Format of the event:

This one-week long collaborative workshop (7-11 July 2025) will give the opportunity to 5 groups of participants to work under the supervision of leader on a research project.

Event Schedule

Monday, July 7th, 2025

09:00-09:05	Opening from MC
09:05-09:10	Speech from chief of committee MID
09:10-09:15	Speech from Christophe Ritzenthaler
09:15-09:20	Speech from Dean FMIPA and opening
09:20-09:40	Pleno speaker 1 + QNA
09:40-10:00	Pleno speaker 2 + QNA
10:00-10:30	Coffee break
10:30-10:50	Pleno speaker 3 + QNA
10:50-11:10	Pleno speaker 4 + QNA
11:10-11:30	Closing from MC and information
11:30-13:00	Lunch break
13:00-15:00	Class Session
15:00-15:30	Coffee break
15:30-17:00	Class Session
18:30-21:00	Dinner

Tuesday, July 8th, 2025

08:30-10:00	Workshop Session
10:00-10:30	Coffee Break
10:30-12:00	Workshop Session
12:00-13:00	Lunch Break
13:00-15:00	Workshop Session
15:00-15:30	Coffee Break
15:30-17:00	Workshop Session
18:30-21:00	Gala Dinner

Wednesday, July 9th, 2025

08:30-10:30	Workshop Session
10:30-11:00	Coffee Break
11:00-12:00	Roundtable Discussion
12:00+	Lunch and Free Time(Open for networking or individual consultation)

Thursday, July 10th, 2025

08:30-10:00	Workshop Session
10:00-10:30	Coffee Break
10:30-12:00	Workshop Session
12:00-13:00	Lunch Break
13:00-15:00	Workshop Session
15:00-15:30	Coffee Break
15:30-17:00	Workshop Session

Friday, July 11th, 2025

08:30-10:10	Group PresentationsEach group: 15 minutes presentation + 10 minutes Q&A
10:10+	Closing Session
13:30-14:00	Campus Tour
14:30-15:30	Going to Saung Udjo
15:30-17:30	Saung Udjo Performance
18:30-20:00	Dinner

Some precisions:

1. Monday 7 (morning): common presentation (colloquium style) of the projects by the group leaders
2. During the week: alternance of supervised slots where the leader can give short lectures on specific tools for the project and time for personal/group work.
3. A round table on the publication system for all participants will take place on Wednesday morning.
4. Friday 11 (morning): presentation by the groups of their results
5. Saturday: time to go back home

What will participants get out of it?

1. an in-depth knowledge of the concepts, notions and perceptions of a research topic
2. experience with several of the most commonly used research methods and skills for conducting research in the area of a research topic
3. working in groups on research level questions
4. ability to report research findings in writing and orally at an academic level
5. start a research network

Organization committee:

1. Intan Muchtadi (Institut Teknologi Bandung, Indonesia)
2. Ikha Magdalena (Institut Teknologi Bandung, Indonesia)
3. Christophe Ritzenthaler (Université de Rennes 1 and Université Côte d'Azur, France)

Group leaders

1. Renier Mendoza (University of the Philipinnes Diliman): Numerical Analysis, Artificial Intelligence, Computational Mathematics
2. Intan Muchtadi (Institut Teknologi Bandung, Indonesia): Algebra, Topology, Computational Mathematics
3. Nuning Nuraini (Institut Teknologi Bandung, Indonesia): Biomath, Mathematical Epidemiology
4. Christophe Ritzenthaler (Université de Rennes 1 and Université Côte d'Azur, France): Algebraic Geometry, Arithmetic
5. Thi Hoai An Ta (Institute of Mathematics, Vietnam Academy of Science and Technology): Analysis, Arithmetic (canceled)

Group leader: Renier Mendoza

Title: Solving Shallow Water Equations using Not-So-Shallow Neural Networks: Modeling Tsunami Wave Propagation using Machine Learning

Topic: Numerical Analysis, Artificial Intelligence, Computational Mathematics

Abstract: This project aims to develop an efficient deep learning-based approach for modeling tsunami wave propagation governed by the Nonlinear Shallow Water Equations (SWEs). First, we numerically solve the SWEs using a finite difference method (FDM), ensuring stability and accuracy. We then generate a dataset by computing FDM solutions across a wide range of initial conditions and model parameters. These solutions serve as training data for a neural network model, where the inputs are the SWE parameters and the outputs are the wave heights at specified wave gauges.

A key objective of this study is to assess whether the trained neural network can provide computationally faster predictions of coastal tsunami wave heights compared to traditional FDM solvers while maintaining accuracy. Furthermore, we explore the use of physics-informed neural networks (PINNs) to integrate physical constraints into the learning process, potentially reducing the amount of training data required. As an additional application, we investigate the feasibility of solving an inverse problem, where unknown model parameters are inferred from observed wave data.

This research is significant as it seeks to overcome the computational limitations of conventional numerical solvers, making large-scale tsunami simulations more efficient. The proposed methodologies offer a promising direction for real-time forecasting, rapid hazard assessment, and coastal engineering applications.

