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

- Hodge numbers are not derived invariants in positive characteristic

With Daniel Bragg.

*Math. Ann.*, to appear. arXiv:2106.09949. - A categorical sl
_{2}action on some moduli spaces of sheaves

With Ryan Takahashi.

*Trans. Amer. Math. Soc.*375(12): 8969–9005, 2022. arXiv:2009.08522. - On the period of Lehn, Lehn, Sorger, and van Straten’s symplectic eightfold

With Franco Giovenzana.

*Kyoto J. Math.*63(1): 71–86, 2023. 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.

- 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.

- 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**P**^{n}.

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**P**^{n}. - 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.

- Oregon:
- Math 206, Fall 2023 (Combinatorics MathLab – “Exploring sums of powers”)
- Math 413, Fall 2023 (Metric spaces and topology)
- 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)