Recent talks and preprints

For earlier papers see my publications list. For talks and preprints related to the Kervaire invariant see my Kervaire invariant page.

Email me if you would like a printer friendly version of any of these slides.

Slides for recent talks

• SUMS lecture at University of Rochester, September 22, 2026.
  “Why are there so many prime numbers?” Slides
• SLMath Hot Topics: Life after the Telescope Conjecture, December 9–13, 2024.
  “Why the telescope conjecture?” Slides
• MFO workshop of October 14–18, 2024
  “Why the telescope conjecture?” Slides Zoom recording
• Plectics Interdisciplinary Colloquium Series:
  “The chromatic conjectures in homotopy theory,” July 21, 2024. Slides Video
• Solar eclipses: Why they happen when they do, March 22, 2024.
  Slides Print friendly version Zoom recording
• eCHT Minicourse of December 5–14, 2023. “What is the telescope conjecture?”
  • Lecture 1: An algebraic prelude to chromatic homotopy theory, December 5, 2023
    Slides Print friendly version Video
  • Lecture 2: Morava's vision and the chromatic spectral sequence, December 7, 2023
    Slides Print friendly version Video
  • Lecture 3: From algebra to geometry, December 12, 2023
    Slides Print friendly version Video
  • Lecture 4: v_h-periodic families and telescopes, December 14, 2023
    Slides Print friendly version
• Princeton special algebraic topology seminar of October 28, 2023. “What is the telescope conjecture?” Slides Print friendly version
• University of Regensburg lecture of August 4, 2023, “What is an ∞-category?” Slides. The slides have more material (on Bousfield localization and spectra) than I was able to cover in the lecture. Here is a preprint form of this material.
• Northwestern University lecture of March 23, 2023, “Hiking in the Alps: C_p-fixed points of Lubin-Tate spectra.” Slides.
• Bonn lecture of October 17, 2022, “The Hill-Lawson spectral sequence and the telescope conjecture.” Slides.
• Glasgow lecture of May 24, 2022, “What is the telescope conjecture? A walking tour of modern homotopy theory.” Announcement and poster Slides Zoom video recording. This talk includes an account of “Morava's vision,” which was first described in his unpublished 1972 preprint, The moduli variety for formal groups, transcribed by John Rognes. Jack sent me this long lost copy shortly after I gave the talk.
• String cobordism at the prime 3
  • UCLA Topology Seminar, May 17, 2021
  • Princeton Topology Seminar, December 9, 2021
  • New Directions Seminar, University of Manchester, January 18, 2022. Zoom recording.
• The eightfold way: how to build the right model structure on orthogonal G-spectra.
  • Trondheim version, A Jolly Pleasant Conference for Greenlees, Norwegian University of Science and Technology, Trondheim, July–August, 2019.
  • Electronic Computational Homotopy Theory Seminar version, October 2019.
• Model category structures for equivariant spectra, Equivariant and motivic homotopy theory, August, 2018. Isaac Newton Institute for Mathematical Sciences. Print friendly version
• Two talks in China, June 2018.
  • Model categories and stable homotopy theory, International Workshop on Algebraic Topology, Shenzhen. Print friendly version.
  • Model categories and spectra, Joint International Meeting of the CMS and AMS, Shanghai. Print friendly version.
• The chromatic conjectures, Chromatic Homotopy Theory: Journey to the Frontier, May, 2018. Video link to conference talks.
• Two equivariant approaches to the telescope conjecture, MIT topology seminar, November, 2017.
• The C₂-equivariant analog of the subalgebra of A generated by Sq¹ and Sq², Homotopy theory: tools and applications, UIUC, July, 2017. Print friendly version Video
• Model categories and spectra, University of Chicago, May, 2017.
• The lost telescope of Z, Electronic Computational Homotopy Theory Seminar, March, 2017. Print friendly version.
• The slice filtration revisited, CMS Winter Meeting, December, 2016.
• What is a G-spectrum?, Geometry-Topology Conference, Lehigh University, May, 2015. Print friendly version
• HKR again: Kuhn's work on generalized group characters, Mid-Atlantic Topology Conference, University of Virginia, April, 2015.
• Inside the proof of the Kervaire invariant theorem or How I got bitten by the equivariant bug, Geometry and Topology. A conference in honor of Martin Bendersky's seventieth birthday and in commemoration of our friend and colleague Sam Gitler, Princeton University, March, 2015.
• Plastic explosives: A C₄ analog of the Kervaire invariant calculation, Conference on Equivariant, Chromatic and Motivic Homotopy Theory, Northwestern University, March, 2013.
• Quillen's work on formal group laws and complex cobordism theory, Conference honoring the legacy of Daniel Quillen, MIT, October, 2012.
• Browder's work on Arf-Kervaire invariant problem, Panorama of Topology: A Conference in Honor of William Browder, Princeton University, May, 2012. Video available at conference website.
• The 3-primary Arf-Kervaire invariant problem (with Mike Hill and Mike Hopkins), Banff Workshop on Algebraic K-Theory and Equivariant Homotopy Theory, February 16, 2012.

Other links

• Complex Cobordism and Stable Homotopy Groups of Spheres, online edition
• Related papers by other authors
• Lecture notes for a graduate course on elliptic cohomology, Fall 2003, Math 549

Preprints and slides for talks up to March 2009

• Slides for talk given at UR, October 12, 2007. These were made with Prosper. Printer friendly version
• Slides for talk given at MIT, March 9, 2009.
• Toward higher chromatic analogs of elliptic cohomology and tmf
  • Preprint of part I, October 28, 2003
  • Preprint of part II (36 pages), June 12, 2008
  • Slides for talk given at Johns Hopkins University, March 10, 2007. These were made with Prosper. Printer friendly version
  • Slides for four talks given at Wayne State University. These were made with Prosper.
    • February 26, 2007. Printer friendly version
    • February 27, 2007. Printer friendly version
    • February 28, 2007. Printer friendly version
    • March 1, 2007. Printer friendly version
  • Slides for talk given at the workshop on Topological Algebraic Geometry, Oslo, September 6, 2006. Illustrative Ext chart of Hopkins-Mahowald.
  • Slides for talk given at Rochester, March 10, 2006
  • Slides for talk given at MIT, December 16, 2005
  • Slides for talk given at MIT, September 26, 2005
  • Slides for talk given at AMS meeting in Newark, DE, April 2, 2005
  • Slides for talk given at CMS meeting in Halifax, June 13, 2004
  • Slides for talk given at AMS meeting at Rider University, April 17, 2004
  • Slides for talk given at San Miguel de Allende, Mexico, December 4, 2003
  • Slides for talk given at Lehigh, June 12, 2003
  • Slides for talk given at Oberwolfach, March 19, 2003
  • Slides for talk given at AMS meeting in Baltimore, January 17, 2003
  • Slides for talk given at the Isaac Newton Institute, December 18, 2002
• Lin Junkun's work on the Adams spectral sequence, slides for talk given in Rochester, November 10, 2006. These were made with Prosper. Here is a printer friendly version.
• A guided tour of the EHP sequence, slides for talk given at the CRM in Montreal, November 20, 2005
• Some early and middle mathematical work of Bob Stong, University of Virginia, November 10, 2007. Alternate version
• The first Adams-Novikov differential for the spectrum T(m) (June 11, 2008)
• The method of infinite descent in stable homotopy theory II (with H. Nakai). (October 20, 2008)
• On beta elements in the Adams-Novikov spectral sequence (with H. Nakai). (October 22, 2008)