Prerequisites: Students should have a strong background in numerical analysis and scientific computing. They must be proficient in at least one programming language, preferably Python or MATLAB, and have a working knowledge of differential equations. Familiarity with machine learning concepts is beneficial but not required.

References:

1. Magdalena, I., La’lang, R., & Mendoza, R. (2021). Quantification of wave attenuation in mangroves in manila bay using nonlinear shallow water equations. Results in Applied Mathematics , 12, 100191.
2. Magdalena, I., La’lang, R., Mendoza, R., & Lope, J. E. (2021). Optimal placement of tsunami sensors with depth constraint. PeerJ Computer Science , 7, e685.
3. Ferrolino, A., Mendoza, R., Magdalena, I., & Lope, J. E. (2020). Application of particle swarm optimization in optimal placement of tsunami sensors. PeerJ Computer Science , 6, e333.
4. Juan, N. P., & Valdecantos, V. N. (2022). Review of the application of Artificial Neural Networks in ocean engineering. Ocean Engineering , 259, 111947.
5. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378, 686-707.

Group leader: Intan Muchtadi

Title: Multipersistent Relative Homology: Theory, Computation, and Applications in Data Analysis

Topic: Algebra, Topology, Computational Mathematics

Abstract: Multiparameter persistent homology improves traditional persistent homology by using multiple factors to analyze data, helping us understand complex structures in more detail. Relative persistent homology, on the other hand, studies how one space relates to a smaller part of it, making it useful for focusing on specific regions of data. However, combining these two methods into one approach, called Multipersistent Relative Homology, is still a developing area of research. This project reviews existing studies on these topics, looking at their theories, how they are calculated, and their real-world uses. The goal is to create new ways to compute multipersistent relative homology, study its mathematical properties, and apply it to complex data.

Prerequisites: A foundational understanding of algebraic topology, particularly homology theory; Knowledge of persistent homology and filtrations in topological data analysis; Some familiarity with multiparameter persistence and its computational challenges; Basic experience with topological data analysis tools.

References:

1. Edelsbrunner, H., & Harer, J. (2010). Computational Topology: An Introduction. American Mathematical Society.
2. Carlsson, G. (2009). "Topology and Data." Bulletin of the American Mathematical Society, 46(2), 255-308.
3. Chazal, F., Michel, B. (2021). An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists. Cambridge University Press.
4. Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017). "A roadmap for the computation of persistent homology." EPJ Data Science, 6(17).

Group leader: Nuning Nuraini

Title: Integrating Mathematical Models for Infectious Disease and Healthcare – A Case Study on Tuberculosis

Topic: Biomath – Mathematical Epidemiology

Abstract: Tuberculosis (TB) remains a significant public health concern in West Java, Indonesia, contributing to a high burden of cases nationwide. Effective strategies for managing TB require a data-driven approach that integrates disease dynamics with healthcare resource optimization. The aim of this research is to develop a hybrid mathematical modeling framework to improve TB case prediction, optimize diagnostic resources, and design effective vaccination strategies in West Java. This study proposes to incorporate a compartmental model to explore the temporal progression of TB cases, predict future trends, and assess the long-term impact of various intervention strategies. This model will capture key aspects of TB transmission, including latent infections, active cases, and recovery, providing insights into the effectiveness of diagnostic and treatment improvements over time. Additionally, the research will employ classification and statistical models to evaluate the utility of Xpert machines for TB diagnosis. The classification model will consider the percentage of operated modules and machine utilization, while the statistical model will analyze population and Xpert machine data. Bayesian methods will be used to estimate positivity and testing rates, addressing potential biases in the data. By clustering regions based on these models, we will develop targeted strategies to optimize diagnostic resource allocation. To further enhance TB control measures, this study will develop a vaccination strategy by incorporating immunization dynamics into the compartmental model. Different vaccination scenarios—including coverage levels, booster doses, and prioritization of high-risk populations—will be evaluated to propose optimal immunization policies. The findings of this research will provide a comprehensive decision-support tool for policymakers, offering evidence-based recommendations on Xpert machine distribution, high-priority regions for intervention, and optimal vaccination policies. Ultimately, this study seeks to bridge mathematical modeling and healthcare planning to enhance TB control efforts and improve public health strategies in West Java.

Prerequisites: differential equation, numerical method, statistical method, optimization

References:

