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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.

About

This wiki is centered around the exploratory project (EP) Mathematics and Data within STRUCTURES and is meant to provide a platform for collaborative work 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

Upcoming Events

May 27 11h-13h SR C
Mapper - Fabian Klos
Stability - Peter Albers

Related 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

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