Curriculum Vitae for John Rognes

Born:

April 28th 1966 in Oslo

Citizenship:

Norwegian

Marital status:

Cohabitant, three sons

Address:

Røahagan 1 G
NO-0754 Oslo
Norway

E-mail:

rognes@math.uio.no

Telephone:

(+47) 91 99 52 89 (cellphone)

Research Interests

The Abel Prize

• Chairman of the Abel Committee, summer 2014 to summer 2018.

International Congress of Mathematicians

• Invited Lecturer in the Topology Section of ICM 2014, Seoul.

Editorial Role

• Editor of Acta Mathematica, September 2010 to July 2014.

Academic Education

• International Baccalaureate diploma, Berg Higher Secondary School, Oslo, June 1984. Result: 45 points of 45 possible.
• Cand. mag. degree (Bachelor's degree), University of Oslo, Faculty of Mathematics and Sciences, December 1985. Major subject: Mathematics. Minor subjects: Computer Science and Statistics. Average grade: 1.09 (Laudabilis prae ceteris).
• Master of Arts degree in Mathematics, Princeton University, October 1987. Major subjects for general examination: Differential Topology and Algebraic Topology.
• Ph.D. degree in Mathematics, Princeton University, June 1990. Thesis advisor: Gunnar Carlsson. Thesis title: "The Rank Filtration in Algebraic K-theory".
• Ph.D. evaluated as comparable to a Norwegian doctor philosophiae, March 1992.
• Faculty development course: Teaching and learning in higher education (one year course in pedagogical methods), University of Oslo, 1995.

Engagements, Posts

• Computer programmer at Luleå University, Sweden, 1982.
• Assistant teacher in Mathematics, University of Oslo, 1983-1986.
• Visiting scholar/exchange Ph.D. student at the University of California at Berkeley, August 1989 to May 1990, in connection with the year in Algebraic Topology at the Mathematical Sciences Research Institute (MSRI).
• Research and computer work during military service at Norwegian Defense Research Establishment, Kjeller, Norway, 1990-1991.
• Member of "Graduiertenkolleg für Mathematik", Universität Bielefeld, June to September 1991.
• Adjunkt (Visiting Researcher) in Mathematics, Aarhus University, September 1991 to May 1992.
• Fakultetsstipendiat (Post Doc.), Mathematics Department, University of Oslo, January 1992 to August 1994.
• Visiting researcher, Sonderforschungsbereich 343, "Diskrete Strukturen in der Mathematik", Universität Bielefeld, June 1993, December 1994 and December 1997.
• Post Doctoral Fellow, year in "Topology and Algebraic K-theory", Mittag-Leffler institute, Stockholm, January to June 1994.
• Førsteamanuensis (Associate Professor), Mathematics Department, University of Oslo, August 1994 to April 1998.
• Visiting Associate Professor, Mathematics Department, Stanford University, January to March 1996.
• Visiting Associate Professor, Mathematics Department, University of Chicago, April to May 1996.
• Professor (Full Professor), Mathematics Department, University of Oslo, from May 1st 1998 to present.
• Long-term participant in the programme "New Contexts for Stable Homotopy Theory", Isaac Newton Institute for Mathematical Sciences, Cambridge, September to December 2002.
• Guest researcher, Max-Planck-Institut für Mathematik, Bonn, July 2005 to June 2006.
• Long-term participant in the programme "Equivariant Homotopy Theory in Context", Isaac Newton Institute for Mathematical Sciences, Cambridge, January to June 2025.

