Date/Time : 29 Aug 2019 17:00
Venue : S17 #06-11
Speaker : Chong Chi Tat, National University of Singapore

Date/Time:29 Aug 2019 17:00 Venue: S17 #06-11 Speaker: Chong Chi Tat, National University of Singapore Revisiting Seetapun’s theorem with his disjunction Ramsey’s theorem RT^n_2 states that if the n-rtuples of the set of natural numbers are coloured in either red or blue, then there is an infinite subset all of whose n-tuples have the same color. The proof-theoretic strength of RT^n_2 has been a prominent line of study in reverse mathematics. The first major breakthrough was obtained by David Seetapun (Seetapun and Slaman (1995)) who showed that RT^2_2 is strictly weaker than RT^3_2. This talk will describe a proof of this theorem using the technique called “Seetapun disjunction” introduced in Chong, Slaman and Yang (2014). Add to calendar: 

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Date/Time : 28 Aug 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Li-Lian Wang, Nanyang Technological University

Date/Time:28 Aug 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Li-Lian Wang, Nanyang Technological University Fast Spectral Methods for PDEs with Integral Fractional Laplacian in Multiple Dimensions PDEs with fractional Laplacian have emerged as a powerful tool in modelling anomalous diffusion and nonlocal interactions, but their numerical solutions can be very difficult especially in multiple dimensions. Many nonlocal models are more physically motivated and naturally set in unbounded domains. In this talk, we shall present a superfast spectral-Galerkin method with two critical components (i) the Dunford-Taylor formulation of fractional Laplacian operator, and (ii) the use of Fourier-like bi-orthogonal mapped Chebyshev functions as basis functions. We shall also report some of our recent attempts for integral fractional Laplacian in bounded domains, which are deemed even more notoriously difficult for effective numerical discretisation. Along this line, we work with the formulation associated with the Fourier transformations, and derive a number of useful analytical formulas which are essential for the algorithm development. Add to calendar: 

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Date/Time : 28 Aug 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Michael Rockner, Bielefeld University

Date/Time:28 Aug 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Michael Rockner, Bielefeld University Solutions of SPDE as zeros of maps on scaled path spaces It has been recently shown that the solutions of a large class of stochastic partial differential equations (SPDE) can be obtained as zeros of properly defined map on a path space equipped with a norm which is “scaled” by the exponential of a function-valued Brownian motion. In the talk this result will be reviewed and connected to current developments about the case where the underlying SPDE is a gradient flow, perturbed by linear multiplicative noise. In this case it follows from the above result and by applying methods from the calculus of variations that the solution minimizes a certain explicit convex functional on the path space. Applications include stochastic porous media equations, stochastic nonlinear parabolic equations (as e.g. the stochastic Cauchy problem for the p-Laplacian)and in the non-gradient case also stochastic nonlinear transport equations. Add to calendar: 

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Date/Time : 22 Aug 2019 17:00
Venue : S17 #06-11
Speaker : Johanna Franklin,

Date/Time:22 Aug 2019 17:00 Venue: S17 #06-11 Speaker: Johanna Franklin Degrees of isometric isomorphism for Banach spaces The degree of isomorphism of a computable presentation of a structure is the least powerful Turing degree that computes an isomorphism from this presentation onto the “standard” copy of the structure, assuming that such a copy exists. I will discuss the degrees of isometric isomorphism of two of the five types of nonzero separable L^p spaces and then consider lowness for isometric isomorphism for these spaces. Time permitting, I will discuss lowness for isometric isomorphism and lowness for isometry in a more general context. Joint work with Tim McNicholl Add to calendar: 

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Date/Time : 21 Aug 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Ma Xiaonan, Université Paris Diderot– Paris 7

We will review the different versions of ‘quantization commutes with reduction’ from Kaehler to symplectic manifolds. We will also consider the non-compact symplectic situation and our most recent result on Cauchy-Riemann version.

