Research Interests

Research Interests

$\bullet$ Algebraic number theory.
$\bullet$ Arithmetic and algebraic geometry.
$\bullet$ Ergodic theory.
$\bullet$ Analysis on manifolds, foliations, dynamical systems.
$\bullet$ von Neumann algebras.

Selected Publications

Selected Publications of Christopher Deninger

$\bullet$ J. Cuntz and C. Deninger. Witt vector rings and the relative de Rham Witt complex. J. Algebra, 440:545–593, 2015. With an appendix by Umberto Zannier.

$\bullet$ J. Cuntz, C. Deninger, and M. Laca. $\mathsf C^*$-algebras of Toeplitz type associated with algebraic number fields. Math. Ann., 355(4):1383–1423, 2013.

$\bullet$ C. Deninger. Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents. J. Reine Angew. Math., 651:165–185, 2011.

$\bullet$ C. Deninger. Fuglede- Kadison determinants and entropy for actions of discrete amenable groups. J. Amer. Math. Soc., 19(3):737–758, 2006.

$\bullet$ C. Deninger and A. Werner. Vector bundles on $p$-adic curves and parallel transport. Ann. Sci. \'Ecole Norm. Sup. (4), 38(4):553–597, 2005.

$\bullet$ C. Deninger. Deligne periods of mixed motives, $K$-theory and the entropy of certain ${\bf Z}^n$-actions. J. Amer. Math. Soc., 10(2):259–281, 1997.

$\bullet$ C. Deninger. Higher order operations in Deligne cohomology. Invent. Math., 120(2):289–315, 1995.

$\bullet$ C. Deninger. Local $L$-factors of motives and regularized determinants. Invent. Math., 107(1):135–150, 1992.

$\bullet$ C. Deninger. Higher regulators and Hecke $L$-series of imaginary quadratic fields: {II}. Ann. of Math. (2), 132(1):131–158, 1990.

$\bullet$ C. Deninger and W. Singhof. The $e$-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups. Invent. Math., 78(1):101–112, 1984.

Current Publications

Current Publications

$\bullet$ Christopher Deninger. Primes, knots and periodic orbits. arXiv e-prints, January 2023. arXiv:2301.11643.

$\bullet$ Christopher Deninger, Theo Grundhöfer, and Linus Kramer. Weyl tensors, strongly regular graphs, multiplicative characters, and a quadratic matrix equation. arXiv e-prints, April 2022. arXiv:2204.02706.

$\bullet$ Christopher Deninger. There is no "Weil-"cohomology theory with real coefficients for arithmetic curves. arXiv e-prints, April 2022. arXiv:2204.02714.

$\bullet$ Christopher Deninger. A pro-algebraic fundamental group for topological spaces. arXiv e-prints, May 2020. arXiv:2005.13893.

$\bullet$ Christopher Deninger and Annette Werner. Parallel transport for vector bundles on $p$-adic varieties. Journal of Algebraic Geometry, 29(1):1–52, January 2020. doi:10.1090/jag/747.

$\bullet$ Christopher Deninger. P-adic limits of renormalized logarithmic Euler characteristics. Groups, Geometry, and Dynamics, 14(2):427–467, January 2020. arXiv:1801.02412, doi:10.4171/GGD/550.

$\bullet$ Christopher Deninger and Anton Mellit. $\mathbb zr$ and rings of Witt vectors $W_S(R)$. Rend. Semin. Mat. Univ. Padova, 142:93–102, June 2019. doi:10.4171/rsmup/32.

$\bullet$ Christopher Deninger. Dynamical systems for arithmetic schemes. arXiv e-prints, July 2018. arXiv:1807.06400.