Teaching Experience

• Assistant Teacher, Calculus (MA 100, MA 001 and Mathematics for Economists), University of Oslo,
  • four semesters 1983-1986,
  • autumn 1996 and
  • autumn 2000.
• Assistant Teacher, Linear Algebra (Mat 10) and Differential Geometry (Geo 1), Aarhus University,
  • autumn 1991 and
  • spring 1992.
• Assistant Teacher, Linear Algebra (MA 104), University of Oslo,
  • autumn 1992,
  • autumn 1995 and
  • autumn 1997.
• Lecturer, Algebraic Topology (MA 362) and Algebraic Topology I (MAT4530), University of Oslo,
  • autumn 1992,
  • autumn 1993,
  • autumn 1999,
  • spring 2002,
  • spring 2007,
  • spring 2016,
  • spring 2019,
  • spring 2024 and
  • spring 2026.
• Lecturer, Algebraic Topology II (MA 422), University of Oslo,
  • spring 1993 (The image of J in algebraic K-theory),
  • spring 1995 (Characteristic classes),
  • spring 1997 (Homotopy theory),
  • spring 1998 (Manifold models for A-theory),
  • spring 1999 (Elliptic curves and chromatic homotopy theory),
  • autumn 2001 (Elliptic cohomology and topological modular forms) and
  • autumn 2003 (Morava K-theory).
• Lecturer, General Topology (MA 245 and MAT3500/4500), University of Oslo,
  • autumn 1994,
  • autumn 2010,
  • autumn 2018,
  • autumn 2021,
  • autumn 2023 and
  • autumn 2024.
• Lecturer, Introduction to Number Theory (MA 366), University of Oslo,
  • spring 1995,
  • spring 2000 and
  • spring 2003.
• Lecturer, Seminar on Four-manifolds and Seiberg-Witten invariants, University of Oslo, autumn 1995.
• Lecturer, Matrix Theory and its Applications (Math 103), Stanford University, Winter Quarter 1996.
• Lecturer, Calculus (MA 100), University of Oslo, autumn 1996.
• Lecturer, Linear Algebra (MA 104), University of Oslo, autumn 1998.
• Lecturer, Mathematical Methods (MA 001), University of Oslo, autumn 2000.
• Lecturer, Topology graduate seminar on Segal's Conjecture and the Steenrod Algebra, University of Oslo, spring 2001.
• Lecturer, "Waldhausen's stable parametrized h-cobordism theorem", University of Oslo, spring 2004.
• Lecturer, Algebraic Topology II (MAT4540), University of Oslo,
  • autumn 2004 (Cohomology and homotopy theory),
  • autumn 2007 (Cohomology theory, Poincaré duality and Steenrod operations),
  • autumn 2011 (Cohomology theory, Poincaré duality, characteristic classes and exotic spheres),
  • autumn 2012 (Cohomology theory, H-spaces and Hopf algebras),
  • autumn 2016 (Cohomology and homotopy theory),
  • autumn 2017 (Cohomology theory),
  • autumn 2020 (Cohomology theory),
  • autumn 2022 (Cohomology and homotopy theory) and
  • autumn 2025 (Cohomology and homotopy theory).
• Lecturer, Discrete Mathematics (MAT1030), University of Oslo, spring 2005.
• Lecturer, Analysis I (MAT1300), University of Oslo, spring 2009.
• Lecturer, Algebraic K-Theory (MAT9570), University of Oslo, spring 2010.
• Lecturer, Calculus and linear algebra (MAT1110), University of Oslo, spring 2011.
• Lecturer, Algebraic Topology III (MAT9580), University of Oslo,
  • spring 2012 (The Adams spectral sequence, stable homotopy groups of spheres and topological modular forms),
  • spring 2015 (The Adams spectral sequence, stable homotopy groups of spheres and the image of J),
  • spring 2017 (Equivariant orthogonal ring spectra),
  • spring 2018 (Model categories for stable, motivic and equivariant homotopy theory),
  • spring 2021 (Spectral sequences) and
  • spring 2023 (Chromatic homotopy theory).
• Lecturer, Manifolds (MAT4520/MAT9520), University of Oslo,
  • spring 2013 and
  • spring 2022.
• Lecturer, Geometric Structures (MAT4510), University of Oslo, autumn 2015.
• Supervision, Project Course (MAT2000), University of Oslo,
  • spring 2007 (Knut Berg),
  • spring 2009 (Vegard Fjellbo),
  • spring 2012 (Eivind Dahl),
  • spring 2013 (Mats Hansen),
  • spring 2016 (Celia Hacker) and
  • spring 2024 (Dev Vorburger, EPFL).
• Problem-solving sessions, Discrete Mathematics (MAT1030), University of Oslo, spring 2007.
• Problem-solving sessions, Analysis I (MAT1300), University of Oslo, spring 2008.
• Problem-solving sessions, Algebraic Topology II (MAT4540), University of Oslo, autumn 2014.
• Developed course notes for MA 422, "Bildet av J-homomorfien i stabil homotopi og algebraisk K-teori", 80 pages, spring 1993.
• Developed course notes for MA 422, "Manifold models for A-theory", spring 1998.
• Developed course notes for MAT9580, "The Adams Spectral Sequence", 161 pages, spring 2012.
• Developed course notes for MAT9570, "Lecture Notes on Algebraic K-Theory", 252 pages, spring 2010.
• Organized Topology seminar, University of Oslo, most semesters 1994-present.
• Organized SUP working seminar on "Trace formulas", University of Oslo, autumn 2003.