1. Ilham Saiful Fauzi, Nuning Nuraini, Regina Wahyudyah Sonata Ayu, Imaniah Bazlina Wardani, Siti Duratun Nasiqiati Rosady, Seasonal pattern of dengue infection in Singapore: A mechanism-based modeling and prediction, Ecological Modelling (501), 111003, (2025). https://doi.org/10.1016/j.ecolmodel.2024.111003.
2. Seprianus, Nuning Nuraini  & Suhadi Wido Saputro, A Simple Modelling of Microscopic Epidemic Process with Two Vaccine Doses on a Synthesized Human Interaction Network, COMMUN. BIOMATH. SCI., VOL. 7, NO. 1, 2024, PP. 106-123. https://doi.org/10.5614/cbms.2024.7.1.6
3. Yuki Novia Nasution, Marli Yehezkiel Sitorus, Kamal Sukandar, Nuning Nuraini, Mochamad Apri & Ngabila Salama, The epidemic forest reveals the spatial pattern of the spread of acute respiratory infections in Jakarta, Indonesia, Scientific Reports, volume 14, Article number: 7619 (2024). https://www.nature.com/articles/s41598-024-58390-3#Sec6.
4. Seprianus, Nuning Nuraini  & Suhadi Wido Saputro, A computational model of epidemic process with three variants on a synthesized human interaction network, Scientific Reports, volume 14, Article number: 7470 (2024). https://www.nature.com/articles/s41598-024-58162-z.
5. Ilham Saiful Fauzi, Nuning Nuraini, Ade Maya Sari, Imaniah Bazlina Wardani, Delsi Taurustiati, Purnama Magdalena Simanullang, Bony Wiem Lestari, Assessing the impact of booster vaccination on diphtheria transmission: Mathematical modeling and risk zone mapping, Infectious Disease Modelling Vol.9, pp. 245-262 (2024), https://doi.org/10.1016/j.idm.2024.01.004.

Group leader: Christophe Ritzenthaler

Title: Arithmetic Statistics for families of genus 4 curves

Topic: algebraic geometry / arithmetic

Abstract: Motivated by applications to cryptography or error-correcting codes, there has been a huge amount of work on the number of rational points on curves over finite fields for the last 40 years. More recently, instead of looking at maximal values only, the community considered statistical distributions: what is the proportion of curves (of a given genus) with a given number of points over a fixed finite field F_p? This new area is now called Arithmetic Statistics. If the general shape of the distribution, when p is large, is predictable (this is the so-called Katz-Sarnak theory), many mysteries remain when trying to understand the refined structure. The present project is mainly exploratory: we will use computer algebra to make numerical experiments for families of genus 4 curves, something that has never be done before. Will we observe new phenomena in comparison with genus 1,2 or 3? On the way, we will learn how to deal with algebraic varieties and arithmetic in an effective way, keeping track of the costs of the operations we want to perform. If we have time, it will be interesting to observe if the conjecture of [BLV] (see the reference) still looks valid.

Prerequisites:

1. Finite fields, basic of Galois theory
2. A bit of knowledge in algebraic geometry will help to understand the background but is not necessary for the computer part
3. Basic knowledge in programming and some familiarities with Sagemath or Magma
4. Basic knowledge in probability theory (notion of weak convergence,…)

References:

1. The general background for curves over finite fields can be watched here and read on the slides attached to the videos.
2. The work proposed is closely related to the articles [BJGR] and [BLV] where experiments were made in genus 2 and 3.

Group leader: Thi Hoai An Ta

Title: Complex and non-Archimedean hyperbolicity with connections to Diophantine Approximation

Topic: Analysis/Arithmetic

Abstract: Diophantine approximation uses geometric techniques to study Diophantine equations. At its core are the fundamental finiteness theorems: Siegel's theorem on integral points on affine curves, Faltings' theorem on rational points on curves, and the Mordell-Weil theorem on the finite generation of rational points on abelian varieties. These theorems have been studied, generalized, and proven by many different authors using various techniques. Osgood, Lang, and Vojta constructed a precise ``dictionary'' between statements and objects in Diophantine approximation and those in Nevanlinna theory, the quantitative theory that grew out of Picard classical result on values omitted by holomorphic functions. For instance, under this correspondence, Roth theorem corresponds to Nevanlinna Second Main Theorem, and Schmidt Subspace Theorem corresponds to Cartan Second Main Theorem. Qualitatively, infinite sets of integral points on a variety X correspond to holomorphic maps f : C -> X. This correspondence has been influential and lucrative for both subjects, often allowing advances in one subject to spur similar advances in the other. One recent line of results involves generalizing Schmidt Subspace Theorem (and analogously, Cartan Second Main Theorem) in various directions. Schmidt Subspace Theorem is one of the central results in Diophantine approximation, and has found numerous and surprising important applications in recent years.

We aim to explore the following topics:

• Investigate new applications of Diophantine Approximation to complex hyperbolicity and function field arithmetic, inspired by recent results [GRTW23]
• Using Levin's [L2015] method to reduce the number of components in the complement so that the Non-Archimedean hyperbolic conjecture holds

Prerequisites: A bit of knowledge in algebraic geometry, analysis (complex and p-adic).

References:

1. [L2009] A. Levin, Generalization of Siegel’s and Picard’s theorems, Annals of Mathematics (2), 170(2009), 609-655.
2. [Ru2009] Min Ru, Holomorphic curves into intersecting hypersurfaces, Annals of Mathematics, 169(2009), 255-267.
3. [29] P. Vojta, Diophantine Approximation and Nevanlinna Theory, CIME notes, 231 pages, 2007.
4. [L2015] A. Levin, On the p-Adic Second Main Theorem, Proc. Amer. Math. Soc. 143 (2015), 633–640.
5. [GRTW23] Carlo Gasbarri, Erwan Rousseau, Amos Turchet, vÃă Julie Tzu-Yueh Wang, Simply connectedness and hyperbolicity, arXiv:2308.13240 [math.AG], 2023