Currently I'm a professor in the math department at the University of Oregon.

Research interests: Algebraic topology, K-theory, commutative algebra.

Here's a Curriculum Vita.

Research Papers

Click for pdf files (or in some cases abstracts and dvi files).

• RO(G)-graded Bredon cohomology of Euclidean configuration spaces, joint with Christy Hazel, 2024 preprint.
• The multiplicative structure on motivic homotopy groups, joint with B.I. Dundas, D.C. Isaksen, and P.A. Ostvaer, 2022 preprint, to appear in Algebraic and Geometric Topology.
• Equivariant Z/l-modules for the cyclic group C_2, joint with Christy Hazel and Clover May, J. Pure and Appl. Algebra 228 (2024), no. 3, Paper No. 107473, 48pp.
• Gysin functors, correspondence categories, and the Grothendieck-Witt category, Theory and Applications of Categories 38 (2022), no. 6, 156-213.
• Involutions on surfaces , J. Homotopy Relat. Struct. 14 (2019), no. 4, 919--992.
• Z/2-equivariant and R-motivic stable stems , Proc. Amer. Math. Soc. 145 (2017), no. 8, 3617-3627.
• Low-dimensional Milnor-Witt stems over R , Annals of K-theory 2-2 (2017), 175--210.
• Involutions in the topologists' orthogonal group , preprint, December 2016.
• Bigraded cohomology of Z/2-equivariant Grassmannians , Geometry and Topology 19 (2015), no. 1, 113--170.
• Grothendieck groups of complexes with null-homotopies, J. K-theory 13 (2014), no. 3, 517--531.
• Coherence for invertible objects and multi-graded homotopy rings, Alg. Geom. Top. 14 (2014), 1055--1106.
• Motivic Hopf elements and relations, joint with D. Isaksen. New York J. Math. 19 (2013), 823-871. Link.
• Mapping spaces in quasi-categories, joint with D. Spivak. Algebraic and Geometric Topology 11 (2011), no. 1, 263-325.
• Rigidification of quasi-categories, joint with D. Spivak. Algebraic and Geometric Topology 11 (2011), no. 1, 225-261.
• The motivic Adams spectral sequence, joint with D. Isaksen. Geometry and Topology 14 (2010), no. 2, 967-1012.
• A curious example of two model categories and some associated differential graded algebras , joint with B. Shipley. Algebr. Geom. Topol. 9 (2009), no. 1, 135-166.
• Eigentheory of Cayley-Dickson algebras, joint with D. Biss, J. D. Christensen, and D. Isaksen. Forum Mathematicum.21 (2009), no. 5, 833-851.
• Etale homotopy theory and sums-of-squares formulas, joint with D. Isaksen. Math. Proc. Cambridge Philos. Society. 145 (2008), 1--25.
• Large annihilators in Cayley-Dickson algebras II, joint with D. Biss, J. D. Christensen, and D. Isaksen. Bol. Soc. Mat. Mexicana (3) 13 (2007), no. 2, 269-292.
• Classification spaces of maps in model categories. Preprint, 2006.
• Postnikov extensions of ring spectra, joint with B. Shipley. Algebr. Geom. Top. 6 (2006), 1785-1829.
• Topological equivalence for differential graded algebras, joint with B. Shipley. Adv. in Math. 212, no. 1 (2007), 37-61.
• Enriched model categories and an application to homotopy endomorphism spectra, joint with B. Shipley. Theory and Application of Categories 18 (2007), no. 15, 400-439.
• Large annihilators in Cayley-Dickson algebras, joint with D. Biss and D. Isaksen. Communications in Algebra 36 (2008), no. 2, 632-664.
• Spectral enrichments of model categories. Homology, Homotopy, Appl. 8 (2006), no. 1, 1-30.
• Algebraic K-theory and sums-of-squares formulas, Documenta Math. 10 (2005), 357-366.
• Motivic cell structures, joint with D. Isaksen. Algebr. Geom. Top. 5 (2005), 615-652.
• The Hopf condition for bilinear forms over arbitrary fields, joint with D. Isaksen. Ann. of Math. (2) 165 (2007), no. 3, 943--964.
• An Atiyah-Hirzebruch spectral sequence for KR-theory. K-theory 35 (2005), no. 3-4, 213-256.
• K-theory and derived equivalences, joint with B. Shipley. Duke Math. J. 124 (2004), no. 3, 587--617.
• Hypercovers and simplicial presheaves, joint with S. Hollander and D. Isaksen. Math. Proc. Cambridge Philos. Soc. 136 (2004), no. 1, 9--51.
• Weak equivalences of simplicial presheaves, joint with D. Isaksen. In "Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K-theory", 97--113, Contemp. Math. 346, Amer. Math. Soc.
• Topological hypercovers and A^1-realizations, joint with D. Isaksen. Math. Z. 246 (2004), no. 4, 667--689.
• Universal homotopy theories. Adv. Math. 164 (2001), no. 1, 144-176.
• Combinatorial Model Categories Have Presentations. Adv. Math. 164 (2001), no. 1, 177-201.
• Replacing Model Categories with Simplicial Ones, Trans. Amer. Math. Soc. vol. 353 (2001), #12, 5003-5027.
• 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). A version of this appeared in the book "Stable categories and structured ring spectra", edited by A. Blumberg, T. Gerhardt, and M. Hill.
• Notes on the Milnor conjecture, (2003).
• Notes on Delta-generated 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

• 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 K-theory, 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 K-theory (2014).
This is one day going to be a textbook on K-theory, with a particular emphasis on connections with geometric phenomena like intersection multiplicities. Somewhat rough, very much a work in progress. Last updated November 2024.

Some Pictures

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.

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