Math & Applied Sciences Seminars
Unless specified, all seminars will be on Room B1-1001, Campus B, 279 Nguyen Tri Phuong.
July 2024, TBA
Tran Minh Binh, Texas A&M University, USA
Title: TBA
Abstract: TBA
January 17, 2024, 10:00-11:00 AM
Soonhak Kwon, Sungkyunkwan Univeristy, Korea
Title: Survey of vectorial Boolean functions and some unsolved problems
Abstract: We introduce brief history of various Boolean functions such as bent functions, and
discuss some related (open) problems.
November 16, 2023 10:00-11:00 AM
Le Ba Khiet, Ton Duc Thang University
Title: Sliding mode observer for set-valued Lur’e systems and chattering removing
Abstract: In this talk, we study a sliding mode observer for a class of set-valued Lur’e systems subject to uncertainties. We show the well-posedness of the problem and highlight the clear advantages of our approach over the existing Luenberger-like observers. Furthermore, we provide a new continuous approximation to remove the chattering effect in the sliding mode technique. Some numerical examples are given to illustrate our theoretical approach.
August 31, 2023 10:00-11:00 AM
Nguyen Trung Tin, Inria centre at the University Grenoble Alpes, France
Title: Summary statistics and discrepancy measures for approximate Bayesian computation via surrogate posteriors
Abstract: A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the simulated and observed data are, often based on a set of summary statistics when the data cannot be compared directly. Unless discrepancies and summaries are available from experts or prior knowledge, which seldom occurs, they have to be chosen, and thus their choice can affect the quality of approximations. The choice between discrepancies is an active research topic, which has mainly considered data discrepancies requiring samples of observations or distances between summary statistics. In this work, we introduce a preliminary learning step in which surrogate posteriors are built from finite Gaussian mixtures using an inverse regression approach. These surrogate posteriors are then used in place of summary statistics and compared using metrics between distributions in place of data discrepancies. Two such metrics are investigated: a standard L2 distance and an optimal transport-based distance. The whole procedure can be seen as an extension of the semi-automatic ABC framework to a functional summary statistics setting and can also be used as an alternative to sample-based approaches. The resulting ABC quasi-posterior distribution is shown to converge to the true one, under standard conditions. Performance is illustrated on both synthetic and real data sets, where it is shown that our approach is particularly useful when the posterior is multimodal. This work is published in Statistics and Computing: https://doi.org/10.1007/s11222-022-10155-6.
June 16, 2023 10:00-11:00 AM
Nguyen Tien Khai, North Carolina State University, Raleigh, USA
Title: Equilibrium solution for an optimal debt management problem
Abstract: I will present recent results on game theoretical formulation of optimal debt management problems in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the risk-neutral lenders will charge a higher interest rate in order to compensate for this possible loss of their investment. Thus, a “solution” must be understood as a Nash equilibrium, where the strategy implemented by the borrower represents the best reply to the strategy adopted by the lenders, and conversely. This leads to highly nonstandard optimization processes.
May 17, 2023, 10:00-11:00 AM
Dao Nguyen Anh, University of Economics, Ho Chi Minh city
Title: Gagliardo–Nirenberg and Sobolev interpolation inequalities on Besov spaces
Abstract: We establish the Gagliardo–Nirenberg and Sobolev interpolation inequalities on Besov spaces. In particular, we improve the recent results of Miyazaki where he proved the inequalities on BMO spaces. This is joint work with Nguyen Lam and Guozhen Lu.
April 26, 2023, 10:00-11:00 AM
Ta Quoc Bao, International University, VNU at Ho Chi Minh city
Title: Portfolio Optimization based on combined approach of machine learning and statistical models
Abstract: The optimal portfolio allocation problem has become one of the most attractive research areas in both academia and industry over the last few decades. The significant framework for optimizing portfolios was first initiated by Harry Markowitz in his groundwork paper in 1952. There are two steps to composing and assessing portfolios. In the first step, investors forecast the future returns and risks of assets in the portfolio. The popular models include traditional econometric models such as ARMA, and GARCH. In the second step, investors consider returns, and risks and then determine the optimal allocation of the investment. However, in this step, estimation errors in the forecast models impact significantly the results of portfolio weights. So improving forecasting models plays an important role in portfolio optimization problems. In this talk we present a combined machine learning and statistical models to forecast the future returns and volatilities of stocks and then solve a portfolio optimization problem.
