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WELCOME TO STRUCTURES | EP Mathematics and Data

a collaboration at the intersection of mathematics and data analysis based at Heidelberg University.

This wiki is centered around the exploratory project (EP) Mathematics and Data within STRUCTURES and is meant to provide a platform for information on data analysis across the fields of pure mathematics and natural sciences.

If you want to find out more about these topics you can follow one of the links below

• What is Topological Data Analysis? - A Primer
• Mathematical Background
• Introductory Reading
• List of Software and respective tutorials
• Case Studies

Events

Seminar

Heidelberg TDA Seminar (Summer 2023)
Thu 11-13h, Mathematikon 00.200
Lukas Hahn, Daniel Spitz

Current and Upcoming Activities

Main article: Activities

Lecture
Geometric Methods in Data Analysis
Tue 16:15 - 17:45, Mathematikon SR C

Block Seminar
High-dimensional geometry and probability with view towards applications in data science
June 28 & July 5 (all day), Mathematikon SR 4

Block Seminar
Topological Data Analysis and Persistent Homology
TBA

Workshop
Geometry, Topology, and Computation
June 12-14 - Heidelberg, Mathematikon

Summer School
Persistent Homology and Barcodes
August 5-9 - JLU Gießen, Schloß Rauischholzhausen

About

Purpose

The purpose of this wiki is to provide a public platform where people can learn about recent approaches to data analysis via topological and geometrical techniques. To achieve this we follow two complementary approaches:

• The foundations of topology and geometry are well known to most mathematicians, but less so to researchers in the natural sciences, who we believe might benefit greatly from incorporating related techniques into their toolbox. To remedy this we collect the most important elements of the underlying theory and provide introductory articles to the relevant subjects.
• Analysing and handling real-life data is an art well-developed in the natural sciences, but may at times seem enigmatic to mathematicians, who usually are not exposed to large sets of data on a daily basis. It is apparent that an implementation of the theoretical ideas on computers is paramount for applications, so we provide a list of existing software and offer a number of short tutorials. We furthermore present case studies of real-life applications.

We hope that in establishing this wiki from these two perspectives, researchers from both mathematics and natural sciences are provided with the relevant background to easily approach each other, laying ground for fruitful collaborations.

Disclaimer

One goal of this wiki is to help make information widely available and usefully related to other information. In this users and contributors are expected to follow traditional academic practice. Whenever useful, references for further reading are given, providing additional information to the reader.

Nonetheless, this wiki is meant neither to be complete nor original.

Contributing to this wiki

Everyone is invited to contribute to this wiki. If you are interested, get in touch with us via mail:

structures-hiwi@mathi.uni-heidelberg.de