Administrative Experience/External Funding

• Member of Matematisk Fagutvalg, University of Oslo, 1984-1985.
• "Blæstsjef" in Realistforeningen, University of Oslo, 1985-1986.
• Vice chairman in the Norwegian Mathematical Society 1995-1999, Board member 2004-2006.
• Representative in Department board, Department of Mathematics, 1997-1999.
• Representative in Computing committee, Department of Mathematics, 1999-present.
• Project leader for Research Council of Norway (RCN) project "Algebraisk K-teori og topologi", 1998-2000.
• Opponent at Morten Brun's public Ph.D. defense, at Aarhus University, February 1998.
• Participant of EU Marie Curie training site `OMATS' (2.0 MNOK) at the University of Oslo, 2001-2004.
• Project leader for RCN project "K-teori og motivisk kohomologi", with P.A. Østvær, 2000.
• Project leader for RCN project "Algebraisk K-teori og topologi", 2001-2003.
• Project leader for RCN project "Forskningsopphold ved Cambridge", with S. Lunøe-Nielsen, 2002.
• Project leader for RCN strategic university program (SUP) in pure mathematics (SUPREMA): "New contexts for geometry and arithmetic" (12.5 MNOK), University of Oslo, 2003-2006.
• Project leader for RCN outstanding younger investigators (YFF) program in algebraic K-theory and topology: "Brave new rings" (7.1 MNOK), University of Oslo, 2005-2010.
• Opponent at Søren Galatius' public Ph.D. defense, at Aarhus University, August 2004.
• Expert referee for Holger Reich's Habilitation, Universität Münster, spring 2005.
• Member of expert assessment committee for Assistant or Associate Professor position at Odense University, winter 2005/2006.
• Member of "Fachmentorat" for Niko Naumann's Habilitation-project, Universität Regensburg, 2006-2008.
• Opponent at Thomas Kragh's public Ph.D. defense, at Aarhus University, September 2007.
• Expert referee for Danish National Research Foundation, 2008.
• Participant of RCN project "Topology" (8.2 MNOK), 2008-2012.
• Expert referee for Volkswagen Foundation, 2009.
• Participant of RCN project "Topology in Norway" (3.7 MNOK), 2012-2016.
• Participant of RCN project "Special Geometries" (4.0 MNOK), 2015-2018.
• Participant of RCN project "Motivic Hopf equations" (6.8 MNOK), 2016-2021.
• Member of "Fachmentorat" for George Raptis's Habilitation-project, Universität Regensburg, 2018-2020.
• Program leader for Master programs in mathematics (pure and applied), University of Oslo, 2021-2024.
• Member of scientific committee for "Professor Ingerid Dal og Søster Ulrikke Greve Dals Stiftelse", 2025-present.

Master Students Supervised

1. Halvard Fausk, Cand. scient. (Master of Arts) student, spring 1994-June 1995. Thesis title: "The chain rule in functor calculus".
2. Paul Arne Østvær, Cand. scient. (Master of Arts) student, autumn 1995-December 1996. Thesis title: "The Bloch-Lichtenbaum spectral sequence and calculations in algebraic K-theory".
3. Erik Strand, Cand. scient. (Master of Arts) student, autumn 1996-December 1998. Thesis title: "Generalized homological algebra".
4. Eirik Anonsen, Cand. scient. (Master of Arts) student. Proposed thesis topic: "Ring structures on Moore spectra".
5. Sverre Lunøe-Nilsen, Cand. scient. (Master of Arts) student, spring 1998-May 2000. Thesis title: "En ekte involusjon på Waldhausens `rigid tube'-avbildning" ("An honest involution on Waldhausen's rigid tube map").
6. Vigleik Angeltveit, Cand. scient. (Master of Arts) student, autumn 2000-June 2002. Thesis title: "Hopf algebra structure on topological Hochschild homology".
7. Hans Jørgen Riddervold, Cand. scient. (Master of Arts) student, autumn 1999-June 2002. Thesis title: "Å realisere avbildninger som determinanter av buntautomorfier" ("To realize maps as determinants of bundle automorphisms").
8. Jo Raabe, Cand. scient. (Master of Arts) student, spring 2000-(incomplete). Thesis topic: "Analytic behavior and functional equations for Dirichlet series arising in chromatic homotopy theory".
9. Håkon Schad Bergsaker, Cand. scient. (Master of Arts) student, autumn 2003-spring 2005. Thesis title: "K(n)-compact spheres".
10. Knut Berg, Master student, autumn 2007 - March 2009. Thesis title: "Edgewise subdivision and simple maps".
11. Vegard Fjellbo, Master student, autumn 2010 - March 2012. Thesis title: "Normal oppdeling og produkt av endelige simplisielle mengder" ("Normal subdivision and products of finite simplicial sets").
12. Eivind Dahl, Master student, autumn 2012 - May 2015. Thesis title: "2-K-teori og elliptisk kohomologi" ("2-K-theory and elliptic cohomology").
13. Jørgen Olsen Lye, Master student, spring 2015. Thesis title: "Orientation reversing gauge transformations".
14. Gard Olav Helle, Master student, spring 2016 - June 2017. Thesis title: "Pairings and convergence of spectral sequences".
15. Niels Bonten, Master student, spring 2017 - June 2018. Thesis title: "Mod two homology of Q_≥0S⁰ as an E_∞ space".
16. Christian Schive, Master student, 2019 - autumn 2021. Thesis title: "Filtration shifting maps and differentials".
17. Ludovico Maria Dziecielski, Master student, autumn 2022 - June 2024. Thesis title: "Iterated Thom spectra".
18. Riley Hexeberg Mæhle, Master student, autumn 2022 - June 2024. Thesis title: "Commutativity and bordism spectra".

