NCTS

10th Pacific Rim Conference of Mathematics
https://www.math.sinica.edu.tw/workshop/PRCM/10th.html

Date : 2026/06/15 (Mon.)~2026/06/19 (Fri.)
Location : Astronomy-Mathematics Building (NTU Campus)

Supporting Organizations :
．Academia Sinica
．National Science and Technology Council
．Taiwan Mathematics Society

Plenary Speakers:
Ben ANDREWS Australian National University
Amir DEMBO Stanford University
Jun-Muk HWANG IBS-Center for Complex Geometry
Toshiyuki KOBAYASHI University of Tokyo
Sarah PELUSE Stanford University
Geoffrey SCHIEBINGER University of British Columbia
Gunther UHLMANN University of Washington
Hong WANG IHÉS & New York University
Ping ZHANG Chinese Academy of Sciences
Jun ZOU Chinese University of Hong Kong

2026 NCTS Summer Course on Mathematical Biology
https://ncts.ntu.edu.tw/events_3_detail.php?nid=402

10:00-12:00, 14:00-16:00 on July 24 and July 27, 2026
Lecture Room B, 4th Floor, The 3rd General Building, NTHU

Speaker(s):
Naveen K. Vaidya (San Diego State University)
Feng-Bin Wang (Chang Gung University)

Organizer(s):
Feng-Bin Wang (Chang Gung University)
Chang-Hong Wu (National Yang Ming Chiao Tung University)
Chang-Yuan Cheng (National Kaohsiung Normal University)

1.Course Background & Purposes

Mathematical modeling can play an important role in the understanding of mechanisms in biological systems. Motivated by this, we intend to introduce mathematicalmodels of Infectious Disease Transmission. Theory of monotone systems has been successfully used to investigate the global dynamics of Infectious Disease models.

Thus, we will provide a brief introduction to monotone systems in this course. We will also discuss how the fitting of the developed models into experimental data of Infectious Disease can be used to validate the models and estimate model parameters. Besides, the interesting topic about Machine Learning Approaches into Models for Disease Control will also be introduced in this summer course.

2.Course Outline & Descriptions

Lecture-1:
Mathematical Models of Infectious Disease Transmission
Speaker: Naveen K. Vaidya (SanDiegoStateUniversity)
Time: 10:00-12:00, July 24, 2026
Abstract:
In this lecture, we will discuss methods for developing mathematical models to describe the transmission dynamics of infectious diseases. We will cover the diseases transmitted directly, through vectors, and via the environment. We will also show how to formulate reproduction numbers from the developed models.

Lecture-2:
Theoretical Model Analysis and Disease Spread Criterion
Speaker: Feng-Bin Wang (ChangGungUniversity)
Time: 14:00-16:00, July 24, 2026
Abstract:
In this lecture, we will present various theoretical techniques for analyzing developed models. Focus will be on establishing threshold criteria for the extinction or persistence of diseases. We will discuss how the global dynamical properties identified by theoretical analysis can be applied to disease control.

Lecture-3:
Data-Informed Phenomena into Disease Models
Speaker: Naveen K. Vaidya (SanDiegoStateUniversity)
Time: 10:00-12:00, July 27, 2026
Abstract:
In this lecture, we will present the computational methods for incorporating real data into the developed models to estimate critical model parameters and threshold values for disease spread. We will also discuss the methods for quantifying uncertainty in data-informed models.

Lecture-4:
Machine Learning Approaches into Models for Disease Control
Speaker: Naveen K. Vaidya (SanDiegoStateUniversity)
Time: 14:00-16:00, July 27, 2026
Abstract:
In this lecture, we will discuss machine learning methods that can be used for data refinement, model simulations, and parameter optimization. The methods will be applied to real data and models of infectious diseases.

3. Registration

https://forms.gle/UHJAkg8B92Zs6NZK6

Contact: Murphy Yu ([email protected]), Vickey Sun

NYCU-NCTS Summer Undergraduate School - Analytical and Computational Study of Traveling Waves and Their Stability
https://ncts.ntu.edu.tw/events_3_detail.php?nid=396

9:00-17:00, July 20-30, 2026
Lecture Room B, 4th Floor, The 3rd General Building, NTHU
& Science Building I, NYCU

Speaker(s):
Hsin-Yuan Huang (National Yang Ming Chiao Tung University)
Te-Sheng Lin (National Yang Ming Chiao Tung University)
Chang-Hong Wu (National Yang Ming Chiao Tung University)

Organizer(s):
Hsin-Yuan Huang (National Yang Ming Chiao Tung University)
Te-Sheng Lin (National Yang Ming Chiao Tung University)
Chang-Hong Wu (National Yang Ming Chiao Tung University)

1. Introduction & Purposes

This program introduces undergraduate researchers to analytical and computational methods for studying traveling wave solutions of evolutional partial differential equations and their stability. A central theme is the distinction between absolute and convective behavior of perturbations, both for homogeneous states and for traveling wave solutions viewed in a comoving frame. The project combines complex analysis (via the Fokas method), numerical simulation, and spectral analysis, guiding students from foundational concepts to focused research projects.



