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From Higher Invariants


Invariants play a dominant role in all of mathematics: Invariants should be fine enough to extract the right information, but coarse enough to be computable in specific cases. Higher invariants are a structural and hierarchical refinement of certain classical invariants. The long term goal of this Collaborative Research Centre is to formulate the principles of construction and computation of higher invariants in a systematic way.

  • Higher Chern classes
  • Volumes, L-functions, and polylogarithms
  • Metric structures on cohomology, vector bundles, and cycles
  • Higher categories and enriched structures

Projects and principal investigators

Publications/Preprints (in reverse chronological order)


  • H. Esnault, M. Kerz. Local systems with quasi-unipotent monodromy at infinity are dense, arXiv:2101.00487; 01/2021


  • B. Ammann, J. Mougel, V. Nistor. A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds arXiv:2012.13902; 12/2020.
  • J.I. Burgos Gil, S. Goswami, G. Pearlstein. Height Pairing on Higher Cycles and Mixed Hodge Structures, arxiv:2007.06036.
  • S.Balchin, J.P.C. Greenlees, L. Pol, J. Williamson. Torsion model for tensor triangulated categories: the one-step case. arXiv:2011.10413; 11/2020
  • T. Bachmann, A. A. Khan, C. Ravi, V. Sosnilo. Categorical Milnor squares and K-theory of algebraic stacks. arXiv:2011.04355; 11/2020
  • P. Dolce, R. Gualdi, Numerical equivalence of ℝ-divisors and Shioda-Tate formula for arithmetic varieties, arXiv:2010.16134; 10/2020
  • M. Ludewig, Z. Yi, A Short Proof of the Localization Formula for the Loop Space Chern Character of Spin Manifolds, arXiv:2010.05892; 10/2020.
  • B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, K. Moi, M. Land, D. Nardin, T. Nikolaus, W. Steimle. Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings arXiv:2009.07225; 09/2020
  • M. Ludewig, G. C. Thiang. Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry. arXiv:2009.07688; 09/2020.
  • B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, K. Moi, M. Land, D. Nardin, T. Nikolaus, W. Steimle. Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity arXiv:2009.07224; 09/2020
  • B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, K. Moi, M. Land, D. Nardin, T. Nikolaus, W. Steimle. Hermitian K-theory for stable ∞-categories I: Foundations arXiv:2009.07223; 09/2020
  • S. Baader, R. Blair, A. Kjuchukova and F. Misev. The bridge number of arborescent links with many twigs. arXiv:2008.00763; 08/2020
  • S. Friedl, T. Kitayama, L. Lewark, M. Nagel and M. Powell. Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. arXiv:2007.15289; 08/2020
  • M. Ludewig, S. Roos. The Chiral Anomaly of the Free Fermion in Functorial Field Theory. arXiv:2010.05892; Ann. Henri Poincare, 21:1191-1233, 06/2020.
  • M. Ludewig, G. C. Thiang. Good Wannier bases in Hilbert modules associated to topological insulators. arXiv:1904.13051; J. Math. Phys., 61, 061902, 06/2020.

  • H. Esnault and M. Kerz. Density of Arithmetic Representations of Function Fields. arXiv:2005.12819; 05/2020
  • S. Boucksom, W. Gubler, F. Martin. Differentiability of relative volumes over an arbitrary non-archimedean field. arXiv:2004.03847; 04/2020
  • A. M. Botero and J. I. Burgos Gil. Toroidal b-divisors and Monge-Ampére measures. arXiv.2004.1405; 04/2020
  • C. Löh. Ergodic theoretic methods in group homology. A minicourse on L2-Betti numbers in group theory. SpringerBriefs in Mathematics, Springer, DOI 10.1007/978-3-030-44220-0 03/2020.
  • T. Barthel, D. Heard, N. Castellana, G. Valenzuela. Local Gorenstein duality for cochains on spaces. arXiv:2001.02580; 01/2020. Journal of Pure and Applied Algebra, Volume 225, Issue 2, February 2021
  • M. Ludewig, A. Stoffel. A framework for geometric field theories and their classification in dimension one. arXiv:2001.05721; 01/2020.