Doctoral Students Supervised

1. Paul Arne Østvær, Dr. scient. (Ph.D.) student, January 1997-August 2000. Thesis title: "Algebraic K-theory; arithmetic and geometry".
2. Sverre Lunøe-Nilsen, Dr. scient. (Ph.D.) student, December 2000-spring 2005. Thesis title: "The Segal conjecture for topological Hochschild homology of commutative S-algebras".
3. Temporary advisor for Gregory Ginot, Ph.D. student from Strasbourg visiting Oslo April-June 2001, under the OMATS Marie Curie training program. Discussion topic: "Lambda operations and the cyclotomic trace map".
4. Håkon Schad Bergsaker, Ph.D. student 2005-January 2009. Thesis title: "Brave new geometry: Foundations and calculations".
5. Thomas Gregersen, Ph.D. student 2006-August 2012. Thesis title: "A Singer construction in motivic homotopy theory".
6. Vegard Fjellbo, Ph.D. student 2012-April 2018. Thesis title: "Nonsingular simplicial sets".
7. Knut Berg, Ph.D. student 2009-(incomplete).
8. Alice Hedenlund, Ph.D. student 2016-January 2021. Thesis title: "Multiplicative Tate spectral sequences".

Post Docs Hosted

1. Stavros Tsalidis, Ph.D. Brown University, EU TMR post doc 1997-1999.
2. Morten Brun, Ph.D. Aarhus University, EU K-Theory network 1998-1999.
3. Iver Ottosen, Ph.D. Aarhus University, EU K-Theory network 1998.
4. Christian Schlichtkrull, Ph.D. Aarhus University, Carlsberg foundation 1998, and RCN SUPREMA post doc 2003-2005.
5. Christian Ausoni, Ph.D. Lausanne University, Swiss research council post doc 1998-1999.
6. Paul Arne Østvær, Ph.D. University of Oslo, UiO post doc 2003-2004.
7. Halvard Fausk, Ph.D. University of Chicago, RCN SUPREMA post doc 2003-2005.
8. Holger Reich, Ph.D. University of Göttingen, RCN SUPREMA visiting researcher 2004.
9. Birgit Richter, Ph.D. Universität Bonn, RCN SUPREMA visiting researcher 2004-2005.
10. Clark Barwick, Ph.D University of Pennsylvania, YFF Brave New Rings postdoc 2006-2008.
11. Steffen Sagave, Ph.D. Universität Bonn, YFF Brave New Rings postdoc 2006-2008.
12. Sverre Lunøe-Nielsen, Ph.D. University of Oslo, YFF Brave New Rings postdoc 2007-2009.
13. Thomas Kragh, Ph.D. Aarhus University, RCN Topology postdoc 2008-2010.
14. Andreas Holmstrom, Ph.D. Cambridge University, KVA scholarship 2012-2013.

