
5月演講

Colloquium, 臺灣大學動力與模擬實驗室 謝佩媛博士
Thursday, May 3, 16:10—17:00 數學系3174
Title: Deconvolution of the Labrador Sea TransitTime Distribution from combined CFC11 and CFC12 Abstract: The Labrador Sea is an important deep water formation site where a large fraction of the ocean’s deep waters had their last contact with the atmosphere. Quantifying the ventilation of the Labrador Sea is therefore crucial for understanding the global ocean circulation. We use yearly hydrographic measurements of CFC11 and CFC12 taken along WOCE repeat section AR7W from 1991 to 2009 to estimate the climatological transittime distributions (TTDs) for three distinct Labrador Sea water masses, namely Labrador Sea Water (LSW), IcelandScotland Overflow Water (ISOW), and Denmark Straight Overflow Water (DSOW). We don’t assume a particular functional form such as an Inverse Gaussian for the TTD, but instead use a Bayesian deconvolution method that allows the shape of the
TTD to be determined from the data and prior information. To take into account the fact that mixing in the ocean leads smooth TTD functions with positive serial correlations, we assume an entropic prior on a hidden function, which produces the TTD when convolved with an intrinsic correlation function. The width of this correlation function, along with three regularization weights that determine the relative importance of three separate sources of
information, namely the CFC11 data, the CFC12 data, and the prior, are determined from the evidence provided by the data. We find that the fraction of the LSW, ISOW, and DSOW that is less than 10 years old is 73±1%, 49±4%, and 55±9% respectively. Our results provide a baseline from which changes in the ventilation of the Labrador Sea can be quantified. We also apply our deconvolution method to estimate an exchangetime distribution (ETD), which
can be used to determine a timedependent airsea disequilibrium for CFC11 and CFC12. We find that the surface waters of the Labrador Sea have a mean airsea equilibration time of approximately 7.5±1.5 years. The long 30 airsea equilibration time reflects the very deep mixed layers present in the Labrador Sea.

Colloquium, 成功大學數學系 林敏雄教授
Thursday, May 10, 15:10—16:00 數學系3174
Title: Scientific Computing on Data Analytics and Engineering Problems Abstract: In this talk, we would like to apply scientific computing to analyze data and solve formerly complex problems. Our discussion includes two major parts. First, we discuss the integer lowrank approximation of integer data matrices. Different from the general lowrank approximations, the integer approximation is discrete; therefore, the conventional techniques for matrix approximation, such as SVD and nonnegative matrix approximation, are inappropriate and unable to solve this problem. Upon recursively finding integer solutions of integer least square problems, we propose a block coordinate descent method to obtain the integer lowrank approximation of integer matrices. Applications on the real world problems such as the association rule mining, and pattern extraction will be given. Second, we propose practical numerical methods for solving a class of initialboundary value problems of spacetime fractional advectiondiffusion equations. First, we offer an implicit way based on twosided Grunwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual method with an easily constructed preconditioner. Because resulting systems are Toeplitzlike, fast Fourier transform can be applied to significantly reduce the computational cost. Numerical experiments are performed to demonstrate the efficiency of the preconditioner, even in cases with variable coefficients.

Colloquium, 中央研究院數學研究所 葉弘裕博士
Thursday, May 10, 16:10—17:00 數學系3174
Title: Mathematical Foundation of Modern Physics Abstract: Physics, knowledge of nature, is the scientific study of matter and energy, the effect that they have on each other, and their motion through space and time. Mathematical physics is the field of the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. In this talk, I will start with giving a brief overview of the principles of fundamental physics which provide a clever and beautiful picture of universe within a mathematically rigorous framework. Nowadays, we need new physics and mathematical framework which are able to explain open and conceptual questions arising from the unification of quantum theory and general relativity. At last I will introduce some progress in my work.

Colloquium, Imperial College London, Prof. Paolo Cascini
Thursday, May 17, 16:10—17:00 數學系3174
Title: On the Minimal Model Program Colloquim Cancelled Abstract: The aim of the Minimal Model Program is to generalize the classification of complex projective surfaces, known in the early 20th century, to higher dimensional varieties. Besides providing a historical introduction, we will discuss some recent results and new aspects of this Program.

PDE Seminar, 清華大學數學系 江金城教授
Monday, May 21, 11:15—15:00 數學系3177
Title: On the Estimates of the Gain Term of the Boltzmann Collision Operator Abstract: NCKUNCTS Reading Seminar on Kinetic Theory

PDE Seminar, 成功大學數學系 郭鴻文教授
Monday, May 21, 11:15—15:00 數學系3177
Title: Existence of Nonlinear Boundary Layers of the Boltzmann Equation Abstract: NCKUNCTS Reading Seminar on Kinetic Theory

Colloquium, 臺灣大學數學系暨國家理論科學研究中心數學組 陳榮凱教授
Wednesday, May 23, 16:10—17:00 數學系3174
Title: Positivity of Pluricanonical Sheaves on Irregular Varieties Abstract: There are various notion of positiveness in algebraic geometry. Over irregular varieties, one can measure positivity in terms of cohomological properties. Together with the standard techniques of vanishing theorems, one can prove stronger results on nonvanishing, generations, birationalities and so on. The purpose of this talk is to demonstrate and compare various notions of positivities on irregular varieties, especially on irregular threefolds. We will also discuss some geometric applications.

Colloquium, 成功大學數學系 劉珈銘教授
Thursday, May 24, 15:10—16:00 數學系3174
Title: Mean Field Equations on Hyperelliptic Curves Abstract: Mean field equations originally came from the study of conformal geometry and are also related to physics. We discovered that using canonical metric on hyperelliptic curves, we are able to use an algebraic method to construct an explicit solution to the mean field equations. In this talk, I will give a recent progress of my result.

Colloquium, 清華大學數學系 張介玉教授
Thursday, May 24, 16:10—17:00 數學系3174
Title: Logarithmic Interpretation of Multiple Zeta Values in Positive Characteristic Abstract: In the classical theory, there is a conjecture asserting that padic multiple zeta values (MZV's) satisfy the same linear relations that the corresponding realvalued MZV’s satisfy. The main result in this talk is to answer the analogue of the conjecture in the function field setting (joint work with Y. Mishiba). Key ideas of the proof via logarithms will be briefly sketched if time is permitted.

Colloquium, 中央研究院數學研究所 程舜仁特聘研究員
Thursday, May 31, 15:10—16:00 數學系3174
Title: Irreducible Characters of Exceptional Lie Superalgebras in BGG Category Abstract: We explain a solution to the irreducible character problem for the finitedimensional exceptional simple Lie superalgebras D(2,1,ζ) and G(3) in the BGG category. This is based on joint works with Weiqiang Wang.





