# Bjørn Ian Dundas

Professor
• E-mailBjorn.Dundas@uib.no
• Phone+47 55 58 28 27+47 976 22 576
Realfagbygget, Allégt. 41
Postboks 7803
5020 Bergen
Textbook
• 2018. A short course in differential topology. Cambridge University Press.
• 2020. Towards an understanding of ramified extensions of structured ring spectra. Mathematical proceedings of the Cambridge Philosophical Society (Print). 435-454.
• 2018. Towards an understanding of ramified extensions of structured ring spectra. Mathematical proceedings of the Cambridge Philosophical Society (Print). 1-20.
• 2018. On higher topological Hochschild homology of rings of integers. Mathematical Research Letters. 489-507.
• 2018. Cubical and cosimplicial descent. Journal of the London Mathematical Society. 439-460.
• 2017. Higher Hochschild homology is not a stable invariant. Mathematische Zeitschrift. 145-154.
• 2017. Finite generation and continuity of topological Hochschild and cyclic homology. Annales Scientifiques de l'Ecole Normale Supérieure. 201-208.
• 2013. Ring completion of rig categories. Journal für die Reine und Angewandte Mathematik. 43-80.
• 2013. Integral excision for K-theory. Homology, Homotopy and Applications. 1-25.
• 2011. Stable bundles over rig categories. Journal of Topology. 623-640.
• 2011. Higher topological cyclic homology and the Segal conjecture for tori. Advances in Mathematics. 1823-1874.
• 2010. Covering homology. Advances in Mathematics. 3166-3213.
• 2008. Excision for K-theory of connective ring spectra. Homology, Homotopy and Applications. 29-39.
• 2008. Divisibility of the Dirac Magnetic Monopole as a Two-Vector Bundle over the Three-Sphere. Documenta Mathematica. 795-801.
• 2004. Two-Vectorbundles and Forms of Elliptic Cohomology. Cambridge University Press. 18-45.
• 2004. The cyclotomic trace for S-algebras. Journal of the London Mathematical Society. 659-677.
• 2003. Motivic functors. Documenta Mathematica. 489-525.
• 2003. Enriched functors and stable homotopy theory. Documenta Mathematica. 409-488.
• 2001. Localization of V-categories. Theory and Applications of Categories. 284-312.
• 2000. The cyclotomic trace for symmetric monoidal categories. Contemporary Mathematics. 121-143.
• 2000. The Cyclotomic trace for symmetric monoidal categories. Contemporary Mathematics. 121-144.
• 1999. K-theory of simplicial rings and degreewise constructions. K-theory. 77-92.
• 1999. Degreewise K-theory. K-theory. 77-92.
• 1998. K-theory theorems in topological cyclic homology. Journal of Pure and Applied Algebra. 23-33.
• 1998. K-theory theorems in topological cyclic homology. Journal of Pure and Applied Algebra. 23-33.
• 1998. Continuity of K-theory: an example in equal characteristics. Proceedings of the American Mathematical Society. 1287-1291.
• 1998. Continuity of K-theory : an example in equal characteristics. Proceedings of the American Mathematical Society. 1287-1291.
• 1997. Relative K-theory and topological cyclic homology. Acta Mathematica. 223-242.
• 1997. Relative K-theory and topological cyclic homology. Acta Mathematica. 223-242.
• 1996. Topological Hochschild homology of ring functors and exact categories. Journal of Pure and Applied Algebra. 231-294.
• 1996. Topological Hochschild homology of ring functors and exact categories. Journal of Pure and Applied Algebra. 231-294.
• 1994. Stable K-theory and topological Hochschild homology. Annals of the Institute of Statistical Mathematics. 685-701.
• 1994. Stable K-theory and topological Hochschild homology. Annals of Mathematics. 685-701.
• 1993. Fibrations and homology sphere bordism. Mathematica Scandinavica. 20-28.
• 1993. Fibrations and homology sphere bordism. Mathematica Scandinavica. 20-28.
Report
• 2006. Higher topological cyclic homology. .
• 2003. Two-vector bundles and forms of elliptic cohomology. .
Lecture
• 2020. Motivic Hochschild homology.
• 2015. Abelprisen til Nash og Nirenberg.
Popular scientific lecture
• 2016. What does it mean that two things are equal?
• 2012. Topologi: matematikkens romforskning.
• 2011. Until this paper by Milnor it was thought that. .
• 2008. Hvilken fasong har universet?
• 2007. Sfærespekteret.
• 2007. Kalkulus.
• 2006. Sfaerespekteret.
• 2020. Motivic Hochschild homology.
• 2018. The geometric diagonal.
• 2018. The Pullback square.
• 2018. Motivic Hochshild homology.
• 2018. Continuity of homology and K-theory.
• 2017. Shapes of Spaces I-IV and the sphere spectrum.
• 2017. Higher Hochschild homology is not a stable invariant.
• 2017. Cyclic products.
• 2016. The trace map.
• 2016. Some calculations of iterated Hochschild homology.
• 2016. A calculation of $T^n\otimes H\mathbb F_p$.
• 2015. Sommerskole, bl.a. foredraget "Rognes' redshift conjecture".
• 2015. Ind Spaces.
• 2015. Detecting Periodic Classes.
• 2015. Being lucky in the category of commutative ring spectra.
• 2014. Redshift.
• 2014. Higher topological Hochschild homology.
• 2014. Continuity of THH.
• 2013. Continuity of (topological) Hochschild and cyclic homology (j/w Matthew Morrow).
• 2012. Higher topological Hochschild homology.
• 2012. Equivariant commutative ring spectra.
• 2012. Algebraic K-theory.
• 2011. Two-vector bundles, and the splitting of the Dirac Monopole.
• 2011. The cyclotomic trace and operad actions.
• 2011. Smash powers of ring spectra.
• 2011. Smash powers of commutative ring spectra.
• 2011. Integral excision in algebraic K-theory.
• 2011. A survey of trace methods in algebraic K-theory.
• 2010. Two vector bundles and the splitting of the Dirac monopole over the three sphere.
• 2010. Redshift and equivariance.
• 2008. Witt Rings.
• 2008. Two-vector bundles I & II.
• 2008. Recent progress on two vector bundles.
• 2008. Mini-cours: 2-vector bundles.
• 2008. Higher Topological Cyclic Homology.
• 2006. Virtual 2-vector bundles defines an "elliptic cohomology theory".
• 2006. Excision in K-theory.
• 2006. Excision in K-theory.
• 2007. Motivic homotopy theory: Lectures at a summer school in Nordfjordeid, Norway, August 2002. Springer.
Non-fiction book
• 2013. The local structure of algebraic K-theory. Springer.
• 2003. Gummistrikkgeometri - fra matematikkens magiske skattekiste. Midtnordisk Vitensenter.
Interview
• 2018. Abelprisen 2018, Intervju med Robert Langlands.
• 2017. Abelprisen 2017- intervju med prisvinner.
• 2016. Forskergruppe får prestisjeopphold.
Programme participation
• 2011. Abels tårn og om Leonard Euler.
• 2016. A calculation of $T^n\otimes HF_p$.