Kirsten Graham Wickelgren

Kirsten Graham Wickelgren
Professor of Mathematics

Office Hours

Tuesday 1:15-2:15pm, Thursday 11-12pm in Math and Physics 025 (in person). Virtual office hours are available by appointment. Please email me for the zoom link.

Current Appointments & Affiliations

Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2019

Contact Information

Background
Education, Training, & Certifications
- Ph.D., Stanford University 2009
Recognition
Awards & Honors
- Member of the K-Theory Foundation. The K-Theory Foundation. 2021
Research
Selected Grants
- A1-Homotopy Theory and Applications to Enumerative Geometry awarded by National Science Foundation 2021 - 2024
- Algebraic Topology and Topological Data Analysis: A Conference in Honor of Gunnar Carlsson awarded by National Science Foundation 2022 - 2023
- Career: Etale amd Motivic Homotopy Theory and Applications to Arithmetic Geometry awarded by National Science Foundation 2019 - 2022
Fellowships, Supported Research, & Other Grants
- Homotopy theory of schemes, Grothendieck's anabelian program, rational points awarded by National Science Foundation 2014 - 2017
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Arcila-Maya, N., C. Bethea, M. Opie, K. Wickelgren, and I. Zakharevich. “Compactly supported A¹-Euler characteristic and the Hochschild complex (Accepted).” Topology and Its Applications 316 (July 1, 2022). https://doi.org/10.1016/j.topol.2022.108108.
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  - Kuhn, Nikolas, Devlin Mallory, Vaidehee Thatte, and Kirsten Wickelgren. “An explicit self-duality,” November 12, 2021.
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  - Pauli, S., and K. Wickelgren. “Applications to A¹ -enumerative geometry of the A¹ -degree.” Research in Mathematical Sciences 8, no. 2 (June 1, 2021). https://doi.org/10.1007/s40687-021-00255-6.
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  - Srinivasan, P., and K. Wickelgren. “An arithmetic count of the lines meeting four lines in P³.” Transactions of the American Mathematical Society 374, no. 5 (May 1, 2021): 3427–51. https://doi.org/10.1090/tran/8307.
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  - Bachmann, T., and K. Wickelgren. “EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY and LINEAR SUBSPACES of COMPLETE INTERSECTIONS.” Journal of the Institute of Mathematics of Jussieu, January 1, 2021. https://doi.org/10.1017/S147474802100027X.
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  - Leo Kass, J., and K. Wickelgren. “An arithmetic count of the lines on a smooth cubic surface.” Compositio Mathematica, January 1, 2021, 677–709. https://doi.org/10.1112/S0010437X20007691.
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  - Kass, J. L., and K. Wickelgren. “A classical proof that the algebraic homotopy class of a rational function is the residue pairing.” Linear Algebra and Its Applications 595 (June 15, 2020): 157–81. https://doi.org/10.1016/j.laa.2019.12.041.
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  - Arcila-Maya, Niny, Candace Bethea, Morgan Opie, Kirsten Wickelgren, and Inna Zakharevich. “Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex,” March 20, 2020.
    Open Access Copy Link to Item
  - Bethea, C., J. L. Kass, and K. Wickelgren. “Examples of wild ramification in an enriched riemann–hurwitz formula.” Contemporary Mathematics 745 (January 1, 2020): 69–82. https://doi.org/10.1090/conm/745/15022.
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  - Kass, J. L., and K. Wickelgren. “The class of Eisenbud-Khimshiashvili-Levine is the local A ¹ -Brouwer degree.” Duke Mathematical Journal 168, no. 3 (February 15, 2019): 429–69. https://doi.org/10.1215/00127094-2018-0046.
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  - Bergner, J. E., R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren. “Classification of problematic subgroups of U(n).” Transactions of the American Mathematical Society 371, no. 10 (January 1, 2019): 6739–77. https://doi.org/10.1090/tran/7442.
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  - Wickelgren, K., and B. Williams. “The simplicial EHP sequence in A¹–algebraic topology.” Geometry and Topology 23, no. 4 (January 1, 2019): 1691–1777. https://doi.org/10.2140/gt.2019.23.1691.
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  - Davis, Rachel, Rachel Pries, and Kirsten Wickelgren. “The Galois action on the lower central series of the fundamental group of the Fermat curve,” August 14, 2018.
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  - Davis, R., R. Pries, V. Stojanoska, and K. Wickelgren. “The Galois action and cohomology of a relative homology group of Fermat curves.” Journal of Algebra 505 (July 1, 2018): 33–69. https://doi.org/10.1016/j.jalgebra.2018.02.021.
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  - Wickelgren, K. “Massey products 〈y,x,x,…,x,x,y〉 in Galois cohomology via rational points.” Journal of Pure and Applied Algebra 221, no. 7 (July 1, 2017): 1845–66. https://doi.org/10.1016/j.jpaa.2016.12.027.
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  - Asok, A., K. Wickelgren, and B. Williams. “The simplicial suspension sequence in A¹-homotopy.” Geometry and Topology 21, no. 4 (May 19, 2017): 2093–2160. https://doi.org/10.2140/gt.2017.21.2093.
