Nicolas Addington

Associate Professor

• Department of Mathematics
• University of Oregon
• E-mail: adding@uoregon.edu
• Office: 208 Fenton Hall

Curriculum Vitae

Papers and Preprints

• Hodge numbers are not derived invariants in positive characteristic
  With Daniel Bragg.
  Math. Ann., to appear. arXiv:2106.09949.
• A categorical sl₂ action on some moduli spaces of sheaves
  With Ryan Takahashi.
  Trans. Amer. Math. Soc., to appear. arXiv:2009.08522.
• On the period of Lehn, Lehn, Sorger, and van Straten’s symplectic eightfold
  With Franco Giovenzana.
  Kyoto J. Math., to appear. arXiv:2003.10984.
• Rational points and derived equivalence
  With Benjamin Antieau, Sarah Frei, and Katrina Honigs.
  Compositio Math. 157(5): 1036–1050, 2021. arXiv:1906.02261.
• Twisted Fourier–Mukai partners of Enriques surfaces
  With Andrew Wray.
  Math. Z. 297:1239–1247, 2021. arXiv:1803.03250
• Some non-special cubic fourfolds
  With Asher Auel.
  Documenta Math. 23:637–651, 2018. arXiv:1703.05923.
• Cubic fourfolds fibered in sextic del Pezzo surfaces
  With Brendan Hassett, Yuri Tschinkel, and Anthony Várilly-Alvarado.
  Amer. J. Math. 141(6):1479–1500, 2019. arXiv:1606.05321.
• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
  With Will Donovan and Ciaran Meachan.
  J. Lond. Math. Soc. (2) 93(3):846–865, 2016. arXiv:1507.02597.
• Mukai flops and P-twists
  With Will Donovan and Ciaran Meachan.
  J. reine angew. Math. 748:227–240, 2019. arXiv:1507.02595.
• On two rationality conjectures for cubic fourfolds
  Math. Res. Lett. 23(1):1–13, 2016. arXiv:1405.4902.
• On the symplectic eightfold associated to a Pfaffian cubic fourfold
  With Manfred Lehn.
  J. reine angew. Math. 731:129–137, 2017. arXiv:1404.5657.
• The Pfaffian–Grassmannian equivalence revisited
  With Will Donovan and Ed Segal.
  Alg. Geom. 2(3):332–364, 2015. arXiv:1401.3661.
• The Brauer group is not a derived invariant
  In Brauer groups and obstruction problems: moduli spaces and arithmetic, volume 320 of Progr. Math., pp. 1–5. Birkhäuser, 2017. arXiv:1306.6538.
• Categories of massless D-branes and del Pezzo surfaces
  With Paul Aspinwall.
  J. High Energy Phys. 7(176):39pp., 2013. arXiv:1305.5767.
• Hodge theory and derived categories of cubic fourfolds
  With Richard Thomas.
  Duke Math. J. 163(10):1885–1927, 2014. arXiv:1211.3758.
• D-brane probes, branched double covers, and noncommutative resolutions
  With Eric Sharpe and Ed Segal.
  Adv. Theor. Math. Phys. 18(6):1369–1436, 2014. arXiv:1211.2446.
• New derived symmetries of some hyperkähler varieties
  Alg. Geom. 3(2):223–260, 2016. arXiv:1112.0487.
• The derived category of the intersection of four quadrics
  Preprint. arXiv:0904.1764.
• Spinor sheaves on singular quadrics
  Proc. Amer. Math. Soc. 130(11):3867–3879, 2011. arXiv:0904.1766.

Theses

• Spinor sheaves and complete intersections of quadrics
  My Ph.D. thesis, advised by Andrei Căldăraru.
  A longer version of the first two papers above, with background.
• A method for recovering arbitrary graphs
  My undergraduate thesis, based on my work in Jim Morrow’s REU.
  Here is the C++ program mentioned in the paper.

