. In this seminar, I will start by giving a short but self-contained overview of this body of work that is generically referred to as reservoir computing. In the second part, I will proceed by describing recent progress on two dimension reduction techniques for the kind of systems that are customarily used in this approach to machine learning. The first one has to do with finite-dimensional random projections of certain universal infinite-dimensional approximants that yield randomly generated state-affine systems with linear readouts that, more importantly, provide a deep geometric explanation of the reservoir computing phenomenon. Finally, we will discuss a second and purely deterministic approach that is an extension to this framework of the so-called “optimal reduction” method that I introduced with Tudor Ratiu twenty years ago in the context of symmetric Hamiltonian systems. Host: Professor Bernhard Schmidt Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

31 March 2020 | Title: Combinatorial Game TheoryDr Urban LarssonTime: 2.30 pm – 3.30 pm Venue: SPMS-MAS-03-06, EC Room 1 Abstract We discuss the classical theory of combinatorial perfect information 2-player games, starting with Bouton’s Nim (1902) and the Sprague-Grundy theory (1930s) for impartial games. Berlekamp, Conway, Guy (1970-1980s) discovered that the class of partizan combinatorial games (such as Chess, Go and Checkers) is a partially ordered group, under the disjunctive sum operator, with large equivalence classes. Conway famously revealed that such games constitute a vast generalization of our standard number system (together with Knuth). We will review this development and learn a rough classification of rulesets according to their temperatures as being ``cold’’, ``tepid’’ or ``hot’’.
Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

14 January 2020 | Title: Towards Optimal Secure Computation protocols Akshayaram Srinivasan Time: 10.00am –11.00am Venue: SPMS-MAS-03-07, EC Room 2 Secure computation allows a set of mutually distrusting parties to compute a joint function of their private inputs such that the parties only learn the output of the functionality and nothing else about the inputs of the other parties. Secure computation is one of the central primitives in cryptography that encompasses several cryptographic abstractions and has many practical applications. The seminal results from the 1980s showed that every efficiently computable functionality can also be computed securely. However, these protocols were prohibitively inefficient and could only be considered as feasibility results. One of the central problems in cryptography is to construct secure computation protocols that are optimal in all efficiency parameters. In this talk, I will give an overview of my recent works that make progress towards constructing such optimal secure computation protocols. Host: Associate Professor Chan Song Heng Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

4 February 2020 | Title: An open conjecture on colliding permutations Professor Claudia Malvenuto Time : 02.30pm – 03.30pm Venue: SPMS-MAS-03-06, EC Room 1 We call two permutations of the first n naturals colliding if they map at least one number to consecutive naturals. The notion has been introduced in 2006 by Jànos Korner and myself. We asked for the maximum number of pairwise colliding permutations of n. We conjectured that such maximum is assumed in the central binomial coefficient $\binom{n}{\lfloor n/2 \rfloor}$. Variations such as cyclic colliding permutations have been considered later (with Gerard Cohen), or graph-different permutations (with J.Korner and Gàbor Simonyi). I will give an account of the 'state of the art' on this still open conjecture. Host: Associate Professor Chan Song Heng |

14 January 2020 | Title: Enumeration of Simultaneous Core Partitions Professor Jaebum Sohn Time: 02.00pm –03.00pm Venue: SPMS-MAS-03-06, EC Room 1 In this talk, we are concerned with (n, n+1, . . . , n+p)-core partitions. Amderberhan conjectured that the number of (n, n+1, n+2)-core partitions is same as the nth Motzkin number. This conjecture was proved by several authors. We give an alternative proof of this result by establishing a bijection between the set of (n, n+1, n+2)-core partitions and that of Motzkin paths of length n. Similarly, we give a bijection between the set of (n, n+1, . . . , n+p)-core partitions and that of Motzkin paths of length n with some restrictions. Also, we show the recurrence relation for the number of (n, n+1, . . . , n+p)-core partitions with certain restrictions. Moreover, we enumerate the number of (n, n+1, . . . , n+p)-core partitions with a specified number of corners. Host: Associate Professor Chan Song Heng Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

6 February 2020 | FinTech Seminar SeriesTitle: From Traditional Career to becoming a FinTech Founder Michele Ferrario (CEO & Co-founder of StashAway) Time: 3:30 PM - 4:30 PM Venue: SPMS-MAS-03-06, EC Room 1 Traditional Career to FinTech Founder: Join StashAway’s
Co-founder and CEO Michele Ferrario as he shares his own experience of
starting out at McKinsey in Italy and New York, transitioning to private
equity, starting in internet companies in Italy, Pakistan and Southeast Asia
and then taking the jump to co-found a FinTech firm.
You will learn one person’s experience of what it takes to make calculated risks, succeed in different work cultures, and endure the ups and downs of starting a business. Host: Asst Prof Pun Chi Seng (Director of MSc in FinTech) |

16 January 2020 | FinTech Seminar SeriesTitle: Frontiers of Financial Inclusion: Marketplace Lending it Raikar (CEO & Co-founder of Validus Capital) Time: 3:30 PM - 4:30 PM Venue: SPMS-MAS-03-06, EC Room 1 Marketplace Lending: Traditionally, banks have been the backbone small businesses relied upon to access financing. With the advent of FinTech and the emergence of online lending in recent years, innovators are disrupting traditional lending models by offering small businesses alternative options to access and easily secure financing.
This session will focus on Marketplace Lending and how it has transformed SME financing. Learn how FinTech innovations can support SME financing, what key drivers of FinTech credit are, and how Marketplace Lending is helping to drive financial inclusion for SMEs in Southeast Asia. Host: Asst Prof Pun Chi Seng (Director of MSc in FinTech) |