Achim Krause

I am currently a postdoc at WWU Münster, in the workgroup of Thomas Nikolaus. Previously I did my PhD at the MPIM Bonn under the supervision of Peter Teichner.
My research centers around stable homotopy theory, with a focus on computational aspects. In my thesis I worked towards a motivic version of the classical nilpotence and periodicity results in stable homotopy theory. I am also interested in equivariant homotopy theory, THH and TC, as well as everything with derived in it.

Preprints and Publications

• Periodicity in motivic homotopy theory and over BP_*BP, thesis (2018), Bonn University
• Vanishing lines for modules over the motivic Steenrod algebra. New York Journal of Mathematics 24 (2018). (with Drew Heard)
• C-motivic modular forms, preprint, arXiv:1810.11050 (with Bogdan Gheorge, Dan Isaksen, Nicolas Ricka)
• Bökstedt periodicity and quotients of DVRs, preprint, arXiv:1907.03477 (with Thomas Nikolaus)
• Witt vectors with coefficients and characteristic polynomials over non-commutative rings, preprint, arXiv:2002.01538 (with Emanuele Dotto, Irakli Patchkoria, Thomas Nikolaus)
• The Picard group in equivariant homotopy theory via stable module categories, preprint, arXiv:2008.05551

Teaching

• Lecture course "Topological Cyclic Homology", winter 2020/21 (with Thomas Nikolaus). YouTube channel here, more information here.
• Lecture course "Homotopy theory II", summer 2020. More information here.
• Lunch Seminar "Condensed Mathematics", summer 2020. More information here.
• Seminar "Sheaves in geometry and logic", winter 2019/20 (with Thomas Nikolaus, Stefano Ariotta, Christoph Schrade)
• Seminar "Simple homotopy theory", summer 2019 (with Thomas Nikolaus)
• Seminar "algebraic K-theory", winter 2018/19 (with Johannes Ebert)

Contact

krauseac[at]wwu.de