2. Outline & Descriptions

The program will run from July 20 to July 30, 2026. During this period, students will participate in lectures and research projects under the supervision of Profs. Hsin-Yuan Huang, Te-Sheng Lin, and Chang-Hong Wu from National Yang Ming Chiao Tung University, together with three graduate student mentors. Students are encouraged to have the relevant prerequisite knowledge. The detailed description of the program is provided below.

l Lectures

l The lectures will cover the following three topics

○ Spectral Representations and the Fokas Method

■ Lecture 1: Fokas method for linear PDEs with various boundary conditions

■ Lecture 2. Fokas method for systems of linear PDEs

■ Lecture 3. Absolute and convective instability for evolutionary PDEs

■ Lecture 4. Wrap-up and discussion

○ Numerical Methods and Visualization of Instability

○ Analysis of Traveling Wave Solutions

l Independent Research projects

Students will work in small groups on focused research projects under faculty supervision. Possible project directions include:

• Classification of absolute versus convective instability for selected parameter regimes

• Comparison of numerical simulations with spectral predictions

• Study of boundary effects using Fokas-type representations

• Investigation of the parametric dependence of wave speed and instability thresholds

• Global/local stability analysis to traveling waves in selected models

l References

○ M. Ablowitz and A. S Fokas (2003), "Complex variables: introduction and applications". Cambridge University Press.

○ B. Deconinck, T. Trogdon, and V. Vasan, "The method of Fokas for solving linear partial differential equations", *SIAM Review* 56 (2014) pp.159-186.

○ P. C. Fife, J. B. McLeod, The approach of solutions of nonlinear diffusion equationstotravellingfrontsolutions,Arch.Ration.Mech.Anal.65(4)(1977) 335–361

○ A.S.FokasandD.T.Papageorgiou,"Absoluteandconvectiveinstabilityfor evolutionPDEsonthehalf-line",*Studies in Applied Mathematics*, 114 (2005)

pp.95–114.

○ T.KapitulaandK.Promislow(2013),"SpectralandDynamicalStabilityof Nonlinear Waves", Springer.

○ H.Kokubu,Homoclinicandheteroclinicbifurcationsofvectorfields,JapanJ. Appl. Math., 5 (1988), pp. 455–501.



3. Registration

https://forms.gle/kvwZdeBEU8DLGt4d9 Deadline: June 10 24:00



Contact: Murphy Yu ([email protected]) & Vickey ([email protected])

2025 NCTS URP 夏季研究成果報告發表會
https://ncts.ntu.edu.tw/events_2_detail.php?nid=568

July 3, 2026
Room 505, Cosmology Building, NTU
Organizers:
Mao-Pei Tsui (National Taiwan University)

1. 活動宗旨

NCTS URP/USRP/RA are three main programs to foster talent undergraduate students in Taiwan. Under the supervision of their chosen mentors, students learn deep and interesting topics for their future studies in mathematics and applied mathematics. In this one-day meeting, students can share their research results and also make good connections with other students and researches.

2. 活動流程與安排

1人20分鐘；2人25分鐘；3人30分鐘(以上時間已含5分鐘的Q&A與換場)，為開放式活動，歡迎大家到場聆聽並交流意見。

Contact: Murphy Yu ([email protected])

NCTS One Day Workshop on Harmonic Analysis
https://ncts.ntu.edu.tw/events_2_detail.php?nid=564

July 3, 2026
Room 515, Cosmology Building, NTU

Organizers:
Chong-Wei Liang (National Taiwan University)
Yu-Hsiang Lin (Purdue University)
Chun-Yen Shen (National Taiwan University)

Aim & Scope

This workshop aims to bring together young researchers working in harmonic analysis, geometric measure theory, and related areas to exchange recent advances and explore emerging directions in the field. The workshop will feature talks on topics including multilinear and sublinear estimates, geometric averaging operators, Brascamp–Lieb inequalities, distance set problems, and the analysis of polynomial and discrete structures. A central goal is to foster collaboration and stimulate new ideas by highlighting both foundational techniques and modern developments across continuous and discrete settings.

