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Bounding convection heat flux in planets and stars by Thierry Alboussiere - IP4RG
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October 24, 2024
Γ-convergence: a 50 years long story
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From November 05, 2024 to December 05, 2024
10th Computational and Systems Neuroscience Retreat
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Threshold phenomena in random structures
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From December 09, 2024 to December 20, 2024
4th Nonlinear Processes in Oceanic and Atmospheric Flows
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CIMPA-ICTP hibrid course by Hero Saremi
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IRP on Modern Trends in Fourier Analysis
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Advanced Courses on Modern aspects of Fourier analysis
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Conference on Modern trends in Fourier analysis
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CIMPA-ICTP hibrid course by Youssef Azouzi
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CRM News Institutional

Criteris de priorització FI per a l’any 2025

09/10/2024
CRM News

El CRM participa un any més a la Nit de la Recerca

30/09/2024
CRM News

Terence Tao Visits Barcelona

27/09/2024
CRM News

12 New Researchers Join the CRM as Affiliated Members

15/09/2024
CRM News

Carme Cascante, New Director of the Centre de Recerca Matemàtica

10/09/2024
CRM News People

18 anys de la Mari Paz Valero al CRM al costat de la Fundació Aura

02/08/2024
CRM News KTT

CRM Researchers Are Developing a New Efficient Data Compression Method

01/08/2024
CRM News

Annual Meeting of CRM’s SAB: A Conversation with Chair Robert MacKay

30/07/2024
CRM News KTT

CRM at the 9th European Congress of Mathematics

24/07/2024
CRM News Outreach

Ten International High School Students Engage in Advanced Mathematics at CRM

17/07/2024
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Collaboration Agreement between CRM-Montréal and CRM-Barcelona

17/07/2024
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4th BMS-BGSMath Junior Meeting 2024: Fostering Connections Between Young Researchers

05/07/2024
CRM News Institutional María de Maeztu

Los Sesgos Inconscientes: Reflexiones de la catedrática Capitolina Díaz

20/06/2024
CRM News Interviews Outreach

“Mates i a xalar” a la ràdio: xerrades de matemàtiques divulgatives a les Terres de l’Ebre

18/06/2024
CRM News María de Maeztu

Hypatia 2024

12/06/2024
CRM News Outreach

El CRM participa un any més a la Festa de la Ciència

11/06/2024
CRM News Institutional

The CRM’s 2023 Annual Report Highlights Growth and Collaboration

05/06/2024
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New Scientific Research Sheds Light on Ecological Dynamics and Late Warning Signals in Conservation Efforts

23/05/2024
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The CRM participates in the MSCA-COFUND TOUCH Project

23/05/2024
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Eva Miranda, Inclosa a la Iniciativa #científicasCASIO

13/05/2024
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Open Calls 

JOB BOARD
PhD Fellowship (PREP 2023): Neural network mechanisms underlying perceptual decision making and working memory

REF. 2024-018-P05005

Deadline for submission of applications: 20th October 2024

PhD Fellowship (PREP 2023): Fourier Analysis and Approximation Theory

REF. 2024-019-P05006

Application Deadline: 15 Oct 2024

PhD Fellowship (PREP 2023): Mitigating environmental contamination via mathematics

REF. 2024-017-P05007

Application Deadline: 15 Oct 2024

María de Maeztu Scientific Communication

REF. 2024-016-P04500

La convocatòria romandrà oberta fins que es trobi a la persona adequada per la posició.

VISITORS & INTERNSHIPS
International Programme for Research in Groups (IP4RG) - stay in 2026
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selected videos

Centre de Recerca Matemàtica

Centre de Recerca Matemàtica
Join Pierre Berger as he guides you through the captivating world of wild dynamics, using stunning images from experiments and simulations to showcase fascinating phenomena. As Director of Research at CNRS-Sorbonne Université, Berger specializes in understanding the complex trajectories of dynamical systems. This talk, co-organized with the Societat Catalana de Matemàtiques, was held at the Institut d’Estudis Catalans on September 18, 2024, and explores the artistic and scientific intersections of light and dynamics. Speaker: Pierre Berger, CNRS, Sorbonne Université. https://www.crm.cat/fluid-dynamics-geometry-and-computer-science-in-interaction-exploration-of-new-horizons/
"Wild Dynamics of Light" by Pierre Berger
Abstract: For centuries, mathematicians have utilized computers for calculations and conjectures. However, with the advent of interactive theorem provers, machine learning, and generative AI, machines are beginning to play a more creative role in mathematical discovery. In this talk, Terence Tao surveys historical and recent advancements in machine-assisted proofs and speculates on their future roles in mathematics. Recorded on September 18, 2024, at the Institut d'Estudis Catalans. Speaker: Terence Tao, University of California, Los Angeles. More information: https://www.crm.cat/crm-colloquium-by-terence-tao/
CRM Colloquium by Terence Tao: "Machine Assisted Proofs"
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.
The Geometry of Data: Curvature and Beyond | 5/5
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: Preliminary Readings: + Steve Oudot: Persistence Theory: From Quiver representations to Data Analysis, https://geometrica.saclay.inria.fr/te... - Chapter 1 + Magnus Bakke Botnan and Michael Lesnick: An Introduction to Multiparameter Persistence - https://arxiv.org/pdf/2203.14289
Algebraic structures in Topological Data Analysis: Persistent homology | 5/5
SPECIAL LECTURE: Differential calculus for modules over posets Lecturer: Ran Levi | University of Aberdeen Abstract: The motivation for this project arises from topological data analysis. The concept of a persistence module was introduced in the context of topological data analysis. In its general form one defines persistence modules as functors from an arbitrary poset (or more generally an arbitrary small category) to some abelian target category. In other words, a persistence module is simply a representation of the source category in the target abelian category. As such much research was dedicated to studying persistence modules in this context. Unsurprisingly, it turns out that when the source category is more general than a linear order, then its representation type is generally wild. In particular, keeping in mind that persistence module theory is supposed to be applicable, computability of general persistence modules is very limited. In this talk I will describe a new set of ideas for local analysis of modules over poset algebras by methods borrowed from spectral graph theory and multivariable calculus.
Differential calculus for modules over posets
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.
The Geometry of Data: Curvature and Beyond | 4/5

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