with Jesse Kass, Marc Levine, and Jake Solomon A quadratically enriched count of rational plane curves, May 2023
with Jesse Kass, Marc Levine, and Jake Solomon A relative orientation for the moduli space of stable maps to a del Pezzo surface, May 2023
with Margaret Bilu, Wei Ho, Padmavathi Srinivasan, and Isabel Vogt Quadratic Enrichment of the Logarithmic Derivative of the Zeta Function, accepted for publication in Transactions of the AMS, 2024.
with Tom Bachmann On quadratically enriched excess and residual intersections, J. Reine Angew. Math. 802 (2023), 77--123.
with Sabrina Pauli Applications to A1-enumerative geometry of the A1-degree, Res. Math. Sci. 8 (2021), no. 2, 24, special volume Arithmetic Topology.
with Niny Arcila-Maya, Candace Bethea, Morgan Opie, and Inna Zakharevich Compactly Supported A1-Euler Characteristic and the Hochschild Complex, Topology Appl. 316 (2022), Paper No. 108108, 24 pp special volume Women in Topology III.
with Tom Bachmann A1-Euler Classes: Six Functors Formalisms, Dualities, Integrality and Linear Subspaces of Complete Intersections, Journal of the Institute of Mathematics of Jussieu, Volume 22, Issue 2, March 2023 pp 681--746.
with Candace Bethea and Jesse Kass Examples of wild ramification in an enriched Riemann–Hurwitz formula Motivic homotopy theory and refined enumerative geometry, 69–82, Contemp. Math., 745, Amer. Math. Soc., Providence, RI, 2020
with Padmavathi Srinivasan, and with an appendix by Borys Kadets, Padmavathi Srinivasan, Ashvin A. Swaminathan, Libby Taylor, and Dennis Tseng An Arithmetic Count of the Lines Meeting Four Lines in P3, Trans. Amer. Math. Soc. 374 (2021), no. 5, 3427--3451.
with Rachel Davis, and Rachel Pries The Galois Action on the Lower Central Series of the Fundamental Group of the Fermat Curve, Israel Journal of Mathematics (2023).
with Jesse Kass An Arithmetic Count of the Lines on a Smooth Cubic Surface, Compos. Math. 157 (2021), no. 4, 677-709.
with Jesse Kass An Etale Realization Functor Which Does Not Exist, New Directions in Homotopy Theory, proceedings of the second Mid-Atlantic Topology Conference, edited by N. Kitchloo, M. Merling, J. Morava, E. Riehl, W.S. Wilson, Contemporary Mathematics, Volume 707, p.11-31, 2018.
with Rachel Davis, Rachel Pries, and Vesna Stojanoska The Galois Action and Cohomology of a Relative Homology Group of Fermat Curves, J. Algebra 505, 2018, p.33-69.
with Jesse Kass The Class of Eisenbud–Khimshiashvili–Levine is the Local A1-Brouwer Degree and Erratum, Duke Mathematical Journal, Vol. 168, No. 3, 429-469 2019.
with Jesse Kass A1-Milnor number, Oberwolfach Report 35(2016), 19 August, 2016.
Massey Products <y,x,x,…,x,x,y> in Galois Cohomology via Rational Points, Journal of Pure and Applied Algebra, Volume 221, Issue 7, July 2017, pages 1845-1866. Journal of Pure and Applied Algebra's special issue in honor of Chuck Weibel, edited by Guillermo Cortiñas, Eric Friedlander, and Christian Haesemeyer. Available on-line at https://authors.elsevier.com/a/1UgGo562D4z7E. March 14, 2016.
with Jesse Kass A Classical Proof that the Algebraic Homotopy Class of a Rational Function is the Residue Pairing, Linear Algebra and Its Applications 595 (2020) 157--181.
with Aravind Asok and Ben Williams The Simplicial Suspension Sequence in A1-homotopy, Geometry & Topology 21-4 (2017), 2093–2160. DOI 10.2140/gt.2017.21.2093.
