This Conference is a Satellite Activity of the 9th European Congress of Mathematics (ECM). Registered participants in the ECM can enjoy a 20% discount in the registration fee (please choose the applicable option when completing your registration).

GATMAID EMS Summer School

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Advanced course / School
From June 25, 2024
to June 29, 2024
Registration deadline 02 / 06 / 2024
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    • Regular registration: 160 euros.*

    • Registration for ECM participants (20% discount): 128 euros.*

*Registration includes coffee breaks and social dinner. Lunch is NOT included.

The main aim of the Summer School is to show how very abstract parts of mathematics, like Geometry, Algebra and Topology (GAT) are nowadays providing new tools and insights in applied areas like Machine Learning, Big Data or Artificial Intelligence. At the same time these areas are posing new challenges to researchers in GAT, and they are even creating new tools that have the potential to change the way the research is traditionally done.

The central topic of the school is Topologically Data Analysis, its impact in other areas of research and its emerging applications in real life problems. The school is organized in three courses of 6/7 hours each: the first one introduces the basic framework, while the other two address specific topics in Algebra and in Geometry that are currently growing out of the impulse of TDA. Each course will have two parts, one presenting the mathematical background and another one showing its potential for applications. Participants will be given information in advance on the recommended background for the school and during the school there will be tutorial/discussion hours.

The scientific part of the school is complemented with:

– few research talks by senior speakers, to illustrate some specific aspects related with them

– a poster session, in which willing participants will be able to present their work

– an activity open to general public. Consisting on a talk on ethic aspects related to Artificial Intelligence, and a round table with title: From pure research to technological transfer: a new era for mathematics?

The courses will be suitable for early PhD students or even Master level students willing to learn on the topic and that may be looking for prospective PhD topics and advisors. It will be a truly international event as speakers and participants will be coming from across the globe (although mostly from Europe) and the summer school is a prelude to the Conference LIGAT.

Related Activities:



Thomas Brüstle

Thomas Brüstle

Université de Sherbrooke and Bishop’s University

Thomas Brüstle is a Full Professor at the Université de Sherbrooke and at Bishop’s University (Sherbrooke, Canada). He holds the Maurice Auslander Research Chair since 2003.

He is a reputed researcher in Representation Theory of Finite dimensional algebras area in which he has been working for more than 25 years. In the recent years his main research interests has been moving to the domain of the applications of algebra, specially of homological methods to Data Analysis (persistence theory) and to Quantum Computing. Currently, he is combining theoretical research work on the classification of persistence modules  with transfer of research  projects with Optina diagnosis, using Data Analysis in early illness detection, and with AlgoLab on Quantum Computing.

Frédéric Chazal

Frédéric Chazal


Frédéric Chazal is Directeur de Recherche of the INRIA, holder of an ANR Chair in Artificial Intelligence, and Director of the DATAIA Institute all them located at the University Paris-Saclay, and Head of the DataShape group located both in Saclay and in Sophia-Antipolis, France.

He is one of the world scientific leaders in developing new mathematical tools and software from the field of data science in order to analyze and use the topological structure of the data. He has authored over 60 publications on the subject, and two celebrated monographs for the SpringerBriefs in Mathematics and the Cambridge Texts in Applied Mathematics series. This theoretical strength is then applied to industrial projects that he leads though the DATAIA Institute.

Besides of being an excellent researcher, he is a reputed lecturer involved in the research oriented Master “Mathématiques, Vision, Apprentissage” where he frequently contributes with courses on Topological Data Analysis.

Ran Levi

Ran Levi

University of Aberdeen

Ran Levi has a strong background on Algebraic Topology and in the past 8 years he has been interested in applications of Topology and has been collaborating with the Blue Brain Project, at the EPFL, Lausanne., specifically with  Kathryn Hess (EPFL) and Henry Markram (Blue Brain Project, EPFL).

He has recently started a Research Group on Neuro-Topology at The School of Natural and Computing Sciences of the University of Aberdeen.

