Christoph Winges

Fakultät für Mathematik
Universität Regensburg
93040 Regensburg
Germany

eMail: christoph dot winges at ur de
Phone: +49 941 943 2793

Office: M 115

Links

Faculty of Mathematics
SFB 1085 Higher Invariants

I am a postdoctoral researcher (Akademischer Rat auf Zeit) in Ulrich Bunke's workgroup. My research interests lie somewhere at the various intersections between algebraic K-theory, homotopy theory, manifold topology and coarse geometry.

I received my PhD in Münster and previously held postdoctoral positions in Münster, at the Max-Planck-Institute for Mathematics and the University of Bonn.

Teaching

During the winter term 2024/25, I am running seminars on Non-standard analysis and Topological K-theory (both links direct to the respective GRIPS page, each of which also contains a seminar programme).

Previous teaching:

SS 24 Topology II (lecture course)
Seminar: Introduction to simplicial homotopy theory and infinity-categories
WS 23/24 Localisation and devissage in algebraic K-theory
WS 23/24 Assistant for Lineare Algebra I
SS 23 Examenskurs Analysis (Lehramt Gymnasium) (links to GRIPS, UR account required)
WS 22/23 Examenskurs Analysis (Lehramt Gymnasium) (jointly with Han-Ung Kufner; links to GRIPS, UR account required)
Seminar: Simple-homotopy theory and the s-cobordism theorem (link to GRIPS)
SS 22 Geometrie für Lehramt Gymnasium
WS 21/22 Seminar: Lie algebras and Lie groups (with Ulrich Bunke)
SS 21 Algebraic K-Theory and the Wall finiteness obstruction
Examenskurs Analysis (Lehramt Gymnasium) (jointly with Stefan Stadlöder; links to GRIPS, UR account required)
WS 20/21 Exercises for Introduction to Coarse Geometry
SS 20 Algebraic Topology II
WS 19/20 Introduction to higher categories (with Fabian Hebestreit)
WS 17/18 Seminar: Knot theory (with Daniel Kasprowski)
WS 15/16 Seminar: Simple-homotopy theory (with Arthur Bartels)

Publications

Controlled objects in left-exact ∞-categories and the Novikov conjecture. To appear in Bull. Math. Soc. Fr., arXiv:1911.02338
(with U. Bunke, D.-C. Cisinski and D. Kasprowski)
Split injectivity of A-theoretic assembly maps. Int. Math. Res. Not. IMRN 2021 (2021), no. 2, 885-947
(with U. Bunke and D. Kasprowski)
Injectivity results for coarse homology theories. Proc. Lond. Math. Soc. 121 (2020), no. 6, 1619-1684
(with U. Bunke, A. Engel and D. Kasprowski)
Transfers in coarse homology. Münster J. Math. 13 (2020), no. 2, 353-424
(with U. Bunke, A. Engel and D. Kasprowski)
Equivariant coarse homotopy theory and coarse algebraic K-homology. K-theory in algebra, analysis and topology, Contemp. Math. 749 (2020), 13-104
(with U. Bunke, A. Engel and D. Kasprowski)
Homotopy theory with marked additive categories. Theory Appl. Categ. 35 (2020), no. 13, 371-416
(with U. Bunke, A. Engel and D. Kasprowski)
Shortening binary complexes and commutativity of K-theory with infinite products. Trans. Amer. Math. Soc. Ser. B 7 (2020), 1-23
(with D. Kasprowski)
K₁-groups via binary complexes of fixed length. Homology Homotopy Appl. 22 (2020), no. 1, 203-213
(with D. Kasprowski and B. Köck)
Coarse homology theories and finite decomposition complexity. Algebr. Geom. Topol. 19 (2019), no. 6, 3033-3074
(with U. Bunke, A. Engel and D. Kasprowski)
On the Farrell-Jones Conjecture for algebraic K-theory of spaces: the Farrell-Hsiang method. Ann. K-Theory 4 (2019), no. 1, 57-138
(with M. Ullmann)
Algebraic K-theory of stable ∞-categories via binary complexes. J. Topol. 12 (2019), no. 2, 442-462
(with D. Kasprowski)
On the Farrell-Jones Conjecture for Waldhausen's A-theory. Geom. Topol. 22 (2018), no. 6, 3321-3394
(with N. Enkelmann, W. Lück, M. Pieper and M. Ullmann)
The A-theoretic Farrell-Jones Conjecture for virtually solvable groups. Bull. Lond. Math. Soc. 50 (2018), no. 2, 219-228
(with D. Kasprowski, M. Ullmann and C. Wegner)
On the transfer reducibility of certain Farrell-Hsiang groups. Algebr. Geom. Topol. 15 (2015), no. 5, 2919-2946
A note on the L-theory of infinite product categories. Forum Math. 25 (2013), no. 4, 665-676

Preprints

Homology manifolds and euclidean bundles. arXiv:2406.14677
(with F. Hebestreit, M. Land and M. Weiss)
Every spectrum is the K-theory of a stable ∞-category. arXiv:2401.06510
(with M. Ramzi and V. Sosnilo)
On the Farrell-Jones conjecture for localising invariants. arxiv:2111.02490
(with U. Bunke and D. Kasprowski)

Other writing

Introduction to the Serre spectral sequence
Notes on simplicial homotopy theory
Notes on Wall's finiteness obstruction
Topology II (lecture notes for a course held at LMU München during the summer term 2024)

Theses

L-Theory of Additive Categories. Diplomarbeit, 2010.
Filtering the Assembly Map in Algebraic K-Theory and Transfer Reducibility of ℤⁿ ⋊ ℤ. PhD thesis, 2014.

Last modified 2024-11-28