Tobias Barthel

I am a Postdoc at the University of Copenhagen, interested in homotopy theory and its various interactions with other areas of mathematics. I finished my PhD thesis under the supervision of Mike Hopkins in 2014 and then spent two years as a postdoc at the Max Planck Institute for Mathematics in Bonn.

Since January 2018, I am supported by an EU Marie Curie Individual Fellowship.

Email: tbarthel (at)

List of publications.

  • Excellent rings in transchromatic homotopy theory, joint with Nathaniel Stapleton, HHA (2017), arXiv link
  • On localization sequences in the algebraic K-theory of ring spectra, joint with Ben Antieau and David Gepner, JEMS (2017), arXiv link
  • Local duality for structured ring spectra, joint with Drew Heard and Gabriel Valenzuela, JPAA (2017), arXiv link
  • Brown--Peterson cohomology from Morava E-theory, joint with Nathaniel Stapleton and with an appendix by Jeremy Hahn, Compositio (2017), arXiv link
  • Auslander--Reiten sequences, Brown--Comenetz duality, and the K(n)-local generating hypothesis, Algebr. Represent. Theory (2017), arXiv link
  • The character of the total power operation, joint with Nathaniel Stapleton, G&T (2017), arXiv link
  • The E_2-term of the K(n)-local E_n-based Adams spectral sequence, joint with Drew Heard, Topol. Appl. (2016), arXiv link
  • Chromatic completion, Proc. AMS (2016), arXiv link
  • Centralizers in good groups are good, joint with Nathaniel Stapleton, AGT (2016), arXiv link
  • Completed power operations for Morava E-theory, joint with Martin Frankland, AGT (2015), arXiv link
  • Six model structures for DG-modules over DGAs, joint with Peter May and Emily Riehl, New York J. Math. (2014), arXiv link
  • On the constructions of functorial factorizations for model categories, joint with Emily Riehl, AGT (2013), arXiv link

List of preprints.

Here is a video of me speaking about ultrachromatic homotopy theory at Ravenel's 70th birthday conference, Reed College, August 2017

The European Talbot Workshop

Together with Sean Tilson, we started the European Talbot Workshop in 2014. The current organizers are: Bertram Arnold, Tobias Barthel, Jack Davies, Alice Hedenlund, Magdalena Kedziorek, and Sean Tilson.

The next workshop will take place in July 2018. The topic is Free loop spaces in geometry and topology, and the mentors are Nathalie Wahl and Alexandru Oancea. We gratefully acknowledge funding from the SFB 1085 and SPP 1786.


In 2018, I'm involved in the organization of two Masterclasses in Copenhagen, together with Jesper Grodal and Markus Hausmann.

In March 2017, Jesper Grodal and I organized a Masterclass on Stratifications and duality in modular representation theory.

My collaborators: Ben Antieau, Omar Antolin-Camarena, Agnes Beaudry, Dan Berwick-Evans, A.K. Bousfield, Natalia Castellana, Martin Frankland, David Gepner, Frank Gounelas, Jeremy Hahn, Markus Hausmann, Drew Heard, Achim Krause, Peter May, Niko Naumann, Thomas Nikolaus, Justin Noel, Eric Peterson, Emily Riehl, Tomer Schlank, Nathaniel Stapleton, Vesna Stojanoska, Gabriel Valenzuela.

The above image (Projet de clavier ultrachromatique, 1943) is taken from the book of writings by Wyschnegradsky (Libération du son: écrits 1916-1979, ed. Pascale Criton. Lyon: Symétrie 2013), Ivan Wyschnegradsky Collection, Paul Sacher Stiftung, Basel.