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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)

2024

  • Z. Li, Y.Qin. On p-torsions of geometric Brauer groups, [1]; 06/2024
  • B. Cnossen, R. Haugseng, T. Lenz, S. Linskens. Normed equivariant ring spectra and higher Tambara functors, arXiv:2407.08399; 07/2024

2023

  • M. Pippi. On some (co)homological invariants of coherent matrix factorizations, J. Noncommut. Geom. (2023), arXiv version: [2]; 08/2023.
  • C. Löh. Exponential growth rates in hyperbolic groups (after Koji Fujiwara and Zlil Sela), Exposée 1206 for the Séminaire Bourbaki (April 2023), arXiv:2304.04424 math.GR; 04/2023
  • T. Annala, M. Hoyois, R. Iwasa. Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory, arXiv:2303.02051 math.AG; 03/2023. To appear in J. Amer. Math. Soc.
  • R. Gualdi. ¿Cuántas raíces de la unidad anulan un polinomio en dos variables?, La Gaceta de la Real Sociedad Matemática Española 26 (2023), 149 — 172; 02/2023 (divulgative article)
  • C. Löh. A comment on the structure of graded modules over graded principal ideal domains in the context of persistent homology, arXiv:2301.11756 math.AC; 01/2023

2022

  • A. Hogadi, S. Yadav. \A^1 connectivity of moduli of vector bundles on a curve. arXiv:2110.05799v2; 12/22 (updated and final version)
  • D. Beraldo, M. Pippi. Non-commutative intersection theory and unipotent Deligne-Milnor formula, arXiv:2211.11717 math.AG; 11/2022.
  • D.-C. Cisinski, M. Pippi. Étale tame vanishing cycles over [A^1_S/G_{m,S}], arXiv:2209.13381; 09/2022.

2021

  • A. A. Khan, C. Ravi. Generalized cohomology theories for algebraic stacks. arXiv:2106.15001; 06/2021
  • F. Hanisch, M. Ludewig. A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold. arXiv:1709.10027; 03/2021
  • B. Güneysu, M. Ludewig. The Chern Character of theta-summable Fredholm Modules over dg Algebras and Localization on Loop Space. arXiv:1901.04721; 03/2021

2020

  • S. Wolf, The pro-étale topos as a category of pyknotic presheaves, Doc. Math. 27, 2067-2106 (2022) 12/2020
  • 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. Proceedings of the London Mathematical Society, 125 (2022), Issue 1, 61-170 [3].
  • P. Capovilla, M. Moraschini, C. Löh. Amenable category and complexity, arXiv:2012.00612; 12/2020.
  • 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
  • N. Heuer, C. Löh, The spectrum of simplicial volume of non-compact manifolds, arXiv:2010.12945; 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.
  • C. Ravi, B. Sreedhar. Virtual equivariant Grothendieck-Riemann-Roch formula. arXiv:2009.09697; 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 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. To appear in Comm. Math. Phys.
  • 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
  • Y. Kezuka, Tamagawa number divisibility of central L-values of twists of the Fermat elliptic curve. arXiv:2003.02772 math.NT; 08/2020
  • 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
  • G. Herrmann and J. P. Quintanilha. The Complex of Hypersurfaces in a Homology Class. arXiv:2007.00522; 07/2020
  • 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
  • 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.


2019

  • M. Moraschini, Alessio Savini. Multiplicative constants and maximal measurable cocycles in bounded cohomology. arXiv:1912.09731; 12/2019
  • R. Frigerio, M. Moraschini. Gromov's theory of multicomplexes with applications to bounded cohomology and simplicial volume, arXiv:1808.07307 math.GT; 12/2019; To appear in Memoirs of the American Mathematical Society.
  • 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
  • N. Heuer, C. Löh. Simplicial volume of one-relator groups and stable commutator length, arXiv:1911.02470 math.GT; 11/2019
  • B. Ammann; J. Mougel; V. Nistor, A comparison of the Georgescu and Vasy spaces associated to the N-body problems. arXiv:1910.10656 math-ph; 10/2019
  • 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
  • D. Fauser, C. Löh, M. Moraschini, J. P. Quintanilha. Stable integral simplicial volume of 3-manifolds, arXiv:1910.06120 math.GT; 10/2019
  • V. Wanner, Energy Minimization Principle for non-archimedean curves. arXiv:1909.11335; 09/2019.
  • 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
  • H.K.Nguyen, Covariant & Contravariant Homotopy Theories, arxiv:1908.06879; 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
  • K. Bohlen, J. M. Lescure. A geometric approach to K-homology for Lie manifolds, arXiv:1904.04069; 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.
  • B. Ammann; K. Kröncke, O. Müller. Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors. Commun. Math. Phys. 387, 77-109 (2021), doi: 10.1007/s00220-021-04172-1, arXiv:1903.02064 math.DG; 03/2019

