Alexandra Kjuchukova's Page

I am an Assistant Professor of Mathematics at the University of Notre Dame.

Department Website

Contact

• Email: akjuchuk🧅nd.edu
• Phone: +1 574 631 9585
• Office: 152A Hurley Bldg

Education

• Ph.D., Mathematics, University of Pennsylvania, PA, 2015
• M.F.A., Poetry, New York University, New York, NY, 2010
• AB, Mathematics, Harvard College, Cambride, MA, 2008

Visiting Positions

• Post-doctoral Scholar, Max Planck Institute for Mathematics - Bonn, Germany (September 2018 - March 2021)
• Van Vleck Assistant Professor (post-doc), University of Wisconsin - Madison (August 2015 - August 2018)
• Teachers & Writers Fellow (creative writing instructor), PS 110, New York City, NY (September 2010 - May 2011)

Research

I currently hold a Simons Foundation Travel Support for Mathematicians award; my research was previously funded by NSF grants DMS-2204349 and DMS-1821257.

Preprints

• Cobordism groups of dihedral branched covers (2026). With V. Bais.
• Extending quotients of knot groups over surfaces in B⁴ (2026). With K. E. Orr.
• Branched covers of open manifolds (2025). With M. Hughes, M. Miller.
• Rep-Tiles (2024). With R. Blair, P. Cahn, H. Schwartz.

Here's a link to my papers on the arXiv.

Selected publications

• Adding a suitable unknot to any link equates bridge number and meridional rank, Mathematical Proceedings of the Cambridge Philosophical Society (2026). With R. Blair, E. Pfaff.
• Slicing knots in definite 4-manifolds, Transactions of the American Mathematical Society (2024). With A. Miller, A. Ray, S. Sakallı.
• A note on three-fold branched covers of S⁴, Annales de l’institut Fourier (2024). With R. Blair, P. Cahn, J. Meier.
• Coxeter groups and meridional rank of links, Mathematische Annalen (2021). With S. Baader, R. Blair.
• Signatures of topological branched covers, International Mathematics Research Notices (2020). With C. Geske, J.L. Shaneson.
• Dihedral branched covers of four-manifolds, Advances in Mathematics, (2018).

Complete publications list

• Cobordism groups of dihedral branched covers (2026), submitted. With V. Bais.
• Extending quotients of knot groups over surfaces in B⁴ (2026), submitted. With K. E. Orr.
• Adding a suitable unknot to any link equates bridge number and meridional rank, Mathematical Proceedings of the Cambridge Philosophical Society (2026). With R. Blair, E. Pfaff.
• The plain sphere number of a link, Pacific Journal of Mathematics 342 (2026), 217–233. With R. Blair, E. Pfaff.
• Branched covers of open manifolds (2025), submitted. With M. Hughes, M. Miller.
• Average four-genus of two-bridge knots, Proceedings of the American Mathematical Society 153 (2025), 357–362. With S. Baader, L. Lewark, F. Misev, A. Ray.
• Brunnian exotic surface links in the 4-ball, Michigan Mathematical Journal 75 (2025), 843–894. With K. Hayden, S. Krishna, M. Miller, M. Powell, N. Sunukjian.
• Rep-Tiles (2024), submitted. With R. Blair, P. Cahn, H. Schwartz.
• Slicing knots in definite 4-manifolds, Transactions of the American Mathematical Society (2024). With A. Miller, A. Ray, S. Sakallı.
• Coxeter quotients of knot groups through 16 crossings, Experimental Mathematics (2024). With R. Blair, N. Morrison.
• A note on three-fold branched covers of S⁴, Annales de l’institut Fourier (2024). With R. Blair, P. Cahn, J. Meier.
• The bridge number of arborescent links with many twigs, Algebraic & Geometric Topology (2023). With S. Baader, R. Blair., F. Misev.
• Coxeter groups and meridional rank of links, Mathematische Annalen (2021). With S. Baader, R. Blair.
• Computing ribbon obstructions for colored knots, Fundamenta Mathematicae (2021). With P. Cahn.
• Linking numbers in three-manifolds, Discrete and Computational Geometry (2021). With P. Cahn.
• Wirtinger systems of generators of knot groups, Communications in Analysis and Geometry, (2020). With R. Blair, R. Velazquez, P. Villanueva.
• Signatures of topological branched covers, International Mathematics Research Notices (2020). With C. Geske, J.L. Shaneson.
• The dihedral genus of a knot, Algebraic and Geometric Topology (2020). With P. Cahn.
• Symmetric quotients of knot groups and a filtration of the Gordian graph, with S. Baader. Mathematical Proceedings of the Cambridge Philosophical Society (2020).
• The incompatibility of crossing number and bridge number for knot diagrams, Discrete Mathematics (2019). With R. Blair, M. Ozawa.
• Dihedral branched covers of four-manifolds, Advances in Mathematics, (2018).

Teaching

Stand-up

Performance

Facilitation

I help organize one virtual seminar and one in the flesh.

• [K-OS], a monthly online seminar on recent developments in topology
• Notre Dame Topology Seminar

In August 2026, I organized the ICM satellite conference Singularities in Topology and Physics with Laurentiu Maxim and Kent Orr.

Poems

Not all my verses are on the arXiv. A couple of them can be found here.