Andreas Ott

Research interests

My research is in geometry, topology and applications in the life sciences. I am currently working on the following topics:

• bounded cohomology and simplicial volume
• special functions (polylogarithms, hypergeometric functions)
• Higgs bundle moduli spaces, harmonic maps and representation varieties
• topological data analysis and computational topology
• topological genomics
• evolution of the coronavirus SARS-CoV-2

I am a member of the KIT Center MathSEE and the DFG Priority Program Geometry at Infinity.

Publications and preprints

• MuRiT: efficient computation of pathwise persistence barcodes in multi-filtered flag complexes via Vietoris-Rips transformations
  (with Maximilian Neumann, Michael Bleher, Lukas Hahn, Samuel Braun, Holger Obermaier, Mehmet Soysal, René Caspart)
  arXiv:2207.03394
• Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2
  (with Michael Bleher, Lukas Hahn, Juan Ángel Patiño-Galindo, Mathieu Carrière, Ulrich Bauer and Raúl Rabadán)
  medRxiv 2021.06.10.21258550
• Simplicial volume and polylogarithms (in preparation)
  (with Michelle Bucher and Andreas Potschka)
• Higgs bundles, harmonic maps, and pleated surfaces
  (with Jan Swoboda, Richard Wentworth and Michael Wolf)
  arXiv:2004.06071
• Bounded cohomology, Higgs bundles, and Milnor-Wood inequalities
  (with Tobias Hartnick)
  arXiv:1105.4323
• Transgression in bounded cohomology and a conjecture of Monod
  Journal of Topology and Analysis, Vol. 13, No. 04, 959-998, 2021.
• Perturbations of the Spence-Abel equation and deformations of the dilogarithm function
  (with Tobias Hartnick)
  Mathematische Annalen 368(3), 1399-1428, 2017.
• Bounded cohomology via partial differential equations, I
  (with Tobias Hartnick)
  Geometry & Topology 19-6, 3603-3643, 2015.
• Removal of singularities and Gromov compactness for symplectic vortices
  Journal of Symplectic Geometry, Vol. 12, No. 2, 1-55, 2014.
• Surjectivity of the comparison map in bounded cohomology for Hermitian Lie groups
  (with Tobias Hartnick)
  International Mathematics Research Notices, No. 9, 2068-2093, 2012.
• The non-local symplectic vortex equations and gauged Gromov-Witten invariants
• On Fano threefolds with b₂ ≥ 2

Activities

• CoVtRec Topological Data Analysis of the ongoing convergent evolution of the coronavirus SARS-CoV-2
• MathSEE Interdisciplinary Mathematical Research at KIT
• Bounded Cohomology Workshop
• STRUCTURES Interdisciplinary Mathematical Research at Heidelberg University
• Asymptotic Invariants and Limits of Groups and Spaces Research Training Group
• Structures & Mathematics Interdisciplinary Seminar Series
• Higgs Bundles in Geometry and Physics Workshop

Teaching

• Applications of Topological Data Analysis (KIT), Spring 2021
• Proseminar Perlen der linearen Algebra (KIT), Spring 2021
• Topological Data Analysis (KIT), Fall 2020
• Geometric Methods in Data Analysis, Spring 2019
• Heidelberg Geometry Seminar, 2018-19
• Seminar Geometry and Mathematical Physics, Fall 2017
• Einführung in die Geometrie, Spring 2016
• Heidelberg Junior Geometry Seminar, 2015-16
• Symplectic Topology (Part III, Cambridge Univ.), Lent 2014