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  - Wickelgren, K. “What is… an anabelian scheme?” Notices of the American Mathematical Society 63, no. 3 (March 1, 2016): 285–86. https://doi.org/10.1090/noti1342.
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  - “Women in Topology,” May 21, 2015. https://doi.org/10.1090/conm/641.
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  - Hopkins, M. J., and K. G. Wickelgren. “Splitting varieties for triple Massey products.” Journal of Pure and Applied Algebra 219, no. 5 (May 1, 2015): 1304–19. https://doi.org/10.1016/j.jpaa.2014.06.006.
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  - Kass, J. L., and K. Wickelgren. “An Abel map to the compactified Picard scheme realizes Poincaré duality.” Algebraic and Geometric Topology 15, no. 1 (March 23, 2015): 319–69. https://doi.org/10.2140/agt.2015.15.319.
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  - Wickelgren, K. “2-Nilpotent real section conjecture.” Mathematische Annalen 358, no. 1–2 (February 1, 2014): 361–87. https://doi.org/10.1007/s00208-013-0967-5.
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  - Wickelgren, Kirsten. “3-nilpotent obstructions to pi_1 sections for P^1_Q - {0,1,infty}.” Edited by Jakob Stix. The Arithmetic of Fundamental Groups Pia 2010, Editor J. Stix, Contributions in Mathematical and Computational Sciences, Vol. 2, Springer Verlag Berlin Heidelberg, 2012, January 1, 2012.
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  - Vakil, R., and K. Wickelgren. “Universal covering spaces and fundamental groups in algebraic geometry as schemes.” Journal De Theorie Des Nombres De Bordeaux 23, no. 2 (January 1, 2011): 489–526. https://doi.org/10.5802/jtnb.774.
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  - Iams, S., B. Katz, C. E. Silva, B. Street, and K. Wickelgren. “On weakly mixing and doubly ergodic nonsingular actions.” Colloquium Mathematicum 103, no. 2 (January 1, 2005): 247–64. https://doi.org/10.4064/cm103-2-10.
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  - Bachmann, Tom, and Kirsten Wickelgren. “On quadratically enriched excess and residual intersections (Submitted),” n.d.
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- Book Sections
  - Wickelgren, Kirsten, and Ben Williams. “Unstable Motivic Homotopy Theory.” In Handbook of Homotopy Theory. CRC Press, 2019.
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  - Kass, J. L., and K. Wickelgren. “An Étale realization which does NOT exist.” In Contemporary Mathematics, 707:11–29, 2018. https://doi.org/10.1090/conm/707/14251.
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  - Wickelgren, K. “On 3-nilpotent obstructions to π1 sections for ℙ¹ℚ-{0,1,∞}.” In The Arithmetic of Fundamental Groups: PIA 2010, 281–328, 2012. https://doi.org/10.1007/978-3-642-23905-2_12.
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- Conference Papers
  - Wickelgren, K. “Desuspensions of S ¹ Λ (P1/Q - {0, 1, ∞ }).” In International Journal of Mathematics, Vol. 27, 2016. https://doi.org/10.1142/S0129167X16400103.
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  - Davis, R., R. Pries, V. Stojanoska, and K. Wickelgren. “Galois Action on the Homology of Fermat Curves,” 3:57–86, 2016. https://doi.org/10.1007/978-3-319-30976-7_3.
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  - Wickelgren, Kirsten. “Cartier’s first theorem for Witt vectors on ℤ_{≥0}ⁿ-0,” 321–28. American Mathematical Society, 2014. https://doi.org/10.1090/conm/620/12396.
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  - Wickelgren, Kirsten. “n-nilpotent obstructions to pi(1)sections of P-1 - {0, 1, infinity} and Massey products.” In Galois Teichmueller Theory and Arithmetic Geometry, edited by H. Nakamura, F. Pop, L. Schneps, and A. Tamagawa, 63:579–600. MATH SOC JAPAN, 2012.
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Teaching & Mentoring
Recent Courses
Advising & Mentoring
- I am currently advising Duke PhD students Cameron Darwin and Stephen McKean, and co-advising University of Pennsylvania PhD student Thomas Brazelton with Mona Merling. I am available to advise and mentor undergraduate, graduate, and Post-Doc mathematics researchers.
Scholarly, Clinical, & Service Activities
Presentations & Appearances
- Colloquium. University of Pennsylvania. December 8, 2021 2021
- Colloquium. Brandeis–Harvard–MIT–Northeastern Joint Mathematics Colloquium . November 18, 2021 2021
Outreach & Engaged Scholarship
- Co-organizer and co-teacher. Mathematics Employment Experience for High School Students. Duke. July 2021 - July 2021 2021
- Co-organizer and co-teacher. Mathematics Employment Experience for High School Students. Duke University. June 2020 2020
Service to the Profession

Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.

Education, Training, & Certifications

Awards & Honors

Selected Grants

Fellowships, Supported Research, & Other Grants

Selected Publications

Academic Articles

Book Sections

Conference Papers

Recent Courses

Advising & Mentoring

Presentations & Appearances

Outreach & Engaged Scholarship

Service to the Profession