Other Stuff

• Videos illustrating some geometry of cubic and quartic surfaces,
  by summer undergraduate research students Izzy Harker and Karl Richter.
• Small resolutions of special three-dimensional varieties
  Translation, with Simon Venter, of Jürgen Werner’s 1987 dissertation
  Kleine Auflösungen spezieller dreidimensionaler Varietäten.
  arXiv:2208.01383.
• complete_intersection
  A program to compute the Hodge diamond of a complete intersection in Pⁿ.
  
  It works, but the algorithm is overly complicated — I didn’t know about Hirzebruch’s generating function when I wrote it. The generating function is given succinctly in this note by Donu Arapura; he’s implemented it in Sage and Maple. I’ve implemented it in Macaulay2, if you prefer that.
• double_cover
  A program to compute the Hodge diamond of a branched double cover of Pⁿ.
• Algebraic geometry of the ring of continuous functions
  Maximal ideals of the ring of continuous functions on a compact space correspond to points of the space.
  What about prime ideals?
• Fiber bundles and non-abelian cohomology
  Talk given at the 2007 Graduate Student Topology Conference.

Teaching

• Oregon:
  • Math 683, Spring 2022 (Algebraic Geometry III)
  • Math 243, Winter 2022 (Introduction to Statistics)
  • Math 202, Fall 2021 (Geometry MathLab – “Geometry of the globe”)
  • Math 205, Fall 2021 (Foundations MathLab – “Exploring math through programming”)
  • Math 637, Fall 2021 (Differential Geometry)
  • Math 607, Winter 2021 (Topics course on Connections and Characteristic Classes)
  • Math 392, Winter 2021 (Abstract Algebra)
  • Math 634, Fall 2020 (Algebraic Topology)
  • Math 391, Fall 2020 (Abstract Algebra)
  • Math 607, Spring 2020 (Homological Algebra)
  • Math 432, Winter 2020 (Manifolds)
  • Math 431, Fall 2019 (Point-Set Topology)
  • Math 206, Fall 2019 (Combinatorics MathLab – “Exploring math through programming”)
  • Math 205, Fall 2019 (Foundations MathLab – “Infinities”)
  • Math 692, Spring 2019 (“What every topologist should know”)
  • Math 320, Spring 2019 (Differential Equations with Theory)
  • Math 252, Winter 2019 (Calculus II, Integration)
  • Math 431, Fall 2018 (Point-Set Topology)
  • Math 683, Spring 2018 (Complex Geometry and Hodge Theory)
  • Math 682, Winter 2018 (Scheme Theory)
  • Math 681, Fall 2017 (Classical Algebraic Geometry)
  • Math 607, Winter 2017 (Topics course on Moduli Spaces of Sheaves)
  • Math 445, Winter 2017 (Group Theory)
  • Math 444, Fall 2016 (Ring Theory)
  • Math 420, Spring 2016 (2nd course in Differential Equations)
  • Math 252, Spring 2016 (Calculus II, Integration)
  • Math 252, Fall 2015 (Calculus II, Integration)
• Duke:
  • Math 621, Spring 2015 (Differential Geometry)
  • Math 401, Spring 2015 (Abstract Algebra)
  • Math 401, Fall 2014 (Abstract Algebra)
  • Math 487, Fall 2013 (Mathematical Logic)
  • Math 212, Fall 2013 (Multivariable Calculus)
  • Math 212, Spring 2013 (Multivariable Calculus)
  • Math 212, Fall 2012 (Multivariable Calculus)
• Imperial:
  • M3P21, Spring 2012 (Algebraic Topology)
  • M3P21, Spring 2011 (Algebraic Topology)
  • M3P21, Spring 2010 (Algebraic Topology)
• Wisconsin (selected):
  • Math 234, Spring 2008 (Multivariable Calculus)
  • Math 541, Fall 2007 (Abstract Algebra)
  • Math 221, Spring 2006 (Calculus I)