演講公告

  • 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。

  • 演講時間:2024年04月02日(二)
    A West Nile Virus model with vertical transmission and periodic incubation periods(論文研討)
    講者:王埄彬教授(長庚大學)

    .演講時間:2024年4月2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. West Nile virus (WNv) is a mosquito-borne disease caused by Flavivirus. To investigate the combined effects of vertical transmission, temperature-dependent incubation periods and environmental heterogeneity on the transmission of WNv, we develop a delay differential system with stage-structure and time-varying delays. We then derive the mosquito reproduction number and WNv reproduction number, respectively, and further show that these two numbers serve as threshold parameters that determine whether WNv will spread or not.

    Numerical simulations support our analytic results and suggest that time-periodic delays and environmental heterogeneity can play important roles in the WNv dynamics

  • 演講時間:2024年03月26日(二)
    Obtaining Approximately Optimal and Diverse Solutions via Dispersion(論文研討)
    講者:蔡詩妤博士(中央研究院資訊科學研究所)

    .演講時間:2024年3月26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. We study diverse solutions to optimization problems and design fair scheduling of demands with different priorities on wireless networks The problem of finding several sufficiently-diverse, yet approximately-optimal solutions to an optimization problem can be described as follows: given an integer k, an approximation factor $\alpha$, and a diversity measure $\sigma$ on a set of solutions to an optimization problem P, find a set of k solutions to P that (a) are all $\alpha$ approximately-optimal for P and (b) maximize the diversity measure $\sigma$ over all such sets of k solutions. The optimization problems considered here are maximum matching, spanning tree, global min-cut, shortest path, and minimum weight bases of a matroid. Here, a solution is a set of edges, and the number of edges two given solutions differ in as the diversity measure of the pair. The diversity measure $\sigma$ of k solutions is the sum of the pairwise Hamming distance between the bit-vectors representing the k solutions. We propose the first polynomial-time algorithms that (except for the unweighted spanning tree), for these five graph problems, guarantee that their diversity is at least 1/4 times the optimal diversity under different $\alpha$.

    This result is applied for minimum weight bases of a matroid, which means it gives us diverse $\alpha$-approximate minimum spanning trees, advancing a step towards achieving diverse $\alpha$-approximate TSP tours.

    相關檔案:Talk_1130326.pdf

  • 演講時間:2024年03月19日(二)
    The Differential Geometry of Curves in Space Forms of Pseudo-Hermitian Manifolds(論文研討)
    講者:黃彥彰教授(臺南大學應用數學系)

    .演講時間:2024年3月19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
    The exploration of submanifolds in spaces of constant sectional curvature is fundamental to Differential Geometry. Since 2015, significant progress has been achieved by Chiu-Huang-Lai and Chiu-Ho, who established the Fundamental Theory of Curves and Surfaces in the Heisenberg group H₁ and the CR sphere S³ respectively. Their research resulted in the identification of a comprehensive set of geometric invariants, specifically curvatures for curves and surfaces. Acting as pseudo-Hermitian manifolds, H₁ and S³ represent special cases of CR manifolds, embodying zero and positive constant sectional curvatures, respectively. Recently, Pak Tung Ho (Tamkang University) and I have extended our research to include the final model case—the constant negative sectional curvature—in the product space consisting of a unit 2-sphere and the real line. This presentation will provide a concise review of our previous findings and will concentrate on developing geometric invariants in this product space. Furthermore, I will explore the proof of the Fundamental Theorem of Curves, supported by a series of intriguing examples.

    相關檔案:Talk_1130319.pdf

  • 演講時間:2024年03月15日(五)
    Factorizing three-dimensional smooth flops(演講)
    講者:陳星谷博士(韓國高級研究所)

    .演講時間:2024年3月15日(五) 上午11:00 –12:00
    .演講地點:(光復校區) 科學一館307室
    .摘要內容:

    Abstract. A flop is a special birational transformation which produces a symmetry between two algebraic varieties. In this talk we will give an explicit description for three-dimensional smooth flops over complex numbers by factorizing them as a sequence of smooth blow-ups and blow-downs.

    相關檔案:Talk_1130315.pdf

  • 演講時間:2024年03月05日(二)
    Numerical Methods for Partial Differential Equations on Surfaces(論文研討)
    講者:Shing Yu Leung教授 (香港科技大學)

    .演講時間:2024年3月5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. We will present recent numerical methods for solving partial differential equations on surfaces. In the first part of the talk, we will introduce a simple discretization called the Modified Virtual Grid Difference (MVGD), which allows for the numerical approximation of the Laplace-Beltrami operator on manifolds sampled by point clouds. In the second part, we will present a diffeomorphic embedding method that has been recently developed for computing differential equations on implicit surfaces. This embedding equation is based on a push-forward operator, which can extend any tangential flux vectors from the surface to a neighboring level surface. The computation of this operator is straightforward and only requires the level set function and the corresponding Hessian. We will provide examples from scalar hyperbolic conservation laws and eigenproblems of the Laplace-Beltrami operators.

    相關檔案:Talk_1130305.pdf

  • 演講時間:2024年01月24日(三)
    Towards decompositions of small transitions of Calabi-Yau 3-folds(演講)
    講者:王賜聖博士 (中研院數學所)

    .演講時間:2024年1月24日(三) 14:00 –15:00
    .演講地點:(光復校區) 科學一館223室
    .摘要內容:

    Abstract.
    The Calabi-Yau manifolds play an important role in geometry and mathematical physics. There is a small transition process for two Calabi-Yau 3-folds, a small birational contraction followed by a complex smoothing. The simplest one is a conifold transition. In this talk, I will introduce a primitive subclass of small transitions as the building blocks and investigate the relation between conifold transitions and primitive ones.

    相關檔案:Talk_1130124.pdf

  • 演講時間:2024年01月12日(五)
    Extensions of Yamamoto-Nayak's asymptotic theorem (演講)
    講者:Tin-Yau Tam 教授 (美國內華達大學雷諾分校)

    .演講時間:2024年1月12日 (五) 11:00 - 12:00
    .演講地點:(光復校區)科學一館 223 室
    .摘要內容:

    詳情請見附件。

    相關檔案:Talk_20240112 .pdf