Conferences Organized

1. "Symposium on ring spectra, K-theory and trace invariants" at University of Oslo, March 26-28th 1998.
2. "Symposium on Algebraic K-theory and Topology" at University of Oslo, May 25-26th 1999.
3. "NORDTOP 2001 Topology conference", algebraic topology section, Nordfjordeid, August 7th-9th 2001, with B. Jahren.
4. "Topology conference" at University of Oslo, May 15-16th 2003.
5. "SUPREMA start-up meeting" at Soria Moria, Oslo, June 5-6th 2003.
6. "SUPREMA conference" at Thorbjørnrud, Jevnaker, May 27-28th 2004.
7. "The Arithmetic of Structured Ring Spectra", YFF conference at the Barony Rosendal, Norway, August 19th-28th 2005.
8. Arbeitsgemeinschaft mit aktuellem Thema: "Modern Foundations for Stable Homotopy Theory" at Mathematisches Forschungsinstitut Oberwolfach, with Prof. Stefan Schwede, October 2nd-8th 2005.
9. Suprema masterclass with Jacob Lurie: "Elliptic Cohomology and Derived Algebraic Geometry", University of Oslo, August 1th-September 1st 2006.
10. "Topological algebraic geometry workshop", University of Oslo, September 4th-8th 2006.
11. Abel symposium on "Algebraic Topology", University of Oslo, August 5th-10th 2007.
12. "Topology symposium" at Thorbjørnrud, May 21st-23rd 2008.
13. "p-Adic Geometry and Homotopy Theory" at Hotel Alexandra, Loen, August 2nd-8th 2009.
14. "Norwegian Topology Meeting", University of Oslo, December 6th-7th 2012.
15. "Norwegian Topology Meeting", University of Oslo, December 3rd-4th 2015.

Invited Talks at Conferences

1. "Filtering the spectrum K(Z) by rank", talk at Topology meeting, Oberwolfach, September 1992.
2. "K₄(Z) is the trivial group", invited talk at International Conference on Algebra and Topology, Kazimierz, June 1993.
3. "K₄(Z) is the trivial group", main talk at Conference on Algebraic K-theory at Université Paris 7 in July 1994, preceding the 1994 International Congress of Mathematicians in Zürich.
4. "Algebraic K-theory and stable smooth pseudoisotopy of discs", invited talk at Sheffield Homotopy Miniconference, Sheffield University, May 1997.
5. "Two-primary algebraic K-theory of spaces and related spaces of symmetries of manifolds", main talk at A.M.S. Summer Research Conference in Algebraic K-Theory, Seattle, July 1997.
6. "Two-primary algebraic K-theory of rings of integers in number fields", main talk at Symposium on Algebraic K-Theory and Applications, ICTP, Trieste, September 1997.
7. "Two-primary algebraic K-theory of pointed spaces", talks at
   • Polynomial Functors conference, Schloß Ringberg, January 1999,
   • Workshop on Stable homotopy theory and algebraic K-theory, Universität Bielefeld, February 1999, and
   • West Coast Topology meeting, Stanford University, April 1999.
8. "Two-primary algebraic K-theory of pointed spaces", main talk at British Topology Meeting, Swansea, April 1999.
9. "Algebraic K-theory of topological K-theory", invited talk at the conference `Topology, geometry and algebra: interactions and new directions', at Stanford University, August 1999.
10. "Algebraic K-theory of topological K-theory", invited talk at the JAMI 2000 conference `Recent Progress in Homotopy Theory', at Johns Hopkins University, March 2000.
11. "Galois-utvidelser av S-algebraer", two talks at Topology conference, NTNU Trondheim, November 2000.
12. "Two-primary algebraic K-theory of pointed spaces", invited talk at Cornell Topology Festival, May 2001.
13. "Elliptic cohomology and algebraic K-theory of 2-vector spaces", invited talk at International Conference in Algebraic Topology, Isle of Skye, June 2001.
14. "The Smooth Whitehead spectrum of a disc at odd regular primes", invited talk at Conference on high-dimensional manifold topology, ICTP Trieste, June 2001.
15. "Galois theory of commutative S-algebras", main talk at NORDTOP 2001 Topology conference, Nordfjordeid, August 2001.
16. "Galois extensions of `brave new rings'", invited talk at Abel Bicentennial Conference, Oslo, June 2002.
17. "Waldhausen's stable parametrized h-cobordism theorem", invited plenary talk at 2002 Barcelona Conference on Algebraic Topology, July 2002.
18. "Galois descent for the K-theory of commutative S-algebras", talk at Newton Institute Workshop on Axiomatic, enriched and motivic homotopy theory, Cambridge, September 2002.
19. "Galois theory for S-algebras", three lectures in Workshop on Structured Ring Spectra, Universität Bonn/MPI Bonn, September 2004.
20. "Motivic truncation and arithmetic duality for some structured ring spectra", NRW Topology seminar, Wuppertal, October 22nd 2005.
21. "Algebraic K-theory of the fraction field of topological K-theory", Schloß Ringberg, November 3rd 2005.
22. "Smooth symmetries of manifolds and arithmetic of the sphere spectrum", opening colloquium of Graduiertenkolleg 1150, Homotopy and Cohomology, Bonn, November 18th 2005.
23. "Topological logarithmic structures", Topology symposium, Bergen, June 12th 2007.
24. "Topological logarithmic structures, I & II", two talks at "New Topological Contexts for Galois Theory and Algebraic Geometry" conference at Banff International Research Station, March 12th and 13th 2008.
25. "Topological Hochschild homology of topological modular forms", Nordic Topology Meeting, NTNU Trondheim, November 2008.
26. "Motivic complexes and the rank filtration", Topology Symposium, Bergen, June 2010.
27. "Introduction to redshift", talk at Topology meeting, Oberwolfach, September 2011.
28. "Redshift", Nordic Topology Meeting, NTNU Trondheim, Desember 2011.
29. "Kan subdivision and products of simplicial sets", Topology Symposium, Bergen, June 2013.
30. "Chromatic Redshift", Introductory Workshop: Algebraic Topology, MSRI, Berkeley, January 2014.
31. "Algebraic K-theory of group rings and topological cyclic homology", Nordic Topology Meeting, NTNU (November 27th 2014).
32. "The Davis-Mahowald spectral sequence", Nils Baas 70, NTNU (December 1st 2016).
33. "Cubical and cosimplicial descent", Ib Madsen 75, Moduli and Traces, Copenhagen (April 21st 2017).
34. "Topological cyclic homology of the second truncated Brown-Peterson spectrum", CIRM/Luminy (January 26th 2023).
35. "The Hahn-Raksit-Wilson even filtration", National Mathematicians meeting 2024, Oslo (September 12th 2024).
36. "Higher arithmetic duality", New horizons for equivariance in homotopy theory, Isaac Newton Institute, Cambridge (May 12th 2025).