Desuspensions of S^{1} /\ P^{1}_{Q}-{0,1,infty}, special issue VBAC 2014 of the International Journal of Mathematics, edited by Oscar Garcia-Prada, Dirk Kreimer, Peter Newstead, Holger Reich and Alexander Schmitt, International Journal of Mathematics, June 2016, Vol. 27, No. 07. doi: 10.1142/S0129167X16400103.
with Ben Williams Errata to Simplicial EHP Sequence in A1-Algebraic Topology March 23, 2020.
with Ben Williams The Simplicial EHP Sequence in A1-Algebraic Topology, Geometry & Topology 23-4 (2019), 1691--1777. DOI 10.2140/gt.2019.23.1691, last updated: June 5, 2018.
with Rachel Davis, Rachel Pries, and Vesna Stojanoska Galois Action on the Homology of Fermat Curves Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop, edited by Ellen E. Eischen, Ling Long, Rachel Pries, and Katherine E. Stange, Association for Women in Math Series Volume 3, Springer International Publishing Switzerland 2016, ISBN 978-3-319-30974-3, pg 57-87.
with Julie E. Bergner, Ruth Joachimi, Kathryn Lesh, and Vesna Stojanoska Classification of Problematic Subgroups of U(n) Trans. Amer. Math. Soc. 371 (2019), no. 10, 6739-6777.
with Julie E. Bergner, Ruth Joachimi, Kathryn Lesh, and Vesna Stojanoska Fixed points of p-toral groups acting on partition complexes Contemporary Math. 641 Women in Topology: Collaborations in Homotopy Theory: August 18-23, 2013, Maria Basterra, Kristine Bauer, Kathryn Hess, and Brenda Johnson editors, AMS, 2015. May 26, 2014.
with Jesse Kass An Abel map to the compactified Picard scheme realizes Poincaré duality Algebraic & Geometric Topology 15-1 (2015), 319–369. DOI 10.2140/agt.2015.15.319 . August 21, 2014.
Cartier's first theorem for Witt vectors on Z^{n}_{>=0}Algebraic Topology: Applications and New Directions, Stanford Symposium 2012, Ulrike Tillmann, Soren Galatius, Dev Sinha editors, Contemporary Mathematics 620, AMS, 2014. November 20, 2013.
with Michael Hopkins Splitting Varieties for Triple Massey Products Journal of Pure and Applied Algebra 219 (2015), pp. 1304-1319. Available online 21 June 2014. (DOI)10.1016/j.jpaa.2014.06.006. May 29, 2014.
n-Nilpotent obstructions to pi_{1} sections of P^{1}-{0,1,infty} and Massey products, Advanced Studies in Pure Mathematics 63, 2012, Proceedings for Conferences in Kyoto (October 2010), Galois-Teichmueller theory and Arithmetic Geometry, H. Nakamura, F. Pop, L. Schneps, A. Tamagawa eds., pp. 579-600. February 21, 2012.
3-Nilpotent obstructions to pi_{1} sections for P^{1}_{Q}-{0,1,infty}, The Arithmetic of Fundamental Groups - PIA 2010, ed. Jakob Stix, Contributions in Mathematical and Computational Sciences, Vol 2., Springer-Verlag Berlin Heidelberg, 2012. July 18, 2011.
2-Nilpotent Real Section Conjecture, Mathematische Annalen: Vol. 358, Issue 1 (2014), pp. 361-387. (DOI) 10.1007/s00208-013-0967-5. December 24, 2012.
with Ravi Vakil, Universal Covering Spaces and Fundamental Groups in Algebraic Geometry as Schemes. Journal de Theorie des Nombres de Bordeaux, 23 no. 2 (2011), p. 489-526. July 18, 2011.
Lower Central Series Obstructions to Homotopy Sections of Curves over Number Fields, thesis. July 21, 2009.
An older paper: with Sarah Iams, Brian Katz, Cesar E. Silva, and Brian Street, On Weakly Mixing and Doubly Ergodic Nonsingular Actions, Colloq. Math 103 (2005), no. 2, 247-264. (From the SMALL Research Experience for Undergraduates at Williams College.)
with Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte An Explicit Self-Duality, Stacks Project Expository Collection, edited by Pieter Belmans, Wei Ho, and Aise Johan de Jong, London Mathematical Society Lecture Note Series 480, Cambridge University Press, 2022.
with Ben Williams Unstable Motivic Homotopy Theory, chapter of the Handbook of Homotopy Theory, edited by Haynes Miller, CRC Press, 2020.
An Arithmetic Count of the Lines on a Smooth Cubic Surface, expository article on joint work with Jesse Kass, Notices Amer. Math. Soc. 65 (2018), no. 4, 404-405. Full issue
WHAT IS…an Anabelian Scheme? Notices of the AMS, March 2016, Volume 63 No 3, p. 285–286. Full issue.
Grothendieck's Anabelian Conjectures The Harvard College Mathematics Review, Spring 2013, Volume 5, p. 77–83.
Notes for a talk given at Stanford Symposium 2012 in honor of Gunnar Carlsson, Ralph Cohen, and Ib Madsen.