Emil Saucan

Emil Saucan

Braude College of Engineering

Emil Saucan is an associate professor at the Braude College of Engineering (Israel). He earned his PhD in Mathematics at the Technion – Israel Institute of Techonology in 2005, with his dissertation ‘The Existence of Quasimeromorphic Mappings’. While continuing to work on Geometric Function Theory, he started to explore its applications in  medical imaging and graphics, which has since led him to combine pure and applied research.

He is pioneer on the study of curvature of data. Together with J. Jost, A. Samal and M. Weber amongst other collaborators he introduced in 2016 the notion of Forman curvature in networks, where he has also studied discrete curvatures and discrete Ricci curvatures.

COURSE 1: Topological Data Analysis
Lecturers: Frédéric Chazal | Inria / Ran Levi | University of Aberdeen

Course Description:

Topological Data Analysis is a sound family of techniques that is gaining an increasing importance for the interactive analysis and visualization of data in imaging and machine learning applications. Given the increasing complexity and size of current collections of acquired or simulated data-sets (2D, 3D and nD), these approaches aim at helping users understand the complexity of their data by providing insights about its topological and geometric structure.

In low dimensions (typically 2 or 3), Topological Data Analysis enables users to rapidly extract, interact with, and classify geometric features defined by level sets or integral lines. Thanks to simplification mechanisms based on Persistent Homology, such algorithms additionally construct multi-scale topological representations of the data, that enable users to perform robust analyses and comparisons despite the presence of noise. The soundness, efficiency and robustness of this class of approaches made it increasingly popular in the last few years in a variety of 2D and 3D imaging analysis applications. In higher dimensions, these techniques have recently been adapted to form the basis of new clustering algorithms and data analysis tools.

The purpose of this course is to introduce the main concepts of the recent field of Topological Data Analysis and illustrate their use in imaging (scientific visualization) and machine learning applications, both from a mathematical and practical point of view.

Course Materials: TBP

COURSE 2: Algebraic structures in Topological Data Analysis: Persistent homology
Lecturers: Thomas Brüstle | Université de Sherbrooke and Bishop’s University

Course Description:

Topological data analysis (TDA) uses topology to identify relevant geometric features of data, such as clusters and loops. This is accomplished by first modelling the data by a family of topological spaces indexed over a poset, and then identifying the topological features that persist over several indices. The field of algebraic topology provides tools to TDA via the language of homology, and persistent homology is the branch of TDA that makes use of methods from representation theory in order to study these representations of posets, referred to as persistence modules.

In this course we will present the basic theory of pointwise finite persistence modules with coefficients in a field. This includes classification results for one-parameter persistence modules where the poset is totally ordered, as well as description of invariants of persistence modules in the multiparameter setting. We will also discuss some notions that are useful in the applications, such as the stability of an invariant, which, roughly speaking means that two persistence modules that come from similar data should have close values of their corresponding invariants.

We will also show how the theory of persistence modules helps in practice in the study of the shape of data.

Course Materials: TBP

COURSE 3: The Geometry of Data: Curvature and Beyond
Lecturers: Emil Saucan | Braude College of Engineering

Course Description:

The geometrization of data, after its timid first steps, has become a mainstream tool in Data Analysis. Among the geometric notions residing at the core of this approach, curvature naturally plays a prominent role. We therefore first explore the various notions of network curvatures, their mathematical motivations, relationships, relative advantages and disadvantages and their applications to network intelligence: classification, sampling and beyond. Extensive experiments and case studies will be included.

Another dominant mathematical tool applied in Data Analysis is that of Persistent Homology. Moreover, there is a connection between it and curvature. Indeed, it was observed experimentally that Persistent Homology of networks and hypernetworks schemes based on Forman’s discrete Morse Theory on the one hand, and on the 1-dimensional version of Forman’s Ricci curvature on the other, not only perform well, but they also produce practically identical results. We show that this apparently paradoxical fact can be easily explained in terms of Banchoff’s discrete Morse Theory. This allows us to prove that there exists a curvature-based, efficient Persistent Homology scheme for networks and hypernetworks. Moreover, we show that the proposed method can be broadened to include more general types of networks, by using Bloch’s extension of Banchoff’s work and even made more efficient by making appeal to quite recent results of Grunert, Kühnel and Rote.

