Master Seminar: Topological Methods in Biophysics
Venue: Philosophenweg 12, Seminar Room
Time: Tuesdays, 14:15  15:45
PLEASE NOTE: Due to obligations, the first meeting will be April 17th 2018!
Topology enters more and more the field of physics and biology. Whereas geometric methods have had a dominating presence in the past, due to new measurement methods that yield topological information and the emergence of big data topological ideas, methods and algorithms from topology are gaining fast track. The seminar explores some these new developments.
This seminar touches upon some of the topics that are currently being actively worked on. Most of these can be expanded to at least two talks. Interested students should ge in contact with me via email.
Objectives:
 Familiarity with basics in topology for physics and biology
Prerequisites:
 Willingness to engage with mathematical concepts, openness to biology
Topics:
 Some basics
 Topological spaces, metric space topology
Simplices, simplicial complexes,
Chech complexes, VietorisRips complexes,homology
Computational topology, Herbert Edelsbrunner and John L. Harer
 Topological spaces, metric space topology
Simplices, simplicial complexes,
Chech complexes, VietorisRips complexes,homology
 Persistent homology
 Persistent homology: theory and practice. 2014
Edelsbrunner H.
http://pub.ist.ac.at/~edels/Papers/2012P11PHTheoryPractice.pdf
 Persistent homology: theory and practice. 2014
 Persistent homology: algorithms
 Persistent Homology — a Survey
Herbert Edelsbrunner and John Harer
http://www.maths.ed.ac.uk/~aar/papers/edelhare.pdf
Computing Persistent Homology
Afra Zomorodian and Gunnar Carlsson
https://geometry.stanford.edu/papers/zccph05/zccph05.pdf
 Persistent Homology — a Survey
 Topological data analysis

An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
Frédéric Chazal and Bertrand Michel
https://arxiv.org/pdf/1710.04019.pdf
Topological data analysis: A promising big data exploration tool in biology, analytical
chemistry and physical chemistry
Marc Offroy, Ludovic Duponchel
Analytica Chimica Acta 910 (2016) 1e11

An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
 Topological data analysis: algorithms

Illustrations of Data Analysis Using the Mapper Algorithm and Persistent Homology
Rami Kraft
http://www.divaportal.org/smash/get/diva2:900997/FULLTEXT01.pdf

Illustrations of Data Analysis Using the Mapper Algorithm and Persistent Homology
 Topological Data Analysis of Biological Aggregation Models

Chad M. Topaz and Lori Ziegelmeier, Tom Halverson
https://doi.org/10.1371/journal.pone.0126383

Chad M. Topaz and Lori Ziegelmeier, Tom Halverson
 Topology and prediction of RNA pseudoknots

Christian M. Reidys, Fenix W.D. Huang, Jørgen E. Andersen, Robert C. Penner,
Peter F. Stadler, and Markus E. Nebel
Bioinformatics 2011

Christian M. Reidys, Fenix W.D. Huang, Jørgen E. Andersen, Robert C. Penner,
Peter F. Stadler, and Markus E. Nebel
 Applications of topology to DNA

Isabel K. Darcy and De Witt Sumners
KNOT THEORY, BANACH CENTER PUBLICATIONS, VOLUME 42 INSTITUTE OF MATHEMATICS
POLISH ACADEMY OF SCIENCES WARSZAWA 1998

Isabel K. Darcy and De Witt Sumners