Marco Schlichting's research

Preprints

[26]	Symmetric versus genuine symmetric forms in Hermitian K-theoryLink opens in a new window.
[25]	Higher K-theory of forms III. From chain complexes to derived categoriesLink opens in a new window, with Daniel Marlowe
[24]	Higher K-theory of forms II. From exact categories to chain complexesLink opens in a new window.
[23]	Homological stability for On,n over a local ring with infinite residue fieldLink opens in a new window, with Sunny Sood.

Published work and work accepted for publication

[22]	On the homology stability range for symplectic groups. Compos. Math., to appear
[21]	The third homology of symplectic groups and algebraic K-theory, with H. P. Sarwar. Amer. J. Math. 147 (2025), no. 3, 819–867
[20]	On the presentation of the Grothendieck-Witt group of symmetric bilinear forms over local rings, with Robert Rogers. Math. Z. 307 (2024), no. 2, Paper No. 41, 14 pp.
[19]	L-theory of C*-algebras, with Markus Land and Thomas Nikolaus. Proc. Lond. Math. Soc. 127 (2023), Issue 5, Pages 1451-1506.
[18]	Grothendieck-Witt groups of some singular schemes, with M. Karoubi and C.A. Weibel. Proc. Lond. Math. Soc. 122 (2021), Issue 4, Pages 521-536.
[17]	Higher K-theory of forms I. From rings to exact categories, J. Inst. Math. Jussieu. 20 (2021), Issue 4 , pp. 1205 - 1273.
[16]	Symplectic and orthogonal K-groups of the integers, C. R. Math. Acad. Sci. Paris 357 (2019), Issue 8, Pages 686-690. Erratum. C. R. Math. Acad. Sci. Paris 362 (2024), 307–308.
[15]	Euler class groups and the homology of elementary and special linear groups, Adv. in Math. 320 (2017), 1-81.
[14]	Hermitian K-theory, derived equivalences, and Karoubi's Fundamental Theorem, J. Pure Appl. Algebra 221 (2017), no. 7, 1729-1844.
[13]	The Witt group of real algebraic varieties, with M. Karoubi and C.A. Weibel, J. Topology (2016) 9 (4): 1257-1302
[12]	The homotopy fixed point theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory (with A.J. Berrick, M. Karoubi and P.A. Østvær) Adv. Math. 278 (2015), 34-55.
[11]	Geometric models for higher Grothendieck-Witt groups in A1-homotopy theory (with Girja S. Tripathi) Math. Ann. 362 (2015), no. 3-4, 1143-1167.
[10]	Higher algebraic K-theory (after Quillen, Thomason and others), Topics in Algebraic and Topological K-theory. Springer Lecture Notes in Math. 2008 (2011), 167-242.
[9]	The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes, Invent. Math. 179 (2010), no. 2, 349 - 433.
[8]	Hermitian K-theory of exact categories, J. K-theory 5 (2010), no. 1, 105 - 165.
[7]	Cyclic homology, cdh-cohomology and negative K-theory (with G. Cortiñas, C. Häsemeyer and C. A. Weibel), Ann. of Math. 167 (2008), 549 - 573.
[6]	Negative K-theory of derived categories, Math. Z. 253 (2006), no. 1, 97 - 134.
[5]	Localization in Hermitian K-theory of rings (with Jens Hornbostel), J. London Math. Soc. 70 (2004), no. 1, 77 - 124.
[4]	Hermitian K-theory: On a theorem of Giffen, K-theory 32 (2004), no. 3, 253 - 267.
[3]	Delooping the K-theory of exact categories, Topology 43 (2004), no. 5, 1089 - 1103.
[2]	A note on K-theory and triangulated categories, Invent. Math. 150 (2002), no. 1, 111 - 116.
[1]	Idempotent completion of triangulated categories (with Paul Balmer), J. Algebra 236 (2001), pp.819 - 834.
[0]	Delooping the K-theory of exact categories and negative K-groups, PhD thesis at Université Paris 7 (2000).

Former PhD students

[9]	Sunny Sood:	On the Homological Stability of Orthogonal and Spin Groups (Warwick 2024)
[8]	Dylan Madden:	Burnside form rings and the K-theory of forms (Warwick 2021)
[7]	James Plowman:	The Chow-Witt group of a scheme with residual complex (Warwick 2019)
[6]	Ferdinando Zanchetta:	Operations in (Hermitian) K-theory and related topics (Warwick 2019)
[5]	Daniel Grech:	Milnor K-theory and Automorphisms (Warwick 2018)
[4]	Heng Xie:	Grothendieck-Witt groups of quadrics and sums-of-squares formulas (Warwick 2015)
[3]	Simon Markett:	The Grayson spectral sequence for hermitian K-theory (Warwick 2015)
[2]	Jeremy Jacobson:	On the Witt groups of schemes (LSU 2012)
[1]	Girja Shanker Tripathi:	Orthogonal Grassmannians and hermitian K-theory in A1-homotopy theory of schemes (LSU 2010)

Current PhD students

Daniel Marlowe (4th+ year)

Federick Carter (1st year)


Other Activities

Editor for Annals of K-theory

Former editor for Journal of K-theory. See the Open letter of the editors about the end of the Journal of K-theory

Teacher for Music Together Kenilworth