  • A. M. Botero, J. I. Burgos Gil and M. Sombra. Convex analysis on polyhrdral spaces. arXiv:1911.04821; 11/2019
  • Y. Kezuka, Y. Li, A classical family of elliptic curves having rank one and the 2-primary part of their Tate-Shafarevich group non-trivial. arXiv:1911.04532 math.NT; 11/2019
  • A. M. Botero. The Convex-Set Algebra and intersection theory on the Toric Riemann-Zariski Space. arXiv.1909.08262; 09/2019
  • S. Friedl, M. Nagel, P. Orson, M. Powell. A survey of the foundations of four-manifold theory in the topological category. arXiv:1910.07372; 10/2019
  • M. Moraschini, Alessio Savini. A Matsumoto-Mostow result for Zimmer's cocycles of hyperbolic lattices. arXiv:1909.00846; 09/2019 To appear in Transformation Groups.
  • Imre Bokor, Diarmuid Crowley, S. Friedl, Fabian Hebestreit, Daniel Kasprowski, Markus Land, Johnny Nicholson Connected sum decompositions of high-dimensional manifolds. arXiv:1909.02628; 09/2019
  • M. Lüders, Algebraization for zero-cycles and the p-adic cycle class map, Mathematical Research Letters, Volume 26 (2019) Number 2, pp. 557-585.
  • M. Lüders, A restriction isomorphism for zero cyclces with coefficients in Milnor K-theory, Cambridge Journal of Mathematics, Volume 7 (2019) Number 1-2, pp. 1-31.
  • H. Esnault, M. Kerz, Etale cohomology of rank one l-adic local systems in positive characteristic, arxiv:1908.08291; 08/2019
  • Y. Kezuka, On the main conjecture of Iwasawa theory for certain non-cyclotomic ℤp-extensions. arXiv:1711.07554 math.NT; J. Lond. Math. Soc., Vol. 100, pp. 107-136, 8/2019
  • Y. Kezuka, J. Choi, Y. Li, Analogues of Iwasawa's μ=0 conjecture and the weak Leopoldt conjecture for a non-cyclotomic ℤ2-extension. arXiv:1711.01697 math.NT; Asian J. Math., Vol. 23, No. 3, pp. 383-400, 7/2019
  • L. Prader, A local–global principle for surjective polynomial maps, arXiv:1909.11690; Journal of Pure and Applied Algebra 223(6), 06/2019, pp. 2371-2381
  • P. Feller, L. Lewark. Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space. arXiv:1905.08305; 05/2019
  • P. Antonini, A. Buss, A. Engel, T. Siebenand. Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras, arXiv:1905.07730 math.KT; 05/2019
  • T. Barthel, D. Heard, N. Castellana, G. Valenzuela. On stratification for spaces with Noetherian mod p cohomology. arxiv:1904.12841; 04/2019
  • V. Ertl. A new proof of a vanishing result due to Berthelot, Esnault, and Rülling. arXiv:1805.06269 math.NT; 04/2019 to appear in the Journal of Number Theory.


  • E. Elmanto, M. Hoyois, A.A. Khan, V. Sosnilo, M. Yakerson. Framed transfers and motivic fundamental classes. arXiv:1809.10666; 09/2018
  • S. Friedl, JungHwan Park, Bram Petri, Jean Raimbault and Arunima Ray, On distinct finite covers of 3-manifolds. arXiv:1807.09861; 07/2018
  • V. Ertl, K. Yamada. Comparison between rigid syntomic and crystalline syntomic cohomology for strictly semistable log schemes with boundary. arXiv:1805.04974 math.NT; 05/2018.
  • G. Herrmann, Sutured manifolds and L^2-Betti numbers. arxiv:1804.09519; 04/2018
  • J. Sprang, The algebraic de Rham realization of the elliptic polylogarithm via the Poincaré bundle. arXiv:1802.04996; 02/2018
  • Y. Kezuka, On the p-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of ℚ(√-3). arXiv:1605.08245 math.NT; Math. Proc. Camb. Philos. Soc., 164, pp. 67-98, 1/2018


  • F. Hebestreit, M. Land, W. Lück, O. Randal-Williams. A Vanishing theorem for tautological classes of aspherical manifolds. arXiv:1705.06232 math.AT; 05/2017
  • F. Binda, J. Cao, W. Kai and R. Sugiyama, Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus, J. of Algebra, Vol. 469, 1, 2017.


  • N. Otoba; J. Petean, Solutions of the Yamabe equation on harmonic Riemannian submersions, arXiv:1611.06709 math.DG; 11/2016
  • V. Ertl. Full faithfulness for overconvergent F-de Rham-Witt connections. arXiv:1411.7182 math.NT; Comptes rendus - Mathématique vol. 354, no. 7, pp. 653-658, 07/2016.
  • D. Scarponi, Sparsity of p-divisible unramified liftings for subvarieties of abelian varieties with trivial stabilizer. arXiv:1602.08755v3; 02/2016
  • O. Gwilliam, D. Pavlov. Enhancing the filtered derived category. arXiv:1602.01515, accepted by J. Pure Appl. Algebra; 02/2016


  • D. Scarponi, The realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne-Beilinson cohomology. arXiv:1512.01997; 12/2015
  • F. Bambozzi, O. Ben-Bassat, K. Kremnizer . Stein Domains in Banach Algebraic Geometry. arxiv:1511.09045 math.AG; 11/2015
  • F. Martin Analytic functions on tubes of non-Archimedean analytic spaces, with an appendix by Christian Kappen arXiv:1510.01178; 10/2015
  • I. Barnea, M. Joachim, S. Mahanta. Model structure on projective systems of C*-algebras and bivariant homology theories. math.KT; 08/2015


  • A. Beilinson, G. Kings, A. Levin. Topological polylogarithms and p-adic interpolation of L-values of totally real fields. arXiv:1410:4741 math.NT; 10/2014