Selected Seminar Talks

• "On Torus Knots", talk at seminar on manifolds, University of Oslo, 1984.
• "Equivariant stable homotopy theory and the Segal conjecture", talk at Topology seminar, University of Oslo, 1989.
• "Rank Filtration in Algebraic K-theory", talks at
  • Algebraic topology seminar, MSRI, Berkeley, 1990,
  • K-theory seminar, Universität Bielefeld, 1991, and
  • Topology seminar, Aarhus University, 1991.
• "Functor Calculus", series of 4 lectures at the University of Oslo, 1990.
• "Equivariant K-theory of Spaces", talk at Topology seminar, Aarhus University, 1991.
• "Bökstedt and Madsen's computations of TC(Z, p)", talk in K-theory seminar, University of Oslo, June 1992.
• "Approximating K_*(Z) through degree five", talk at K-theory seminar, Université Paris 7, October 1992.
• "K₄(Z) is the trivial group", talks at
  • Topology seminar, University of Oslo, February 1993,
  • Topology seminar, Aarhus University, May 1993,
  • K-theory seminar, Université Paris 7, May 1993,
  • K-theory seminar, Universität Bielefeld, June 1993,
  • Algebraic K-theory meeting, Oberwolfach, June 1993, and
  • Colloquium, Universität Wuppertal, September 1993.
• "The multiplication on THH(Z)", talk at Mittag-Leffler institute, Stockholm, February 1994.
• "Algebraic K-theory, some applications and computations", colloquium talk at University of Trondheim, AVH, March 1994.
• "TC and K-theory of the two-adic integers", talk at Mittag-Leffler institute, Stockholm, May 1994.
• "The Hatcher-Waldhausen map is an infinite loop map", talk at
  • Topology seminar, University of Oslo, August 1994, and
  • Topology meeting, Oberwolfach, September 1994.
• "Vassiliev's knot invariants", 3 talks at Topology seminar at University of Oslo, October 1994.
• "Algebraic K-theory of the two-adic integers", talk at Topology seminar, University of Oslo, April 1995.
• "Fixed points of topological Hochschild homology at two", talk at Topology seminar, University of Oslo, April 1995.
• "The fiber of the linearization map from A(*) to K(Z)", talks at
  • Topology meeting, Oberwolfach, September 1995, and
  • the University of Chicago, April 1996.
• "Algebraic K-theory of the two-adic integers", talks at
  • Algebraic K-theory and Homotopy Theory meeting, Oberwolfach, November 1995,
  • Stanford University, January 1996,
  • Northwestern University, April 1996,
  • the University of Chicago, May 1996,
  • M.I.T., May 1996, and
  • Algebraic K-theory meeting, Oberwolfach, June 1996.
• "Introduction to topological cyclic homology", two talks at the University of Chicago, April 1996.
• "Two-primary algebraic K-theory of rings of integers in number fields", talks at
  • Topology seminar, University of Oslo, November 1996,
  • Topology meeting, Oberwolfach, September 1997,
  • Topology seminar, Aarhus University, December 1997, and
  • Algebraic Geometry and Number Theory seminar, Université de Paris Sud XI, Orsay, February 1998.
• "The chain rule in functor calculus", talk at Topology seminar, University of Oslo, February 1997.
• "Equivariant stable homotopy theory", series of 4 talks at Topology seminar, University of Oslo, April 1997.
• "Homology and cohomology operations", series of 3 talks at Topology seminar, University of Oslo, November 1997.
• "Cohomology of the smooth Whitehead spectrum", talks at
  • Topology seminar, Universität Bielefeld, December 1997,
  • Topology seminar, University of Oslo, January 1998,
  • Symposium on ring spectra, K-theory and trace invariants, Oslo, March 1998,
  • Barcelona conference on Algebraic Topology, Bellaterra, June 1998 and