Invited Speakers

Guo-Dong Hong (California Institute of Technology)

Yung-Chang Hsu (Rutgers University)

Chong-Wei Liang (National Taiwan University)

Yu-Hsiang Lin (Purdue University)

Chun-Kai Tseng (Michigan State University)

Jian-An Wang (Virginia Tech)


Registration: https://forms.gle/pZuSZxr9mo756TpZ7

Title & Abstract: https://drive.google.com/file/d/1mDIsxBgLWos29IwdTndICesfi9iriJxJ/view?usp=sharing

Contact: Peggy Lee ([email protected])

2026 Summer School in Algebraic Geometry
https://ncts.ntu.edu.tw/events_3_detail.php?nid=401

10:00-17:00, June 29 to July 17, 2026
Room 505, Cosmology Building, NTU

Speaker(s):
Jungkai Chen (National Taiwan University)
Jiun-Cheng Chen (National Tsing Hua University)
Ching-Jui Lai (National Cheng Kung University)
Jheng-Jie Chen (National Central University)
Hsueh-Yung Lin (National Taiwan University)
Kwan-Wen Lai (Tunghai University)
Chih-Wei Chang (National University of Kaohsiung)
Hsin-Ku Chen (National Chung Cheng University)
Chi-Kang Chang (RIKEN)

Organizer(s):
Jheng-Jie Chen (National Central University)
Hsin-Ku Chen (National Chung Cheng University)

1. Introduction & Purposes

The aim of this summer school is to introduce basic knowledge and different aspects of algebraic geometry. Participants are supposed to be undergraduate/graduate students without any preliminaries in algebraic geometry.

2. Outline & Descriptions

This is a three-weeks summer school. In the first two weeks we plan to introduce the basic notion of algebraic geometry. In the third week we will assign a topic each day, and introduce important results and recent researches on each topic. Topics including: birational geometry, toric varieties, applied algebraic geometry.

3. Schedule
https://ncts.ntu.edu.tw/events_3_detail.php?nid=401

4. Registration

https://forms.gle/HTfcG19mj6BoYZS86 Deadline May 31



Contact: Murphy Yu ([email protected])

ncts The aim of this summer school is to introduce basic knowledge and different aspects of algebraic geometry. Participants are supposed to be undergraduate/graduate students without any preliminaries in algebraic geometry.

2026 NCTS Workshop on Spreading Dynamics in Discrete and Continuous Systems
https://ncts.ntu.edu.tw/events_2_detail.php?nid=557

June 29, 2026

Room 515, Cosmology Building, NTU

Organizers:
Jung-Chao Ban (National Chengchi University)
Feng-Bin Wang (Chang Gung University)

Aim & Scope

In response to the increasing need to better understand transmission dynamics after the pandemic, this workshop brings together domestic experts working on both continuous and discrete spread models. Through open discussions and academic exchange, we hope to build stronger connections among research groups and explore new collaborative directions, particularly in improving numerical methods and model accuracy. Our goal is to further strengthen interdisciplinary research on transmission dynamics and their applications in complex systems.

Invited Speakers

Khagendra Adhikari (Chang Gung University & Tribhuvan University)

Chang-Yuan Cheng (National Kaohsiung Normal University)

Jyy-I Hong (National Chengchi University)

Cheng-Yu Tsai (National Chengchi University)

Chu-Yang Tsou (National Chengchi University)

Feng-Bin Wang (Chang Gung University)

Chang-Hong Wu (National Yang Ming Chiao Tung University)



Agenda
https://drive.google.com/file/d/1s0WinTx9JtgxUEspoii7enTT505A-1U-/view?usp=sharing

Registration
https://forms.gle/1Daooy2ep7x47U937

Contact: Peggy Lee ([email protected])

Complex Systems Arising from Evolution Biology
https://ncts.ntu.edu.tw/events_3_detail.php?nid=399

10:00-11:00, June 18, 24, and 14:00-15:00, June 22, 2026
Room 509, Cosmology Building, NTU

Speaker(s):
Wei-Kuo Chen (University of Minnesota)

Organizer(s):
Wai Kit Lam (National Taiwan University)
Yuan-Chung Sheu (National Yang Ming Chiao Tung University)

1. Introduction & Purposes

The primary goal of this lecture series is to introduce several emerging topics in evolutionary biology. In particular, we will focus on the NK model, introduced by Kauffman, Levin, and Weinberger, which is a random fitness function defined on the genomes of certain species with N genetic loci, each interacting with K others. This model has broad applicability in the study of evolution and natural selection, as it captures the inherent ruggedness of fitness landscapes.

2. Outline & Descriptions

Throughout the series, we will highlight recent developments, outline the underlying mathematical approaches, and present open problems that are especially well suited for graduate students and junior researchers seeking to broaden their research directions.

3. Prerequisites

Participants are expected to be familiar with material from at least a first-semester graduate course in probability.

