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
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Education, Training, & Certifications
- Ph.D., Stanford University 2009
- Recognition
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Awards & Honors
- Research
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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
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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
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Academic Articles
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Arcila-Maya, N., C. Bethea, M. Opie, K. Wickelgren, and I. Zakharevich. “Compactly supported A1-Euler characteristic and the Hochschild complex.” Topology and Its Applications 316 (July 1, 2022). https://doi.org/10.1016/j.topol.2022.108108.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text Open Access Copy
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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
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Link to Item
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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Basterra, Maria, Kristine Bauer, Kathryn Hess, and Brenda Johnson, eds. “Women in Topology,” May 21, 2015. https://doi.org/10.1090/conm/641.Full Text Open Access Copy
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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.Full Text
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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.Full Text
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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.Full Text
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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.Link to Item
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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.Full Text
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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.Full Text
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Bachmann, Tom, and Kirsten Wickelgren. “On quadratically enriched excess and residual intersections (Submitted),” n.d.Link to Item
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Book Sections
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Kuhn, Nikolas, Devlin Mallory, Vaidehee Thatte, and Kirsten Wickelgren. “An explicit self-duality.” In Stacks Project Expository Collection (SPEC), edited by Pieter Belmans, Wei Ho, and Aise Johan de Jong, Vol. 480. Cambridge University Press, 2022.
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Wickelgren, Kirsten, and Ben Williams. “Unstable Motivic Homotopy Theory.” In Handbook of Homotopy Theory. CRC Press, 2019.Link to Item
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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.Full Text
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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.Full Text
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Conference Papers
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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.Full Text
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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.Full Text
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Bergner, J. E., R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren. “Fixed points of p-toral groups acting on partition complexes,” 641:83–96, 2015. https://doi.org/10.1090/conm/641/12860.Full Text
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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.Full Text
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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.Link to Item
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Preprints
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Bilu, Margaret, Wei Ho, Padmavathi Srinivasan, Isabel Vogt, and Kirsten Wickelgren. “Quadratic enrichment of the logarithmic derivative of the zeta function,” October 6, 2022.Link to Item
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- Teaching & Mentoring
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Recent Courses
- MATH 602: An Introduction to Commutative Algebra and Algebraic Geometry 2023
- MATH 790-90: Minicourse in Advanced Topics 2023
- MATH 799: Special Readings 2023
- MATH 601: Groups, Rings, and Fields 2022
- MATH 602: An Introduction to Commutative Algebra and Algebraic Geometry 2022
- MATH 799: Special Readings 2022
- MATH 601: Groups, Rings, and Fields 2021
- MATH 790-90: Minicourse in Advanced Topics 2021
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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
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Presentations & Appearances
- Colloquium. Brown University. October 26, 2022 2022
- Colloquium. UNC. September 15, 2022 2022
- A quadratically enriched zeta function. Motivic Geometry. Univerisity of Oslo, Centre for Advanced Study. August 2022 2022
- A Residual Intersection Formula in Hermitian K-theory. K-theory. Mathematisches Forschungsinstitut Oberwolfach. May 2022 2022
- Colloquium. Rutgers University. February 2, 2022 2022
- Colloquium. University of Pennsylvania. December 8, 2021 2021
- Colloquium. Brandeis–Harvard–MIT–Northeastern Joint Mathematics Colloquium . November 18, 2021 2021
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Outreach & Engaged Scholarship
- Co-organizer and co-teacher. Mathematics Employment Experience for High School Students. Duke. July 2022 2022
- 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
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Service to the Profession
- Co-organizer. Algebraic Topology and Topological Data Analysis: a Conference in Honor of Gunnar Carlsson. August 2022 2022
- Editorial Board New York Journal of Mathematics. March 2022 2022
- Editorial Board Annals of K-theory. 2022 2022
- Editorial Board Journal of Topology. London Mathematical Society. December 2021 2021
- Co-organizer. Motivic Homotopy: Theory and Applications. IAS Park City Mathematics Institute summer program. July 2021 2021
- Broadening Participation Advisory Committee (formerly HRAC). MSRI . April 2021 - April 2024 2021 - 2024
- Member of the Committee to select the winner of the Veblen Prize. AMS. 2021 2021
- Co-organizer. Motivic Geometry. The Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters in Oslo. September 2020 2020
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