Scholars@Duke

• Background
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  Education, Training, & Certifications

  • Ph.D., Stanford University 2009
• Research
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  Selected Grants

  • A1-Homotopy Theory and Applications to Enumerative Geometry awarded by  National Science Foundation 2021 - 2024
  • Career: Etale amd Motivic Homotopy Theory and Applications to Arithmetic Geometry awarded by  National Science Foundation 2019 - 2022
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  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
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  Selected Publications

  • Academic Articles

    • 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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    • Pauli, Sabrina, and Kirsten Wickelgren. “Applications to A(1)-enumerative geometry of the A(1)-degree.” Research in the Mathematical Sciences 8, no. 2 (June 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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    • 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, 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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    • 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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    • Hopkins, M. J., and K. G. Wickelgren. “Splitting varieties for triple Massey products.” Journal of Pure and Applied Algebra 219, no. 5 (January 1, 2015): 1304–19. https://doi.org/10.1016/j.jpaa.2014.06.006.
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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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    • Arcila-Maya, Niny, Candace Bethea, Morgan Opie, Kirsten Wickelgren, and Inna Zakharevich. “Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex,” n.d.
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    • Bachmann, Tom, and Kirsten Wickelgren. “A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections,” n.d.
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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,” 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
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  Recent Courses

  • MATH 601: Groups, Rings, and Fields 2021
  • MATH 790-90: Minicourse in Advanced Topics 2021
  • MATH 611: Algebraic Topology I 2020
  • MATH 790-90: Minicourse in Advanced Topics 2020
  • MATH 690-10: Topics in Topology 2019
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  Advising & Mentoring

  • I am currently advising Duke PhD student 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
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  Outreach & Engaged Scholarship

  • Organizer. Mathematics Employment Experience for High School Students. Duke University. June 2020  2020

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