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Date/Time : 21 Aug 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Wang Weicheng, National Tsing Hua University, Taiwan

Date/Time:21 Aug 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Wang Weicheng, National Tsing Hua University, Taiwan An Efficient Solver for Fractional Diffusion Equations The fractional order differential operators have attracted considerable attention recently as an essential tool for developing more sophisticated mathematical models that can accurately describe complex anomalous systems. Since the fractional order differential operators are nonlocal, the corresponding linear system involves a dense, structured Toeplitz matrix. Many research activities are devoted to developing robust and efficient solvers for such linear systems. In this talk, we propose a numerical method for the fractional diffusion equations based on a new preconditioner that can be used to develop direct and iterative solvers for fractional diffusion equations with total $O(N \log N)$ operations per time step. Numerical results suggests the new method is a competitive alternative to existing methods. Add to calendar: 

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Date/Time : 14 Aug 2019 16:00
Venue : 16:00 S17 #05-11 SR5
Speaker : Simon Etter, National University of Singapore

Date/Time:14 Aug 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Simon Etter, National University of Singapore Polynomial and Rational Approximation for Electronic Structure Theory Density Functional Theory (DFT) and related electronic structure models are some of the largest consumers of computing power in supercomputing centres worldwide, and the bulk of this time is spent on evaluating functions of large, sparse matrices. Traditionally, such matrix functions have been computed by means of the eigenvalue decomposition, but the cubic scaling of standard eigensolvers with respect to the matrix size renders this ansatz prohibitively expensive in many applications. Several alternative algorithms have been developed in recent decades, among which the Pole Expansion and Selected Inversion (PEXSI) algorithm by Lin Lin and collaborators stands out for its ease of use and excellent parallel scaling. However, the runtime of the PEXSI scheme grows with $N^{3/2}$ for two-dimensional systems of $N$ atoms and with $N^2$ for three-dimensional systems, which is an important drawback of this method compared to most of its competitors. The first part of this talk will present a modification of the PEXSI algorithm which reduces its cost to linear in the system size regardless of the dimension. This modification is based on the observation that the LU factorisation of a sparse, well-conditioned matrix is localised, i.e. the magnitudes of the fill-in entries decay exponentially as we move away from the nonzero entries of the original matrix. The second part of this talk will discuss conductivity calculations, which introduce a new twist to the theory of electronic structure algorithms in that the matrix function to evaluate in this case is a bivariate one. The runtime of such calculations is proportional to the number of significant Chebyshev coefficients of the function $f(x,y) := 1/(x – y + s)$ with small imaginary $s$, and we will see that this number scales with only $|s|^{3/2}$ rather than $|s|^2$ as one might expect based on one-dimensional arguments. Add to calendar: 

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Date/Time : 14 Aug 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Zhou Chao, National University of Singapore

After the last financial crisis, model uncertainty attracted academics and practitioners’ attention. New theories have been established to improve the way of quantifying model uncertainty. And innovative work has been done on the research of optimal portfolio strategy under model uncertainty. Stochastic control techniques have been widely used in these recent works. In this talk, I will present my contribution to several problems under model uncertainty in Quantitative Finance. Moreover, I will provide the necessary background to understand the results.

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Date/Time : 08 Aug 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Yu Weichuan, Hong Kong University of Science and Technology

Date/Time:08 Aug 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Yu Weichuan, Hong Kong University of Science and Technology PTM-Invariant Peptide Identification Using Coding Method In computational proteomics, the identification of peptides with an unlimited number of post-translational modification (PTM) types is a challenging task. The computational cost associated with database search increases exponentially with respect to the number of modified amino acids and linearly with respect to the number of potential PTM types at each amino acid. The problem becomes intractable very quickly if we want to enumerate all possible PTM patterns. We proposed a novel method named PIPI to achieve PTM-invariant peptide identification. It first codes peptide sequences into Boolean vectors and codes experimental spectra into real-valued vectors. For each coded spectrum, it then searches the coded sequence database to find the top scored peptide sequences as candidates. After that, PIPI uses dynamic programming to localize and characterize modified amino acids in each candidate. We used simulation experiments and real data experiments to evaluate the performance in comparison with restricted tools (i.e., Mascot, Comet, and MS-GF+) and unrestricted tools (i.e., Mascot with error tolerant search, MS-Alignment, ProteinProspector, and MODa). Comparison with restricted tools shows that PIPI has a close sensitivity and running speed. Comparison with unrestricted tools shows that PIPI has the highest sensitivity except for Mascot with error tolerant search and ProteinProspector. The simulation experiments also show that PIPI has the lowest false discovery proportion and the highest PTM characterization accuracy among the unrestricted tools. This is a joint work with Fengchao Yu and Ning Li. Add to calendar: 

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