Andreas Ott

Research

Geometry, topology and applications in data & life sciences

• topological data analysis and computational topology
• geometric and topological methods in omics data analysis
• bounded cohomology and simplicial volume
• Higgs bundle moduli spaces, harmonic maps and representation varieties
• geometry of special functions (polylogarithms, hypergeometric functions)

I am a member of the Helmholtz Information & Data Science School for Health HIDSS4Health and the DFG Priority Program Geometry at Infinity.

Publications

• Higgs bundles, harmonic maps, and pleated surfaces
  Andreas Ott, Jan Swoboda, Richard Wentworth, Michael Wolf
  Geometry & Topology 28:7, 3135-3220, 2024
• MuRiT: efficient computation of pathwise persistence barcodes in multi-filtered flag complexes via Vietoris-Rips transformations
  Maximilian Neumann, Michael Bleher, Lukas Hahn, Samuel Braun, Holger Obermaier, Mehmet Soysal, René Caspart, Andreas Ott
  arXiv:2207.03394
• Topological data analysis identifies emerging adaptive mutations in SARS‑CoV‑2
  Michael Bleher, Lukas Hahn, Maximilian Neumann, Juan Ángel Patiño-Galindo, Mathieu Carrière, Ulrich Bauer,
  Raúl Rabadán, Andreas Ott
  medRxiv 2021.06.10.21258550
• Bounded cohomology, Higgs bundles, and Milnor-Wood inequalities
  Tobias Hartnick, Andreas Ott
  arXiv:1105.4323
• Transgression in bounded cohomology and a conjecture of Monod
  Andreas Ott
  Journal of Topology and Analysis, Vol. 13, No. 04, 959-998, 2021
• Perturbations of the Spence-Abel equation and deformations of the dilogarithm function
  Tobias Hartnick, Andreas Ott
  Mathematische Annalen 368(3), 1399-1428, 2017
• Bounded cohomology via partial differential equations, I
  Tobias Hartnick, Andreas Ott
  Geometry & Topology 19:6, 3603-3643, 2015
• Removal of singularities and Gromov compactness for symplectic vortices
  Andreas Ott
  Journal of Symplectic Geometry, Vol. 12, No. 2, 1-55, 2014
• Surjectivity of the comparison map in bounded cohomology for Hermitian Lie groups
  Tobias Hartnick, Andreas Ott
  International Mathematics Research Notices, No. 9, 2068-2093, 2012
• The non-local symplectic vortex equations and gauged Gromov-Witten invariants
  Andreas Ott
• On Fano threefolds with b₂ ≥ 2
  Andreas Ott

Software

• CoVtRec Topological Data Analysis of the ongoing convergent evolution of the coronavirus SARS‑CoV‑2

Activities

• Mathematics and the Formal Turn MathSEE featured talk by Jeremy Avigad
• 4th Workshop on Topological Methods in Data Analysis Synergies between TDA and the life sciences
• MathSEE Symposium 2023 Conference on applications of mathematical sciences at KIT
• MathSEE Interdisciplinary mathematical research at KIT
• Bounded Cohomology Workshop
• Asymptotic Invariants and Limits of Groups and Spaces Research training group
• Structures & Mathematics Interdisciplinary seminar series
• Higgs Bundles in Geometry and Physics Workshop

Teaching

• Topological Methods in Omics Data Analysis
• Persistent homology and viral evolution
• Applications of Topological Data Analysis (KIT)
• Proseminar Perlen der linearen Algebra (KIT)
• Topological Data Analysis (KIT)
• Geometric Methods in Data Analysis
• Heidelberg Geometry Seminar
• Seminar Geometry and Mathematical Physics
• Einführung in die Geometrie
• Heidelberg Junior Geometry Seminar
• Symplectic Topology (Part III, Cambridge University)