4. Registration

https://forms.gle/D9XjevbBKhbd71Fh8



Contact: Murphy Yu ([email protected])

Invariance Principle and Dynamics
https://ncts.ntu.edu.tw/events_3_detail.php?nid=398

10:30-11:45, 13:00-14:45, June 18, 2026
Room 505, Cosmology Building, NTU

Speaker(s):
Francois Ledrappier (University of Notre Dame)

Organizer(s):
Chih-Hung Chang (National University of Kaohsiung)

1. Introduction & Purposes

The primary goal of the lecture is to explore the ergodic theory behind various examples of the "Invariance Principle" in dynamical systems. In the study of dynamical systems, analyzing the asymptotic properties of successive iterations is an active field of research, frequently utilizing Lyapunov exponents to understand a system's stability under perturbations. While systems that uniformly lack vanishing Lyapunov exponents exhibit established forms of stability, this lecture specifically addresses the question of how to understand systems where vanishing Lyapunov exponents do occur for invariant probability measures.

It turns out that the presence of vanishing Lyapunov exponents often implies the non-trivial invariance of a specific mathematical object, a phenomenon nicknamed the action of an "Invariance Principle." A common mechanism across these varying examples involves introducing a type of entropy—typically an average of Liebner-Küllback information—that quantifies how a given measure is distorted by the system's dynamics. When the Lyapunov exponent vanishes, it forces this entropy to also vanish. Consequently, the vanishing entropy necessitates the desired invariance, which is mathematically demonstrated by applying the equality case in Jensen's inequality.

Historically, the Invariance Principle unifies several classical findings into a single phenomenon. It connects earlier foundational work, such as Furstenberg's criterion for random walks, discoveries regarding Schrödinger operators, and findings on independent products of diffeomorphisms, revealing them all to be manifestations of this exact same underlying principle. The complete nonlinear version of the principle, along with its catchy name and numerous applications, was primarily formalized by A. Avila and M. Viana.

2. Outline & Descriptions

(1) Introduction of the "Invariance Principle" (IP), explain how vanishing Lyapunov exponents in dynamical systems force a non-trivial invariance of specific mathematical objects.

(2) Review of foundational, classical results that led to the formalization of the IP. This includes Furstenberg’s criterion for random matrix products, one-dimensional Schrödinger operators, random homeomorphisms, and compact extensions of hyperbolic systems.

(3) Formalize the modern, non-linear IP established by Avila and Viana. It details the abstract mathematical setting, sketches the core theorem's proof utilizing entropy, and discusses related extensions like deformations and regularities.

(4) Explore direct, modern applications of the formal IP to hyperbolic systems utilizing invariant foliations and non-uniformly expanding random diffeomorphisms.

(5) Examine partially hyperbolic systems with invariant center laminations, specifically focusing on discretized Anosov flows and systems possessing quasi-isometric central leaves.

3. Prerequisites

Basic knowledge on measure theory and ergodic theory are strongly recommended.

4. Registration

https://forms.gle/j8XgbfGiZJ6QiEWw7





Contact: Murphy Yu ([email protected])

Derivation, Analysis and Applications of Water-Wave Models
https://ncts.ntu.edu.tw/events_3_detail.php?nid=400

10:30-12:00 and 13:30-15:00
on June 4, June 10 and June 12, 2026
Room 505, Cosmology Building, NTU

Speaker(s):
Jerry L. Bona (University of Illinois Chicago)
Hongqiu Chen (University of Memphis)

Organizer(s):
Chun-Hsiung Hsia (National Taiwan University)
Juan-Ming Yuan (Providence University)

1. Introduction & Purposes
This is a lecture series consisting of six 90-min talks to introduce the modelling of the water waves and the mathematical theory on water wave equations. In particular, the lectures will focus on the existence and application of conservation laws and existence and properties of solitary waves.

2. Outline & Descriptions
In this set of lectures, we will briefly indicate how water-wave models arise from more complete descriptions of wave motion. We then pass to some particular models such as the Koteweg-de Vries equation, Boussinesq systems and the like. We will study the mathematical properties of these waves, including existence and application of conservation laws and existence and properties of solitary waves. These studies of particular models suggest a range of questions that would arise in more general settings. These include questions of long-term stability which are tied to issues of global well-posedness. Some of these issues will occupy us for the remainder of the course.

3. Prerequisites
Undergraduate level PDE course

4. Registration
https://forms.gle/qh4TXAuBfinikTYy5

5. Join Online
Find the links in:
https://ncts.ntu.edu.tw/events_3_detail.php?nid=400

Contact: Murphy Yu < [email protected] >

ncts 1. Introduction & Purposes This is a lecture series consisting of six 90-min talks to introduce the modelling of the water waves and the mathematical theory on water wave equations. In particular, the lectures will focus on the existence and application of conservation laws and existence and propert...