Nicolas Addington
Associate Professor
Current Teaching
Papers and Preprints
- Hodge numbers are not derived invariants in positive characteristic
With Daniel Bragg.
Submitted.
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
Computer Programs
- complete_intersection computes the Hodge diamond of a complete intersection in Pn.
This program 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 computes the Hodge diamond of a branched double cover of Pn.
Old Notes
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:
- Imperial:
- Wisconsin (selected):