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Revision as of 20:28, 16 May 2019

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

Upcoming Events

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

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

Further Information

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

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-<div style="margin:0.4em; width:60%; text-align:center;">
+<div style="margin:0.4em; width:100%; text-align:center;">
 <div style="font-size:162%; padding:.1em;">WELCOME TO [[STRUCTURES| STRUCTURES | EP Mathematics and Data]]</div>
 <div style="font-size:95%;"> a collaboration at the intersection of mathematics and data analysis based at Heidelberg University.</div>
 </div>
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-<li style="position:absolute; left:33%; top:3.2em;">[[Portal:Science|Science]]</li>
-<li style="position:absolute; left:25%; top:0em;">[[Introductory reading|Introductory Literature]]</li>
-<li style="position:absolute; left:25%; top:1.6em;">[[List of Software]]</li>
-<li style="position:absolute; left:75%; top:0em;">[[Activities]]</li>
-<li style="position:absolute; left:75%; top:1.6em;"><strong>[[Main Page#Structure of this wiki|About]]</strong></li>
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-<!-- -->
 <!--        ABOUT        -->
-| id="MiddleBanner-left" class="MainPageBG" style="width:50%; border:1px solid #cef2e0; padding:0; background:#f5fffa; vertical-align:top; color:#000;" |
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-About</h2>
-<!-- -->
 <div style="padding:0.1em 0.6em;">
-This wiki is centered around the [[STRUCTURES#Organization|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.
+This wiki is centered around the [[STRUCTURES#Organization|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.
 </div>
-<div style="padding:0.1em 0.6em;">
+{| role="presentation" id="MiddleBanner" style="width: 100%; margin-top:4px; margin-bottom:4px; border-spacing: 0.6em;"
+| id="MiddleBanner-left" style="width:55%; padding:0; vertical-align:top; color:#000;" |
+<!--        LINKS        -->
+<div id="mp:IntroductoryLinks">
 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]]
@@ Line 44: / Line 21: @@
 * [[Case Studies]]
 </div>
-<!-- -->
+<!--        EVENTS        -->
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-<!-- -->
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-<!--        ACTIVITIES        -->
-<!-- -->
-| id="mp-right" class="MainPageBG" style="width:50%; border:1px solid #cedff2; padding:0; background:#f5faff; vertical-align:top;"|
-<!-- -->
-<h2 id="mp-itn-h2" style="margin:0.5em; background:#cedff2; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; color:#000; padding:0.2em 0.4em;">
 Upcoming Events</h2>
-<!-- -->
+<div id="mp-itn" style="padding:0.1em 0.6em; text-align:center;">
-<div id="mp-itn" style="padding:0.1em 0.6em;">
 May 27 11h-13h SR C <br>
 Mapper - Fabian Klos <br>
 Stability - Peter Albers
 </div>
-<!-- -->
+| id="MiddleBanner-border" |
+|}
+</div>
+<!--        ACTIVITIES  BANNER        -->
+{| role="presentation" id="MiddleBanner" style="width: 100%; margin-top:4px; border-spacing: 0px;"
+| id="MiddleBanner-left" class="MainPageBG" style="width:50%; border:1px solid #cef2e0; padding:0; background:#f5fffa; vertical-align:top; color:#000;" |
+<!--        ACTIVITIES        -->
 <h2 id="mp-itn-h2" style="margin:0.5em; background:#cedff2; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; color:#000; padding:0.2em 0.4em;">
-Related Activities</h2>
+Current and Upcoming Activities</h2>
 <div style="padding:0.1em 1em;"> {{main|Activities}} </div>
 <div style="padding:0.1em 0.6em;">
@@ Line 68: / Line 48: @@
 Tue 16:15 - 17:45, Mathematikon SR C
-'''Block Seminar''' - ''[https://www.mathi.uni-heidelberg.de/~swoboda/teaching/SS19/Seminarankuendigung.pdf High-dimensional geometry and probability with view towards applications in data science] -'' June 28 & July 5 (all day) - Mathematikon SR 4
+'''Block Seminar''' <br>
+''[https://www.mathi.uni-heidelberg.de/~swoboda/teaching/SS19/Seminarankuendigung.pdf High-dimensional geometry and probability with view towards applications in data science] '' <br>
+June 28 & July 5 (all day),  Mathematikon SR 4
-'''Block Seminar''' - ''[https://nps.math.uni-heidelberg.de/TDA_SS19/ Topological Data Analysis and Persistent Homology] -'' TBA
+'''Block Seminar''' <br>
+''[https://nps.math.uni-heidelberg.de/TDA_SS19/ Topological Data Analysis and Persistent Homology]'' <br>
+TBA
-'''Workshop''' - ''[https://sites.google.com/view/geometry-topology-computation Geometry, Topology, and Computation] -'' June 12-14 - Heidelberg, Mathematikon
+'''Workshop''' <br>
+''[https://sites.google.com/view/geometry-topology-computation Geometry, Topology, and Computation]'' <br>
+June 12-14 - Heidelberg, Mathematikon
-'''Summer School''' - ''[https://sites.google.com/view/persistenthomologyandbarcodes/ Persistent Homology and Barcodes] -'' August 5-9 - JLU Gießen, Schloß Rauischholzhausen
+'''Summer School'''<br>
+''[https://sites.google.com/view/persistenthomologyandbarcodes/ Persistent Homology and Barcodes]'' <br>
+August 5-9 - JLU Gießen, Schloß Rauischholzhausen
 </div>
 <!-- -->
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 <div id="mp-tfa" style="padding:0.1em 0.6em;">
 <!--        PURPOSE           -->
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+<h2 id="mp-itn-h2" style="margin:0.5em; background:#cedff2; font-family:inherit; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; color:#000; padding:0.2em 0.4em;">
+Further Information</h2>
+<h3 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
 Purpose
-</h2>
+</h3>
 <div style="padding:0.1em 0.6em;">
 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:
@@ Line 94: / Line 84: @@
 </div>
 <!--        DISCLAIMER        -->
-<h2 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
+<h3 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
-Disclaimer</h2>
+Disclaimer</h3>
 <div style="padding:0.1em 0.6em;">
 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.
@@ Line 102: / Line 92: @@
 </div>
 <!--        CONTRIBUTING       -->
-<h2 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
+<h3 style="margin:0.5em; font-family:inherit; font-size:110%; font-weight:bold; padding:0.2em 0.4em;">
-Contributing to this wiki</h2>
+Contributing to this wiki</h3>
 <div style="padding:0.1em 0.6em;">
 Everyone is invited to contribute to this wiki. If you are interested, get in touch with us via mail: