Lectures

Some mathematical lectures

• K_4(Z) = 0 (PDF)
  Paris (July 1994).
• Kohomologi av knuterom, etter Vassiliev (PDF)
  Oslo (October 1994).
• Vassilievs spektralfølge (PDF)
  Oslo (October 1994).
• The Seiberg-Witten moduli space (PDF)
  Oslo (November 1995).
• Fixed points of topological Hochschild homology and K-theory of the two-adic integers (PDF)
  Stanford (January 1996).
• Notes on topological cyclic homology and the cyclotomic trace map (PDF)
  Chicago (April 1996).
• Kjerneregelen i funktorkalkulus (PDF)
  Oslo (February 1997).
• Ekvivariant stabil homotopiteori (PDF)
  Oslo (April 1997).
• Algebraic K-theory and stable smooth pseudoisotopy of discs (PDF)
  Sheffield (May 1997).
• Homology and cohomology operations (PDF)
  Oslo (August 1997).
• Gruppehomologi (PDF)
  Oslo (April 1998).
• Unstable modules and Sullivan's conjecture (PDF)
  Oslo (May 1998).
• Cohomology of the smooth Whitehead spectrum (PDF)
  Oberwolfach (September 1998).
• On trace maps (PDF)
  Oslo (October 1998).
• Algebraic K-theory of symmetric monoidal Gamma-space categories with weak equivalences (PDF)
  Oslo (October 1998).
• Topological cyclic homology of S-algebras (PDF)
  Oslo (November 1998).
• Two-regular number fields and algebraic K-theory (PDF)
  Oslo (March 1999).
• Two-primary algebraic K-theory of pointed spaces (PDF)
  Swansea (April 1999).
• On the image of Milnor's K_4 in Quillen's K_4 for number fields (PDF)
  Oslo (May 1999).
• Higher fixed points of topological Hochschild homology of the integers (PDF)
  Oslo (June 1999).
• The stable parametrized h-cobordism theorem (PDF)
  Oslo (October 1999).
• Algebraic K-theory of finitely presented spectra (PDF)
  Oberwolfach (September 2000).
• Topological cyclic homology of S-algebras (PDF)
  Oslo (April 2001).
• Two-primary algebraic K-theory of pointed spaces (PDF)
  Cornell (May 2001).
• Elliptic cohomology and algebraic K-theory of 2-vector spaces (PDF)
  Isle of Skye (June 2001).
• Galois extensions of ``brave new rings'' (PDF)
  Abel Bicentennial Conference, Oslo (June 2002).
• Waldhausen's stable parametrized h-cobordism theorem (PDF)
  BCAT 2002, Barcelona (July 2002).
• Topologisk K-teori og Bott periodisitet (PDF)
  Oslo (May 2003).
• Automorphisms of spheres, number fields, motives and spectra (PDF)
  Oslo (June 2005).
• Motivic truncation and arithmetic duality for some structured ring spectra (PDF)
  Fourth NRW Topology Meeting, Wuppertal (October 2005).
• Algebraic K-theory of the fraction field of topological K-theory (PDF)
  Schloß Ringberg proposal (November 2005).
• Smooth symmetries of manifolds and arithmetic of the sphere spectrum (PDF)
  Bonn colloquium (November 2005).
• On the stable parametrized h-cobordism theorem (DVI) (PDF)
  Bonn lectures (January/February 2006).
• Mahowald's infinite family (PDF)
  Bonn AG (February 2006).
• Algebraic K-theory and the chromatic filtration (PDF)
  Bonn seminar (March 20th, 2006, in preparation).
• Arithmetic of some brave new rings (PDF)
  Bonn seminar (March 29th, 2006).
• Algebraic K-theory and the chromatic filtration (PDF)
  Muenster Symposion (June 8th, 2006, in preparation).
• THH and TAQ (PDF)
  Oslo (fall 2006).
• The fraction field of topological K-theory (PDF)
  Banff poster (March 11th, 2008).
• Topological logarithmic structures (PDF)
  Banff talk (March 13th, 2008).
• Topological Hochschild homology of topological modular forms (PS)
  Nordic Topology Conference, NTNU (November 28th, 2008).
• Connective structures on gerbes and two-vector bundles (PDF)
  Oslo seminar talk (March 6th, 2009).
• Postnikov towers and k-invariants for S-modules, S-algebras and commutative S-algebras (PDF)
  Oslo seminar talk (May 15th, 2009).