  • Topology meeting, Oberwolfach, September 1998.
• "K₄(Z) is the trivial group, revisited", talk at Topology seminar, University of Oslo, March 1998.
• "Étale avbildninger av S-algebraer", talk at Topology seminar, University of Oslo, March 2000.
• "Algebraic K-theory of topological K-theory", talks at
  • ETH Zürich and
  • Université Lausanne, June 2000.
• "Algebraic K-theory of finitely presented ring spectra", talk at Topology meeting, Oberwolfach, September 2000.
• "Symmetric spectra", five talks at Topology seminar, University of Oslo, October 2000.
• "Elliptic cohomology and algebraic K-theory of 2-vector spaces", talk at topology seminar, EPFL Lausanne, April 2001.
• "Two-vector bundles and elliptic objects", talk at the Mathematical Institute, Oxford University, November 2002.
• "Galois theory of commutative S-algebras", talk at Homotopy Theory meeting, Oberwolfach, March 2003.
• "Stably dualizable groups", talk at Topology conference, University of Oslo, May 2003.
• "Trace formulas for flows", 5 talks in SUPREMA working seminar, University of Oslo, September-October 2003.
• "Smooth symmetries of manifolds and arithmetic of the sphere spectrum", Hamburg colloquium November 22nd 2005.
• "Arithmetic of the sphere spectrum", Göttingen colloquium, February 2nd 2006.
• "Mahowald's infinite family", Bonn Arbeitsgemeinschaft, February 9th 2006.
• "Arithmetic properties of some brave new rings", Oberseminar Topologie, MPIM-Bonn, March 20th 2006.
• "Arithmetic properties of some brave new rings", Fachbeirat presentation, March 29th-30th 2006.
• "K-theory of the fraction field of K-theory", Topology seminar, Universität Bielefeld, April 3rd 2006.
• "Towards a motivic Segal conjecture", 5 lectures, Topology seminar, University of Oslo, September-October 2014.
• "Spaces of manifolds", Topology seminar, Oslo, February 5th 2016.
• "The weight and rank filtrations", 2 lectures, Oslo, October 21st and 28th 2016.
• "The stable parametrized h-cobordism theorem", Topology seminar, Oslo, February 21st 2017.
• "Cubical and cosimplicial descent", Topology seminar, Oslo, May 3rd 2017.
• "The Adams spectral sequence for topological modular forms", 4 lectures, Oslo, October-November 2017.
• "THH of F_p and Z", Topology seminar, Oslo, February 21st 2018.
• "TC of F_p", Topology seminar, Oslo, March 7th 2018.
• "TC of Z", Topology seminar, Oslo, March 8th 2018.
• "Logarithmic de Rham-Witt complexes", Topology seminar, Oslo, March 21st 2018.
• "Duality for topological modular forms", Homotopy theory meeting, Oberwolfach, August 2019.
• "Norms of Real bordism", eCHT seminar, October 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 2022.
• "The Segal conjecture for smash powers", Topology seminar, Oslo, September 9th 2024.
• "The Segal conjecture for smash powers, II", Topology seminar, Oslo, September 30th 2024.
• "Theorems of Mahowald and Hopkins-Mahowald", Topology seminar, Oslo November 21st 2025.
• "Introduction to spectral sequences I, II", Topology seminar, Oslo January/February 2026.
• "The Bökstedt spectral sequence", Topology seminar, Oslo February 2026.
• "The Pirashvili-Brun-Höning spectral sequence", Topology seminar, Oslo March 2026.
• "Topological cyclic homology I, II", Topology seminar, Oslo April 2026.

Guest Lecture Series

• "Elliptic Cohomology", 6 lectures at NTNU, Trondheim, February 2001.
• "Topological Modular Forms", 6 lectures at NTNU, Trondheim, March 2001.
• "The stable parametrized h-cobordism theorem", 6 lectures at University of Bonn, January/February 2006.

