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.
I am currently participating in the program Homotopy Harnessing Higher Structures at the Newton Institute in Cambridge, UK.
Email: tbarthel (at) math.ku.dk
List of publications.
- Local duality in algebra and topology, joint with Drew Heard and Gabriel Valenzuela, accepted for publication in Advances in Mathematics (2018), arXiv link
- On the comparison of stable and unstable p-completion, joint with A. K. Bousfield, accepted for publication in Proc. Amer. Math. Soc. (2018), arXiv link
- Algebraic chromatic homotopy theory for BP_*BP-comodules, joint with Drew Heard, accepted for publication in Proc. Lond. Math. Soc. (2018), arXiv link
- The chromatic splitting conjecture for Noetherian commutative ring spectra, joint with Drew Heard and Gabriel Valenzuela, accepted for publication in Math. Z. (2018), arXiv link
- Excellent rings in transchromatic homotopy theory, joint with Nathaniel Stapleton, Homology Homotopy Appl. (2017), arXiv link
- On localization sequences in the algebraic K-theory of ring spectra, joint with Ben Antieau and David Gepner, J. Eur. Math. Soc. (2017), arXiv link
- Local duality for structured ring spectra, joint with Drew Heard and Gabriel Valenzuela, J. Pure Appl. Algebra (2017), arXiv link
- Brown--Peterson cohomology from Morava E-theory, joint with Nathaniel Stapleton and with an appendix by Jeremy Hahn, Compos. Math. (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, Geom. Topol. (2017), arXiv link
- The E_2-term of the K(n)-local E_n-based Adams spectral sequence, joint with Drew Heard, Topology Appl. (2016), arXiv link
- Chromatic completion, Proc. Amer. Math. Soc. (2016), arXiv link
- Centralizers in good groups are good, joint with Nathaniel Stapleton, Algebr. Geom. Topol. (2016), arXiv link
- Completed power operations for Morava E-theory, joint with Martin Frankland, Algebr. Geom. Topol. (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, Algebr. Geom. Topol. (2013), arXiv link
List of preprints.
- Derived completion for comodules, joint with Drew Heard and Gabriel Valenzuela (2018)
- Appendices A and B (joint with Krause) to Completing perfect complexes by Henning Krause, with another appendix by Bernhard Keller (2018)
- Stratifications and duality for homotopical groups, joint with Natalia Castellana, Drew Heard, and Gabriel Valenzuela (2017)
- Chromatic homotopy theory is asymptotically algebraic, joint with Tomer Schlank and Nathaniel Stapleton (2017)
- The Balmer spectrum of the equivariant homotopy category of a finite abelian group, joint with Markus Hausmann, Niko Naumann, Thomas Nikolaus, Justin Noel, and Nathaniel Stapleton (2017)
- Gross--Hopkins duals of higher real K-theory spectra, joint with Agnes Beaudry and Vesna Stojanoska (2017)
- Chromatic fracture cubes, joint with Omar Antolin-Camarena (2014)
- A simple universal property of Thom ring spectra, joint with Omar Antolin-Camarena (2014)
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.
- Tensor triangular geometry and equivariant stable homotopy theory, mentored by Paul Balmer and Justin Noel, March 2018.
- Rigidity and algebraic models in stable homotopy theory, mentored by John Greenlees and Stefan Schwede, April 2018.
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, Bernhard Keller, Achim Krause, Henning 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.