Daniel Dugger
Department of Mathematics, University of Oregon
Fenton Hall, Room
Eugene, OR 97403
EMail: ddugger AT math DOT uoregon DOT edu
Phone: (541)3464790
Currently I'm a professor in the math department at the
University of Oregon.
Research interests: Algebraic topology, Ktheory,
commutative algebra.
Here's a
Curriculum Vita.
Teaching
I am not teaching this quarter.
Research Papers
Click for pdf files (or in some cases abstracts and dvi files).

Involutions in the topologists' orthogonal group
, preprint, December 2016.

Involutions on surfaces
, J. Homotopy Relat. Struct. 14 (2019), no. 4, 919992.

Z/2equivariant and Rmotivic stable stems
, Proc. Amer. Math. Soc. 145 (2017), no. 8, 36173627.

Lowdimensional MilnorWitt stems over R
, Annals of Ktheory 22 (2017), 175210.

Bigraded cohomology of Z/2equivariant Grassmannians
, Geometry and Topology 19 (2015), no. 1, 113170.

Grothendieck groups of complexes with nullhomotopies, J. Ktheory
13 (2014), no. 3, 517531.

Coherence for invertible objects and multigraded homotopy rings,
Alg. Geom. Top. 14 (2014), 10551106.

Motivic Hopf elements and relations, joint with D. Isaksen.
New York J. Math. 19
(2013),
823871. Link.

Mapping spaces in quasicategories,
joint with D. Spivak.
Algebraic and Geometric Topology 11 (2011), no. 1, 263325.

Rigidification of quasicategories,
joint with D. Spivak.
Algebraic and Geometric Topology 11 (2011), no. 1, 225261.

The motivic Adams spectral sequence,
joint with D. Isaksen.
Geometry and Topology 14 (2010), no. 2, 9671012.

A curious example of two model categories and some associated
differential graded algebras
,
joint with B. Shipley. Algebr. Geom. Topol. 9 (2009), no. 1, 135166.

Eigentheory of CayleyDickson algebras,
joint with D. Biss, J. D. Christensen, and D. Isaksen.
Forum Mathematicum.21 (2009), no. 5, 833851.
 Etale
homotopy theory and sumsofsquares formulas, joint with
D. Isaksen. Math. Proc. Cambridge Philos. Society. 145 (2008), 125.

Large annihilators in CayleyDickson algebras II,
joint with D. Biss, J. D. Christensen, and D. Isaksen.
Bol. Soc. Mat. Mexicana (3) 13 (2007), no. 2, 269292.

Classification spaces of maps in model categories.
Preprint, 2006.

Postnikov extensions of ring spectra, joint with B. Shipley.
Algebr. Geom. Top. 6 (2006), 17851829.
 Topological
equivalence for differential graded algebras, joint with
B. Shipley. Adv. in Math. 212, no. 1 (2007), 3761.

Enriched model categories and an application to homotopy endomorphism
spectra, joint with B. Shipley. Theory and
Application of Categories 18 (2007), no. 15, 400439.
 Large
annihilators in CayleyDickson algebras, joint with D. Biss and
D. Isaksen. Communications in Algebra 36 (2008), no. 2, 632664.
 Spectral
enrichments of model categories. Homology, Homotopy,
Appl. 8 (2006), no. 1, 130.
 Algebraic
Ktheory and sumsofsquares formulas, Documenta Math. 10 (2005),
357366.
 Motivic
cell structures, joint with D. Isaksen. Algebr. Geom. Top. 5
(2005), 615652.

The Hopf condition for bilinear forms over arbitrary fields, joint
with D. Isaksen. Ann. of Math. (2) 165 (2007), no. 3, 943964.

An AtiyahHirzebruch spectral sequence for KRtheory.
Ktheory 35 (2005), no. 34, 213256.

Ktheory and derived equivalences, joint with B. Shipley.
Duke Math. J. 124 (2004), no. 3, 587617.
 Hypercovers
and simplicial presheaves, joint with S. Hollander and D. Isaksen.
Math. Proc. Cambridge Philos. Soc. 136 (2004), no. 1, 951.

Weak equivalences of simplicial presheaves, joint with
D. Isaksen. In "Homotopy theory: relations with algebraic geometry,
group cohomology, and algebraic Ktheory", 97113,
Contemp. Math. 346, Amer. Math. Soc.

Topological hypercovers and A^1realizations, joint with
D. Isaksen.
Math. Z. 246 (2004), no. 4, 667689.

Universal homotopy theories. Adv. Math. 164 (2001), no. 1,
144176.

Combinatorial Model Categories Have Presentations.
Adv. Math. 164 (2001), no. 1, 177201.

Replacing Model Categories with Simplicial Ones,
Trans. Amer. Math. Soc. vol. 353 (2001), #12, 50035027.

Betti Numbers of Complete Intersections, Ill. J. Math. vol
44, #3 (2000).
Short Notes and Expository Papers

Stable categories and spectra via model categories, (2020). [This
is to be a chapter in the book Stable Categories and Structured Ring
Spectra, edited by Blumberg, Gerhardt, and Hill.]

Notes on the Milnor conjecture, (2003).

Notes on Deltagenerated spaces, (2003).

Multiplicative structures on homotopy spectral sequences I, II. Preprint,
2003.

The Zariski and Nisnevich descent theorems. Preprint, 2001.

The Polar Form of the Gradient. 1999.

Sheaves and Homotopy Theory. Abandoned draft, not to be
taken too seriously (but still
pleasant reading), 1999.
Longer Expository Projects
These projects are incomplete, and moving along somewhat slowly.

A primer on homotopy colimits (2008).
This is intended to be an introduction to homotopy colimits,
accessible to graduate students. The first few sections are fairly
solid, but in the later sections there may be lots of silly mistakes.
Last updated in January 2017.

Navigating the motivic world (2008).
This is growing into a book on motives, algebraic Ktheory, and
all kinds of related topics. Several chapters are partially complete,
but only the first two have been revised carefully.

Quantum theory for topologists (2011).
This is based on my attempt to learn about quantum field theory and
its connections to topology. Some of the text is very rough, and the
sections haven't really been merged together well yet. In particular,
the introduction doesn't currently connect with anything else in the
text!

A geometric introduction to Ktheory (2014).
This is one day going to be a textbook on Ktheory, with a particular
emphasis on connections with geometric phenomena like intersection
multiplicities. Somewhat rough, very much a work in progress.
Some Pictures
These are mostly pictures from hiking trips around Oregon.
Diamond Peak
Oregon
dunes, outside of Reedsport
The lower
foothills in the spring
Mt. Washington
Smith Rock:
Pic 1 ,
Pic 2 .
The Painted Hills:
Pic 1 ,
Pic 2 .
Jefferson Park in the fall
North and Middle Sister, from Golden Lake
Wildflowers in the Coastal Range
You can email me:
ddugger AT math.uore remove this part gon.edu
Back to the math department's home
page.
