演講公告

  • 演講時間:2024年06月14日(五)
    Tight Bound on Joints Problem and Partial Shadow Problem(演講)
    講者:趙庭偉博士

    .演講時間:2024年6月14日(五) 11:00 –12:00
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract
    Given a set of lines in R^d, a joint is a point contained in d linearly independent lines. Guth and Katz showed that N lines can determine at most O(N^{3/2}) joints in R^3 via the polynomial method.
    Yu and I proved a tight bound on this problem, which also solves a conjecture proposed by Bollob\'as and Eccles on the partial shadow problem. It is surprising to us that the only known proof to this purely extremal graph theoretic problem uses incidence geometry and the polynomial method.

    相關檔案:Talk_1130614.pdf

  • 演講時間:2024年05月28日(二)
    A brief introduction to semiclassical analysis for Schrödinger equations(論文研討)
    講者:李俊璋教授(清華大學)

    .演講時間:2024年5月28日14:00 –15:00
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract. Nonlinear Schrödinger equations are a widely studied topic due to their various applications in nonlinear optics and Bose–Einstein condensates. The semiclassical analysis serves as a link between quantum mechanics and classical mechanics, providing insight into how classical physics emerges from quantum mechanical principles, with Planck's constant playing a crucial role.

    In this talk, I will first apply Madelung's transform to the Schrödinger equation and formally derive the hydrodynamic equations. Then, I will introduce a mathematical method for investigating the semiclassical limits of Schrödinger equations. The focus will be on introducing a modulated energy functional to govern mass density and linear momentum, particularly in relation to the compressible Euler equations. Finally, I will introduce my ongoing work about a nonlocal Schrödinger equation, drawing connections to a nonlocal compressible Euler equation.

    相關檔案:Talk_1130528.pdf

  • 演講時間:2024年05月14日(二)
    Improved Approximation Algorithm for Capacitated Facility Location with Uniform Facility Cost(論文研討)
    講者:高孟駿教授(國立陽明交通大學資訊工程學系)

    .演講時間:2024年5月14日 13:30-14:20
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract. We consider the hard-capacitated facility location problem with uniform facility cost (CFL-UFC). This problem arises as an indicator variation between the general CFL problem and the uncapacitated facility location (UFL) problem, and is related to the profound capacitated k-median problem (CKM). In this work, we present a rounding-based 4-approximation algorithm for this problem, built on a two-staged rounding scheme that incorporates a set of novel ideas and also techniques developed in the past for both facility location and capacitated covering problems. Our result
    improves the decades-old LP-based ratio of 5 for this problem due to Levi et al. since 2004. We believe that the techniques developed in this work are of independent interests and may further lead to insights and implications for related problems.

    相關檔案:Talk_20240514-1.pdf

  • 演講時間:2024年05月14日(二)
    Dissecting the Causality of Pressure Forces in Vortex Dominated Flows - From Fish Schools to Noisy Drones(論文研討)
    講者:Rajat Mittal (約翰·霍普金斯大學)

    .演講時間:2024年5月14日(二) 14:30 –15:20
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract
    Pressure-induced drag and lift are key to the performance of wings, rotors and propellers; undulating fins and flapping wings generate forces that are key to locomotion in fish, birds and insects; time-varying fluid dynamic forces drive flutter and flow-induced vibrations of flexible structures in engineering and biology, and these same forces enable the extraction of energy from flow via devices such as wind-turbines. Pressure on a body immersed in a flow is however induced simultaneously by vortices, acceleration reaction (a.k.a. added mass) effects associated with body and/or flow acceleration, and viscous diffusion of momentum, and determining the relative contribution of these different mechanisms on surface pressure remains one of the most important and fundamental issues in fluid dynamics. I will describe the force partitioning method (FPM), a new data-enabled method that partitions pressure forces into components due to vorticity, acceleration reaction and viscous diffusion. FPM has been used to gain new insights into a variety of vortex dominated flows including dynamic stall in pitching foils, vortex-induced vibration of bluff-bodies, hydrodynamics of schooling fish and rough-wall boundary layers, and results from these analyses will be presented. Application of FPM to data generated from experiments will also be described. Finally, FPM has been extended to aeroacoustics, and applications of the aeroacoustic partitioning method (APM) to dissect aeroacoustic noise in engineering and biological flows will be presented.

    相關檔案:Talk_20240514-2.pdf

  • 演講時間:2024年05月07日(二)
    Global classical nozzle flows near or away from vaccum states(論文研討)
    講者:洪盟凱教授(中央大學數學系)

    .演講時間:2024年5月7日(二) 14:00 –15:00
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract. In this talk, we consider some nonlinear hyperbolic systems of balance laws near resonance. We focus on the classical solutions near or away from vacuum state (resonance ) to the compressible Euler equations for either isentropic or non-isentropic flows through non-uniform ducts. We establish the global existence of classical solutions for both cases. By the normalization of systems, maximum principle, generalized Lax transformation and the detail study of Riccati equations, we are able to obtain uniformly bounded C^1 norms of those solutions . The asymptotic behavior of solutions is also studied.

    This series of projects are the joint works with Hsin-Yi Lee, Jay Chu, Ying-Chieh Lin, Shih-Wei Chou and Shih-Ming Wang.

    相關檔案:Talk_1130507.pdf

  • 演講時間:2024年04月23日(二)
    Multiple-collapsing blowup solutions for the 2D Keller-Segel system(論文研討)
    講者:Van Tien Nguyen 教授(台大數學系)

    .演講時間:2024年4月23日(二) 14:00 –15:00
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract. It is well known that the 2D Keller-Segel system has finite time blowup solutions if the initial density has total mass greater than and finite second moment. We have several constructive examples showing that the solution blows up with the only -mass concentration. We will exhibit a new blowup mechanism formed by a collision of two sub-collapses, resulting in a -mass concentrating solution. A similar phenomenon appears in the 2D mass critical NLS by the work of Martel-Raphael in 2018, where the construction relies on two specific features: a conformal invariance and a minimal mass blowup constraint. These properties are not available for parabolic equations such as the Keller-Segel system. We bring here for the first time a directly rigorous construction of such a multiple-collapsing blowup solution.

    相關檔案:Talk_1130423.pdf

  • 演講時間:2024年04月16日(二)
    Johnson graphs and Clebsch-Gordan coefficients of U(sl2) along with their q-analogues(論文研討)
    講者:黃皜文教授 (中央大學數學系)

    .演講時間:2024年4月16日 14:00 - 15:00
    .演講地點:線上演講
    .摘要內容:

    演講網址:meet.google.com/bfa-aykg-mjt

    相關檔案:Talk_20240416.pdf

  • 演講時間:2024年04月12日(五)
    Hokudai-NYCU Joint Workshop on Applied Mathematics(研討會)
    講者:

    .演講時間:2024年4月11-12日 9:00起
    .演講地點:
    .摘要內容:

    更多詳情請參考附件。