Bjørn Ian Dundas
 Office
 4A4d Realfagbygget, Allegaten 41, 4 etg
 Email address:
 dundas
at math.uib.no
 Phone:
 (47) 5558 2827
 Facsimile:
 (47) 5558 9672
 Snail mail address:
 Department of Mathematics
University
of Bergen
Postboks 7800
5020 Bergen

 Home
 Address:
 A. Solheia
7
 N5251 Søreidgrend
 Phone:
 home: (47) 5512 0614,
 mobile: (47) 976 22 576

Scientific Interests
(Algebraic) Ktheory, (motivic or stable) homotopy theory,
(topological) cyclic homology, and so
on.
If you don't feel that this list tells you very much, you may
consult my pages Topologi på roterommet, "Romforskning", Goodwillie calculus or The sphere spectrum (some in Norwegian,
they are really my notes for some popular lectures) where I try to give a brief and
inadequate idea of various aspects of topology. You may also benefit from
the "survey articles for the general public" posted
on Hopf and the Wikipedia topology, algebraic
topology and algebraic
Ktheory entries.
For what it's worth, my published papers have been
classified according to the AMS Mathematics Subject
Classification under 11, 13,
14, 16, 18, 19,
55, 57 and 81, with 19 by far the most frequent.
Classes
Books

The Local structure of algebraic Ktheory
Bjørn Ian Dundas, Tom G. Goodwillie and Randy
McCarthy
Algebra and Applications,
Springer, 2012, XV, 435 p. 5 illus. ISBN 9781447143925

An introduction used for the course on
manifolds at NTNU the last ten years. Since it has been available on
the internet it has been used at several universitites, either
as main text or as supplementary reading (and kindly
mentioned in the Mathematical Intelligencer).
The most recent version can always be found as http://www.math.uib.no/~dundas/dt/dtcurrent.pdf.
The version as of
Jan. 10, 2013 (the one that was most recent at the beginning of
the spring semester 2013),
Jan. 23, 2013 (minor modification fixing up some typos).
If you need older
versions, you can find some here.
Please report any known issues with
the current or metastable edition asap.
If you plan to use these notes as course material or
otherwise have them tested on a wider audience, or if you
just have some comments on the notes, please contact me. (old versions:
(2007, A4, 2002,
US letter size, 2002))

Dundas, B.I., Levine, M., Østvær, P.A., Röndigs, O., Voevodsky,
Unversitext/Springer 2007. X 226p, Jahren (ed). ISBN 9783540458975
"This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject.
Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject."