We conclude with an exploration of the power in networks classification and understanding of other types of (geo-)metric invariants, introduced in the theoretical setting by Grove and Markvorsen. Their efficiency is illustrated by experiments with complex networks and images.

Course Materials: TBP

Open activities TO GENERAL PUBLIC
DATE: June 27th, 2024

LOCATION: Institut d’Estudis Catalans (IEC) 


Artificial Intelligence and Fair Algorithms (project with Hermes Foundation)



Mercedes Siles Molina

Universidad de Málaga

Mercedes Siles Molina is full Professor at the University of Malaga and a full member of the Malaga Academy of Sciences. Additionally, she is a member of the Advisory Board of the Hermes Institute, and of Anaya’s University Advisory Board. She has developed a strong research career working in non-commutative algebra. Beyond her academic roles, she has served as the Director-General of the National Agency for Quality Assessment and Accreditation (ANECA). Siles Molina is actively involved in knowledge transfer. She has curated exhibitions on the intersection of Art and Mathematics (El sabor de las Matemáticas and Universos Paralelos Dialogando), presented at prestigious institutions worldwide. In addition, she has promoted activities of mathematics in developing countries via a close collaboration with CIMPA. She has received several awards, including the “Farola Science Prize” in 2019 and the “Dosta con el Corazón Prize” in 2020 for her support of Romani women. Siles Molina has been recognized as one of the Top 100 Women Leaders in both 2019 and 2020.

*If you wish to attend the General Talk, which is a free activity, please confirm your attendance by filling out the following form:


From pure research to technological transfer: a new era for mathematics?


*Open to General Public

Poster Session
Participants have the option to contribute with a poster presentation if they wish to do so. The poster boards that are available at the CRM are DIN A0 format (1189×841 mm). Any poster size within these limits is fine. To apply, please select the relevant option during the registration process.
    • Deadline for poster submission: April 30th, 2024.
    • Resolutions will be sent on May 15th, 2024.
Registration and Accommodation Grants
In order to increase the number of young researchers participating in this activity, the CRM offers grants to cover the registration and lodging expenses.
To apply, you must complete the registration process; please go to SIGN IN, choose the General registration option at cost 160€ indicate in the OTHERS section that you wish to apply for a registration and/or accommodation grant; you will be asked to attach your CV. Please click on the Reservation option before finishing the process.


Application deadline for grants is April 30th, 2024.
Resolutions will be sent on May 15th, 2024.


IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.
*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to with your name and the institution internal reference number that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed.
Paying by credit card
IF YOU PAY VIA CREDIT CARD but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).
Name Institution
Pan Ye Li Centre de Recerca Matemàtica
Elena Isasi Theus Universitat Politècnica de Catalunya
Dolors Herbera Espinal Universitat Autònoma de Barcelona
Massimiliano Pellacchia IU International University of Applied Sciences
Ramon Antoine Riolobos Universitat Autònoma de Barcelona
Francesc Perera Domenech Universitat Autònoma de Barcelona
Lodging information




Laurent Cantier

Czech Academy of Sciences | Universitat Autònoma de Barcelona

Dolors Herbera Chair

Universitat Autònoma de Barcelona | CRM

Roberto Rubio

Universitat Autònoma de Barcelona

Simone Virili

Universitat Autònoma de Barcelona

Antonio Viruel

Universidad de Málaga


This activity is an initiative of the  research group LIGAT-Laboratori d’Interaccions entre Geometria, Àlgebra i Topologia (2021 SGR 01015). We also thank the funding of 

We are also grateful to Red Temática de Álgebra no Conmutativa (RED2022-134631-T) for its collaboration.


For inquiries about this event please send an email to


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