陽明交通大學應用數學系

Abstract.
Wetting phenomena are common in daily life, such as water droplets sliding on a window during rainy days. Recent research has focused on wetting behavior on soft solid materials such as elastomers and polymeric gels, which have promising applications, for example in biomedicine, tissue engineering, and soft robotics. Studies have shown that droplets move significantly slower on soft solids than on rigid surfaces—by orders of magnitude—due to dominant viscoelastic dissipation within the material. In this talk, I will introduce a model that explores contact line motion and the dissipation mechanisms arising from both viscoelasticity and poroelasticity in soft solids. Understanding these dissipation processes is essential for accurately describing droplet motion across different solid materials.

Abstract. The study of reaction-diffusion equations on metric graphs has been drawing attention recently. Two different research directions will be introduced. First topic is related to the question of whether excitation waves propagate along the branching of axons of nerve cells or not. Namely, we are going to consider a scaler reaction diffusion equation on a star-shaped metric graph. We can observe propagation blocking depending on the numbers of input and output edges. We also discuss the related problem. Second, we study pattern dynamics on compact metric graphs. We consider systems of reaction-diffusion equations on compact metric graphs with Turing or Wave instability. We construct eigenfunctions of Laplacian on specific metric graphs to see pattern onsets depending on the lengths of the edges. By using the normal form analysis and symmetry arguments we study the local bifurcation structures around the bifurcation points. In both cases, we impose natural boundary conditions, namely, Neumann‒Kirchhoff conditions at the junction.

Abstract
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations, which consists of a bifurcation without parameters and a classical bifurcation. Our main result classifies the hybrid bifurcation when a line of equilibria with an exchange point of normal stability vanishes. We showcase the efficacy of our approach by proving stable periodic coexistent solutions in an ecosystem of two competing predators with Holling’s type II functional response. This is a joint work with Alejandro López Nieto, Phillipo Lappicy, Nicola Vassena, and Hannes Stuke.

Abstract
The group of algebraic cycles, i.e, formal sums of algebraic subvarieties of a fixed algebraic variety, is a fundamental invariant in algebraic geometry. Since the group is too large, we usually consider its quotients by adequate equivalence relations. Numerical equivalence is one of such equivalence relations given abstractly. In this talk, I will explain a description of the quotient by numerical equivalence (with rational coefficients) as cohomology of some geometric object under suitable assumption.

Abstract
In this talk, I will share my journey from being an uncertain mathematics undergraduate to becoming a professional researcher in quantitative finance. I will recount the pivotal moments in my academic path and discuss how I transitioned into the field of finance. Additionally, I will introduce my research areas, including Bayesian statistics, statistical computing (with applications such as Greeks calculation, importance sampling, and spherical Monte Carlo methods), machine learning, and FinTech. By bridging financial applications and statistical methodologies, I aim to provide insights into how mathematics can be a powerful foundation for a career in finance. This talk is designed to inspire and guide math students who are curious about pursuing opportunities in the finance industry.

Abstract
This talk considers the 3-D guidance law based on target lead angle information and the state-dependent differential Riccati equation (SDDRE) scheme. In an application-oriented manner, it presents theories to significantly improve critical computational performance and thus aims at a fast implementation for impact-angle-constrained interception of agile maneuvering targets. More specifically, regarding the two major computational burdens using SDDRE, we have replaced the burden in numerical applicability checking by a simple, equivalent, and closed-form condition for the entire state space, which is actually the dominant burden as supported by complexity analysis and extensive validations. Notably, the proposed analysis not only complements the early findings of applicability guarantee in literature, but also promotes the efficiency of the proposed philosophy when compared to the classic method, where the latter has caused concerns/reservations due to its feasibility and difficulty. On the other hand, we have largely mitigated the second major burden of SDDRE by—after exhaustive trials—selecting the most efficient Riccati-equation solver until the latest benchmarks. Such evaluations are: 1) in favor of a much-less-known achievement, rather than the common QR-based benchmark and 2) subject to both numerical and hardware experiments including, notably, implementations on microcontrollers and field-programmable gate arrays.

Abstract.
A statistical model is said to be calibrated if it has the appropriate level of confidence in its own predictions: that is, the confidence that it assigns to a predicted outcome should accurately reflect that outcome's likelihood. For example, if a weather model is calibrated, then out of all of the days when the model predicts a 30% chance of rain, we should expect that it actually will rain on 30% of them. Calibration is crucial for managing the risks associated with incorrect predictions, but modern deep learning models are systematically miscalibrated: they are overconfident when they are incorrect. To make matters worse, theorists can't agree about how miscalibration should be quantified! The prevailing miscalibration metric in engineering applications is the expected calibration error (ECE), which has been widely criticized because it is discontinuous: a tiny change in the model can lead to a large change in the error. In this talk, I'll try to convince you that this problem isn't really a problem, that ECE was fine all along, and that engineers should feel free to keep using it the way they always have (at least for binary classification tasks). The argument will require us to answer a strange but fundamental question about the topological properties of the conditional expectation operator.