2018

  • F. Binda,S. Saito, Semi-purity for cycles with modulus arXiv:1812.01878; 12/2018.
  • B. Ammann; N. Große; V Nistor, Analysis and boundary value problems on singular domains: an approach via bounded geometry. arXiv:1812.09898 math.AP; 12/2018
  • B. Ammann; N. Große; V Nistor, The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with bounded geometry. arXiv:1810.06926 math.AP; 10/2018
  • 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.
  • M. Marcinkowski, Aut-invariant word norm on right angled Artin and Coxeter groups. arXiv:1803.00294; 03/2018
  • 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
  • V. Wanner, Comparison of two notions of subharmonicity on non-archimedean curves. arXiv: 1801.04713; 01/2018

2017

  • G. Cortiñas, J. Cuntz, R. Meyer, and G. Tamme, Weak completions, bornologies and rigid cohomology. arXiv:1712.08004 math.AG; 12/2017
  • T. Barthel, T. Schlank, N. Stapleton, Chromatic homotopy theory is asymptotically algebraic. arXiv:1711.00844; 11/2017
  • P. Jell, J. Rau, K. Shaw Lefschetz (1,1)-theorem in tropical geometry. Epijournal de Géometrie Algébrique, volume 2, article no. 11 (2018)arXiv:1711.07900;11/2017
  • F. Binda and A. Krishna, Zero cycles with modulus and zero cycles on singular varieties, to appear in Compositio Math, arXiv:1512.04847v4 [math.AG].
  • G. Cortiñas, J. Cuntz, R. Meyer, and G. Tamme, Nonarchimedean bornologies, cyclic homology and rigid cohomology. arXiv:1708.00357 math.AG; 08/2017
  • 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
  • S.P. Reeh, T.M. Schlank, N. Stapleton, A formula for p-completion by way of the Segal conjecture. arxiv:1704.00271 math.AT; 04/2017
  • F. Binda, Torsion zero cycles with modulus on affine varieties.arXiv:1604.06294 math.AG, to appear in J. of Pure and App. Algebra.
  • 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.

2016

  • U. Jannsen, S. Saito, Y. Zhao. Duality for relative logarithmic de Rham-Witt sheaves and wildly ramified class field theory over finite fields. arXiv:1611.08720 math.AG; 11/2016
  • N. Otoba; J. Petean, Solutions of the Yamabe equation on harmonic Riemannian submersions, arXiv:1611.06709 math.DG; 11/2016
  • B. Ammann; N. Große; V Nistor, Well-posedness of the Laplacian on manifolds with boundary and bounded geometry arXiv:1611.00281 math.AP; 11/2016
  • S. Baader, P. Feller, L. Lewark, R. Zentner, Khovanov width and dealternation number of positive braid links, arXiv:1605.04534 math.GT; 10/2016
  • 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
  • O. Raventós. Transfinite Adams representability. arXiv:1304.3599; new version 02/2016

2015

  • 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
  • B. Ammann; Klaus Kröncke, Hartmut Weiß, Frederik Witt. Holonomy rigidity for Ricci-flat metrics, arXiv:1512.07390 math.DG; 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
  • O. Müller, N. Nowaczyk, A universal spinor bundle and the Einstein-Dirac-Maxwell equation as a variational theory, arXiv:1504.01034 math.DG; 10/2015
  • P. Feller, S. Pohlmann, R. Zentner, Alternating numbers of torus knots with small braid index, arXiv:1508.05825; 08/2015
  • I. Barnea, M. Joachim, S. Mahanta. Model structure on projective systems of C*-algebras and bivariant homology theories. math.KT; 08/2015
  • R. Nakad, M. Pilca. Eigenvalue Estimates of the spin^c Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds. arXiv:1502.05252 math.DG; 07/2015
  • O. Raventós. The hammock localization preserves homotopies. arXiv:1404.7354; new version 05/2015
  • S. Mahanta. Algebraic K-theory, K-regularity, and T-duality of O∞-stable C*-algebras. arXiv:1311.4720 math.KT; new version 04/2015
  • B. Ammann, N. Große. Relations between threshold constants for Yamabe type bordism invariants. arxiv:1502.05232 math.DG; 02/2015
  • R. Cluckers, F. Martin. A definable, p-adic analogue of Kiszbraun’s Theorem on extensions of Lipschitz maps. arxiv:1502.03036 math.AG; 02/2015
  • S. Mahanta. Symmetric monoidal noncommutative spectra, strongly self-absorbing C*-algebras, and bivariant homology. arXiv:1403.4130 math.KT; new version 02/2015
  • S. Mahanta. Colocalizations of noncommutative spectra and bootstrap categories. arXiv:1412.8370 math.KT; new version 01/2015

2014

  • X. Shen. On the l-adic cohomology of some p-adically uniformized Shimura varieties. arXiv:1411.0244 math.NT; 11/2014
  • F. Martin. Overconvergent subanalytic subsets in the framework of Berkovich spaces arXiv:1211.6684; 10/2014
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