joint with Nils Kristian Rossing. Vitensenteret i
Trondheim, juli 2003, ISBN 8292088199. A popular
exposition of some topological features (in Norwegian)
written for teachers and other interested laymen. It can be
ordered from Vitensenteret by sending a
mail to postkasse
at viten.ntnu.no.
Papers
 Dundas, Bjørn Ian. Fibrations and homology sphere bordism.
Math. Scand. 72 (1993), no. 1, 2028. 57Q20 (55R05)
 Dundas, Bjørn Ian; McCarthy, Randy. Stable $K$theory and topological
Hochschild homology. Ann. of Math. (2) 140 (1994),
no. 3, 685701. 19D55 (18G60 19D06)
 Dundas, Bjørn Ian; McCarthy, Randy. Topological Hochschild homology of ring
functors and exact categories. J. Pure Appl. Algebra
109 (1996), no. 3, 231294. 19D55 (16E40 18G30 18G60)
 Dundas, Bjørn Ian. Relative Ktheory and topological cyclic
homology. Acta Math. 179 (1997), no. 2, 223242.
19D55
 Dundas, Bjørn Ian. Ktheory theorems in topological cyclic
homology. J. Pure Appl. Algebra 129 (1998), no. 1,
2333. 19XX (16Exx)
 Dundas, Bjørn Ian. Continuity of Ktheory: an example in equal
characteristics. Proc. Amer. Math. Soc. 126 (1998),
no. 5, 12871291. 11Sxx (13Jxx 19D45 19D55)
 Dundas, Bjørn Ian. Degreewise Ktheory. Ktheory 18 (1999),
7792. 19D06, 18G30, 19D25, 16N20
 Dundas, Bjørn Ian. The Cyclotomic trace for symmetric monoidal
categories. in "Geometry and Topology: Aarhus
(1998)", 121143, Contemp. Math., 258, Amer. Math. Soc.,
Providence, RI, 2000. 19D23 (18D20 19D55 55P43)
 Dundas, Bjørn Ian. Localization of Vcategories.
Theory Appl. Cat. 8 (2001), pp. 284312. 18D20 (18G55)
 Dundas, Bjørn Ian; Röndigs, Oliver and
Østvær, Paul Arne, Enriched functors and stable homotopy
theory.
Documenta
Mathematica, Vol. 8 (2003), 409488. 55P42 (18D20 55P91
55U35)
 Dundas, Bjørn Ian; Röndigs, Oliver and
Østvær, Paul Arne, Motivic Functors, Documenta
Mathematica, Vol. 8 (2003), 489525. 55P42 (14F42)
 Baas, Nils A.; Dundas, Bjørn Ian and Rognes, John
Twovector bundles and forms of elliptic
cohomology. In Topology, Geometry and Quantum
Field Theory, LMS Lecture note series 308, Cambridge University Press. Ed. Ulrike
Tillmann (2004), p. 1845. 55N34 (18D05 57T30)
 Dundas, Bjørn Ian, The cyclotomic trace for
Salgebras. J. London Math. Soc. (2) 70 (2004),
no. 3, 659677. 19D23 (18D20 19D55 55P43)
 Dundas, Bjørn Ian, Prerequisites in
algebraic topology in "Motivic Homotopy
Theory" Unversitext/Springer 2007,
Dundas/Levine/Østvær/Röndigs/Voevodsky. Jahren (ed).
 Dundas, Bjørn Ian and Kittang, Harald Excision
for Ktheory of connective ring spectra, Homology, Homotopy and Applications, vol. 10(1), 2008,
pp. 29  39
 Ausoni, Christian; Dundas, Bjørn Ian; Rognes, John Divisibility of the Dirac magnetic monopole as a twovector bundle over the threesphere. Doc. Math. 13 (2008), 795801.
 Brun, Morten; Carlsson, Gunnar and Dundas, Bjørn
Ian Covering homology. Adv. Math. 225 (2010), 31663213.
 Carlsson, Gunnar; Douglas, Cristopher L. and Dundas, Bjørn
Ian Higher topological cyclic homology and the Segal
conjecture for tori. Adv. Math. 226 (2011), 18231874.
 Baas, Nils A.; Dundas, Bjørn Ian;
Richter, Birgit and Rognes, John
Stable bundles over rig categories.
J. Topology 4 (2011), 623640.
 Baas, Nils A.; Dundas, Bjørn Ian;
Richter, Birgit and Rognes, John
Ring completion of rig categories.
J. Reine Angew. Math. 674 (2013), 43  80
 Dundas, Bjørn Ian and Kittang, Harald Integral excision
for Ktheory, Homology, Homotopy and Applications, vol. 15(1), (2013),
pp. 1  25.
Preprints.
Finite generation and continuity of topological Hochschild and cyclic homology, Dundas and Morrow. Submitted
The cyclotomic trace preserves operad actions, Dundas. Retracted: the homotopy nerve is only monoidal wrt. the smash based over the positive reals (not the one claimed in the pp), but the appropriate mapping space in TC demands a fibrancy condition that is not known to be monoidal. At present the only known fix is to abandon the homotopy nerve and go with the more restrictive setup in The Cyclotomic trace for symmetric monoidal categories using EKMMspectra.
On higher topological Hochschild homology of rings of integers, Dundas, Lindenstrauss and Richter. Submitted
Norwegian topology symposia, and some other conferences I have
(co)organized or given lecture series in.
 The schedule for the mini symposium on ring
spectra, KTheory and trace invariants in Oslo, March
26th28th 1998.
 The schedule for the mini symposium in algebraic
Ktheory and homotopy theory in Trondhjem, November 5th6th
1998.
 The schedule for the mini symposium on
algebraic KTheory and topology in Oslo, May 25th26th
1999.
 The schedule for the mini symposium on topology in
Trondhjem, November 16th17th 1999.
 The workshop on mathematics education for
engineering students in Trondhjem, May 2930, 2000.
 The schedule for the mini symposium on topology in
Trondhjem, November 9th10th 2000.
 The ski and mathematics meeting in Oppdal January
4th7th 2001.
 The summer school Motivic homotopy theory Sophus Lie
Conference Center, Nordfjordeid, Norway, 12.16. August
2002
 The ski and mathematics meeting at Rondablikk January
9th12th 2003.
 The schedule for the topology meeting in Oslo,
May 15th16th 2003.
 The schedule
for the topology symposium in Trondhjem, November
25th26th 2004.
 Homological methods in algebra and topology, session at the
24th Nordic and 1st FrancoNordic Congress of
Mathematicians, Reykjavik, Iceland, January 6th  9th 2005
 The schedule for the topology symposium in Oslo, June
2nd3rd 2005.
 The Nordic Conference in Topology in Trondhjem, November
24th25th 2006.
 The topology symposium in Bergen, June
11th12th 2007.
 The Abel symposium in Oslo, August
5th10th 2007.
 Spring symposium, May 21st23rd 2008 at Thorbjørnrud near Oslo
 Nordic topology
meeting, November 27  28 2008, Trondheim
 The algebraic
topology session at the 25th Nordic and 1st
BritishNordic congress of Mathematicians, 2009.
 The Nordic topology symposium in Bergen, June
1011 2010.
 The Algebra, Topology and Fjords!
Summer School,
Nordfjordeid, Norway June 3rd  11th 2011.
 The Advances in Ktheory West coast algebraic topology
summer school 2012, Stanford University, July 1621 2012
 The Topology symposium in Bergen, June
1314 2013.
 The Invariants of Structured Ring Spectra European Talbot Workshop 2015, 28 June  4 July, 2015
Klosters, Switzerland
Current students
Kristian Alfsvåg (PhD, 2019) 
Kim Haugland (master, 2016) 
Anders Husebø (PhD, 2018) 
Valentin Krasontovitsch (PhD, 2016) 
Stefano Piceghello (PhD, 2019) 
Andrea Tenti (master, 2016) 
Former students at UiB.
List of old
projects at NTNU.
RCN projects
Computational aspects of Univalence (PI Marc Bezem (Dept. of Computer Science, UiB) and BID)
Topology in Norway, (Current RCN
project, PI by C. Schlichtkrull)
Topology, (RCN
project 20082012, PI BID)
TiN,
(RCN
project "Topology in Norway", 20042007, PI BID)
Bjørn Ian Dundas
Last modified: Last modified: Thurs Dec 17 13:48:12 CET 2013