Popularized Talks

• "Knuter og Uknuter", talk for high school students, at University of Oslo, March 1993.
• "Vassilievs Knuteinvarianter", talk for visiting students from Aarhus University, at University of Oslo, October 1994.
• "Fermats Siste Teorem", talk for high school teachers at
  • Allmennpedagogisk dag, University of Oslo, January 1995, and
  • as popularized talk during Bjørnegildet, March 1995.
• "Algebraisk K-teori og symmetrier av mangfoldigheter", 2 talks at Ski og Matematikk winter conference, Rondablikk, January 1998.
• "Knuteteori", talk for finalists of the N.H. Abel competition, March 1998.
• "Smultringsspiraler", mathematical modeling for an artistic project by Verksmester Knut Natvik, Kunsthøgskolen i Oslo, May 2000.
• "Ren og skjær matematikk", talk at Norsk PEN and MUNIN seminar at the Nobel institute in Oslo, June 2000.
• "Vidunderlige nye ringer", talk at The Norwegian Mathematical Society's year meeting in Oslo, March 2002.
• "Riemann-hypotesen", colloquium talk in Oslo, May 2002.
• "The work of Jean-Pierre Serre in algebraic topology", colloquium talk in Oslo, May 2003.
• "Om Atiyah-Singer indeks-teoremet", official presentation of the work of the Abel prize winners for 2004, at the Norwegian Academy of Science and Letters, March 2004.
• "Spaces of Manifolds", Abel in Zürich, ETH Zürich, January 2016.
• "Fermat, Taniyama-Shimura-Weil and Andrew Wiles", two colloquium lectures in Oslo, May 2016.
• "Andrew Wiles, modularitetsformodningen og Fermats siste sats", lecture at the Norwegian Mathematical Council's yearly meeting, Hamar, September 2016.
• "Yves Meyer: restoring the role of mathematics in signal and image processing", two colloquium lectures in Oslo, May 2017.
• "On the Langlands program", colloquium lecture in Oslo, May 2018.

Contributions in Media

• Radio interview in "Dagsnytt atten", NRK P1, concerning Simon Singh's book Fermat's Last Theorem. October 1998.
• Portrait interview in "Apollon", Science and Research Magazine from the University of Oslo, vol. 2/2000, pp. 24-28.
• Popularized article "Vidunderlige nye ringer" in "Apollon", Science and Research Magazine from the University of Oslo, vol. 3/2000, pp. 29-31.
• End report of NFR project "Algebraisk K-teori og topologi" presented in "Forskningsrådets årsrapport 2000" as an example of a well completed project.
• Consulted for article "Matteproblem nesten løst" on the solution of the Arf-Kervaire invariant problem, at forskning.no, May 12th 2009.

Competitions

• Niels Henrik Abel konkurransen. Three 1st prizes and one 2nd prize, 1981-1984.
• Chemistry Olympics, Timisoara, Rumania, 1983. 3rd prize.
• Mathematics Olympics, Prague, Czechoslovakia, 1984. 3rd prize.
• Young Scientists competition in Norway, and International Final in Eindhoven, Holland, 1984. 1st prize in both.

Grants, Fellowships, Prizes

• Kong Haakon den 7des utdannelsesstipend for norsk ungdom, 1985.
• Several student scholarship grants, University of Oslo, 1984-1986.
• Scientific stipends, University of Oslo, 1985-1993, from H. Ths. Heftyes legat, Hans E. Hurums minnefond, Professor S. A. Sexes legat (3 times), Stud. med. Morten Dedekam Harboes legat (2 times), Gustav Adolf Bruuns legat, and Professor Fredrik Petersens fond.
• Fulbright-Hays Fellowship for graduate studies in Mathematics in U.S.A., 1986-1987.
• NTNF (Royal Norwegian Council for Scientific and Industrial Research), Research fellowship for advanced studies in U.S.A., 1986-1987.
• Several honor fellowships from Princeton University, 1986-1990.
• Norway-America Association, Cornelia Glomme-Drolsom Award for Ph.D. studies in Mathematics at Princeton University, 1987-1988.
• NAVF (Norwegian Research Council for Science and the Humanities), Dr. stipend (Doctoral fellowship) for Ph.D. studies in Mathematics at Princeton University, 1987-1990.
• Professor Ingerid Dal og søster Ulrikke Greve Dals pris for humanistisk forskning, 1999.

Membership in Scientific Societies

• Norwegian Mathematical Society, 1980-1981 and 1992-present.
• American Mathematical Society, 1986-1991.
• Det Kongelige Norske Videnskabers Selskab, elected member from 2003.
• The Norwegian Academy of Science and Letters, elected member from 2009.
• The K-Theory Foundation, elected member from 2025.