April 26, 2023, 9:00-10:00 AM
Pham Duy Khanh, Ho Chi Minh University of Education
Title: A New Inexact Gradient Descent Method with Applications to Nonsmooth Convex Optimization
Abstract:We propose and develop a novel inexact gradient method (IGD) for minimizing C1-smooth functions with Lipschitzian gradients, i.e., for problems of C^{1,1} optimization. We show that the sequence of gradients generated by IGD converges to zero. The convergence of iterates to stationary points is guaranteed under the Kurdyka-Lojasiewicz (KL) property of the objective function with convergence rates depending on the KL exponent. The newly developed IGD is applied to designing two novel gradient-based methods of non- smooth convex optimization such as the inexact proximal point methods (GIPPM) and the inexact augmented Lagrangian method (GIALM) for convex programs with linear equality constraints. These two methods inherit global convergence properties from IGD and are confirmed by numerical experiments to have practical advan- tages over some well-known algorithms of nonsmooth convex optimization.
April 07, 2023, 14:00-15:00 AM
Le Quoc Huy, Tan Tao University
Title: Cryptography: When Mathematics protects your wallet (and many other things)
Abstract: Cryptography is known simply as a scientific field that studies the methods and means to transform (a.k.a. encrypt) information for safe transmission/exchange. Starting from the initial stage with very simple tools and purposes (i.e., applications), Cryptography has now developed significantly in both tools and purposes. Nowadays, Cryptography plays an extremely crucial role in almost all areas of human life such as military, economic and financial, communication, etc.
Cryptography is actually an interdisciplinary science. However, the remarkable development of Cryptography as mentioned above comes from the significant role of Mathematics. Mathematics is the foundation, the tool, ... for the development of Cryptography. It can be said that without the partnership of Mathematics, Cryptography would forever remain an art (as roughly defined by the Oxford Dictionary "Cryptography: the art of writing and solving codes"), rather than becoming an essential science as we see today.
In this report, the speaker will:
(1) introduce some information about Cryptography and the history of its development, while pointing out the partnership of Mathematics in each major development period,
(2) show the way Mathematics is used in Modern Cryptography,
(3) discuss a recent branch of Cryptography as an illustration for (2) - this branch is based on a mathematical object called "lattices", and this cryptography branch is considered to be able to resist the power of quantum adversaries, and
(4) give some upcoming development issues of Cryptography.
April 05, 2023, 15:00-16:00
Chun-Chi Lin, National Taiwan Normal University
Title: Some problems in geometric analysis and its application in quantum computation
Abstract: In this talk, I would like to share some progress of our research on variational problems and geometric flows, which are motivated from quantum computation. As time allows, I would also introduce our research programs in mathematical sciences in the college of science at NTNU. Hopefully, it bridges up the collaboration or connection for faculty and students between the two sides of universities in the near future.
January 09, 2023, 9:00 -10:00 AM
Nguyen Phuoc Tai, Masaryk University, Czech Republic
Title: Nonlinear Schrodinger Equations With A Singular Potential : Global Existence Versus Finite Time Blowup.
Abstract: In this talk, I will discuss the focusing nonlinear Schrodinger (NLS) equation with an inverse-square potential. The presence of the potential yields substantial difficulties and requires a fine analysis. I will show the existence of a minimizer of Hardy-Gagliardo-Nirenberg inequality and the uniqueness of the ground state solution to the NLS equation. As a consequence, I will show that any minimizer can be represented by the ground state solution. Then I will establish global existence versus finite time blowup for the focusing NLS equation.