• Topological logarithmic structures
  25th Nordic and 1st British-Nordic Congress of Mathematicians, Oslo (June 9th, 2009).
• Logarithmic THH and TC
  p-Adic Geometry and Homotopy Theory, Loen (August 6th, 2009).
• Motivic complexes from the stable rank filtration
  Nordic Topology Symposium, Bergen (June 10th, 2010).
• Introduction to redshift
  Oberwolfach (September 2011).
• Notes on the Adams spectral sequence
  Oslo (January to May 2012).
• Chromatic redshift (slides) (video)
  MSRI, Introductory Workshop: Algebraic Topology (January 28th, 2014).
• Algebraic K-theory of strict ring spectra (slides) (video)
  Seoul ICM 2014 (August 18th, 2014).
• Towards a motivic Segal conjecture (part 2) (part 3) (part 4) (part 5)
  Oslo (September-October 2014).
• Algebraic K-theory of group rings and topological cyclic homology (slides)
  Nordic Topology Meeting, NTNU (November 27th, 2014).
• The weight and rank filtrations
  Oslo (October 21st and 28th, 2016).
• The Davis-Mahowald spectral sequence
  Nils Baas 70, NTNU (December 1st, 2016).
• Cubical and cosimplicial descent
  Moduli and Traces, Copenhagen (April 21st, 2017).
• Topological modular forms - I
  Oslo (October 25th, 2017).
• Topological Hochschild homology of the prime fields and the integers
  Oslo (February 21st, 2018).
• Topological cyclic homology of the prime fields and the integers
  Oslo (March 7th, 2018).
• Logarithmic de Rham-Witt complexes
  Oslo (March 21st, 2018).
• Duality for topological modular forms
  Oberwolfach (August 2nd, 2019).
• Norms of Real bordism
  eCHT seminar (October 19th, 2020).
• The Adams spectral sequence for the image-of-J spectrum
  Princeton algebraic topology seminar (May 2021).
• Algebraic K-theory of elliptic cohomology
  Institut Mittag-Leffler seminar (April 2022).
• Group actions on homotopy spheres
  eCHT seminar (November 8th, 2022).
• Topological cyclic homology of the second truncated Brown-Peterson spectrum (video)
  CIRM/Luminy (January 26th, 2023).
• The Hahn-Raksit-Wilson even filtration
  Oslo, NMM 2024 (September 12th, 2024).
• Lichtenbaum-Quillen for truncated Brown-Peterson spectra
  Oberwolfach (October 16th, 2024).
• Higher arithmetic duality (video)
  Cambridge (May 12th, 2025).
• Theorems of Mahowald and Hopkins-Mahowald
  Oslo (November 21st, 2025).
• Introduction to spectral sequences, I
  Oslo (January 23rd, 2026).
• Introduction to spectral sequences, II
  Oslo (February 6th, 2026).
• The Bökstedt spectral sequence
  Oslo (February 20th, 2026).
• The Pirashvili-Brun-Höning spectral sequence
  Oslo (March 6th, 2026).
• Topological cyclic homology, I
  Oslo (April 10th, 2026).
• Topological cyclic homology, II
  Oslo (April 17th, 2026).
• Topological cyclic homology of the integers, and related topics
  Oslo (May 29th, 2026).
• Rank filtrations in algebraic K-theory
  Oslo (September 2nd, 2026).

Some popularized lectures

• Algebraic K-theory, some applications and computations (PDF)
  Trondheim (1994).
• Fermats siste teorem (PDF)
  Oslo (1994).
• Algebraisk K-teori og symmetrier av mangfoldigheter (PDF)
  Rondablikk (1998).
• Knuteteori (PDF)
  Oslo (1998).
• Vidunderlige nye ringer (PDF)
  Oslo (2002).
• Riemann-hypotesen (PDF)
  Oslo (2002).
• Jean-Pierre Serre: algebraisk topologi (PDF)
  Oslo (2003).
• Ringen av endelige mengder (PDF)
  Oslo (October 2010).
• Spaces of Manifolds
  Zürich (January 2016).
• Fermat, Taniyama-Shimura-Weil and Andrew Wiles
  Oslo (May 2016).
• Andrew Wiles, modularitetsformodningen og Fermats siste sats
  Hamar (September 2016).
• Yves Meyer: restoring the role of mathematics in signal and image processing
  Oslo (May 2017).
• Symmetries of Manifolds
  Oxford (January 2018).
• On the Langlands program
  Oslo (May 2018).