Publications
Book
The disc embedding theoremCo-editors: Stefan Behrens, Boldizsár Kalmár, Min Hoon Kim, and Mark Powell
Co-contributors: Stefan Behrens, Xiaoyi Cui, Christopher W. Davis, Peter Feller, Boldizsár Kalmár, Daniel Kasprowski, Min Hoon Kim, Duncan McCoy, Jeffrey Meier, Allison N. Miller, Matthias Nagel, Patrick Orson, JungHwan Park, Wojciech Politarczyk, Mark Powell, Henrik Rüping, Nathan Sunukjian, Peter Teichner, Daniele Zuddas.
In the press: New math book rescues landmark topology proof
Errata
Papers and preprints
- On a volume invariant of 3-manifolds.
(With Marc Kegel, Jonathan Spreer, Em Thompson, and Stephan Tillmann) - Slice knots and knot concordance. Winter Braids Lecture Notes, Vol. 8, Course no II, p. 1-31, 2021.
- A note on surfaces in CP2 and CP2#CP2. Proceedings of the AMS Ser. B, 11, 187-199, 2024.
(With Marco Marengon, Allison N. Miller and András Stipsicz) - Gluck twists on concordant or homotopic spheres. Math. Research Letters, Vol. 30, No. 6, pp. 1787-1811, 2023.
(With Daniel Kasprowski and Mark Powell) - Counterexamples in 4-manifold topology. EMS Surveys in Mathematical Sciences, 9, No. 1, 193-249, 2022.
(With Daniel Kasprowski and Mark Powell) - Embedding surfaces in 4-manifolds. Geometry and Topology 28-5 (2024), 2399--2482.
(With Daniel Kasprowski, Mark Powell, and Peter Teichner) - Slicing knots in definite 4-manifolds. Transactions of the AMS, 377, no. 8, 5905-5946, 2024.
(With Alexandra Kjuchukova, Allison N. Miller and Sümeyra Sakallı) - Isotopy and equivalence of knots in 3-manifolds.
(With Paolo Aceto, Corey Bregman, Christopher W. Davis, and JungHwan Park) - The 4-dimensional disc embedding theorem and dual spheres.
(With Mark Powell and Peter Teichner) - Embedding spheres in knot traces. Compositio Mathematica, 157(10), 2242-2279, 2021.
(With Peter Feller, Allison N. Miller, Matthias Nagel, Patrick Orson, and Mark Powell) - Null, recursively starlike-equivalent decompositions shrink. Glasgow Mathematics Journal, 65, no. 2, 328–336, 2023.
(With Jeffrey Meier and Patrick Orson) - Average four-genus of two-bridge knots. To appear: Proceedings of the AMS.
(With Sebastian Baader, Alexandra Kjuchukova, Lukas Lewark, and Filip Misev) - On distinct finite covers of 3-manifolds. Indiana University Mathematics Journal, 70 no. 2, 809-846, 2021.
(With Stefan Friedl, JungHwan Park, Bram Petri, and Jean Raimbault) - Linear independence of cables in the knot concordance group. Transactions of the AMS, 374 no. 6, 4449-4479, 2021.
(With Christopher W. Davis and JungHwan Park) - Pretzel links, mutation, and the slice ribbon conjecture. Math Research Letters, 28(4), 945-966, 2021.
(With Paolo Aceto, Min Hoon Kim, and JungHwan Park) - Concordance of knots in S1xS2. Journal of the LMS (2)98 no. 1, 59-84, 2018.
(With Christopher W. Davis, Matthias Nagel, and JungHwan Park) - 4-dimensional analogues of Dehn's lemma. Journal of the LMS (2)96 no. 1, 111–132, 2017.
(With Daniel Ruberman) - A family of non-split topologically slice links with arbitrarily large slice genus. Proceedings of the AMS 146(1), 439–448, 2018.
(With JungHwan Park) - On the Upsilon invariant and satellite knots. Mathematische Zeitschrift 292 no. 3-4, 1431-1452, 2019.
(With Peter Feller and JungHwan Park) - A new family of links topologically, but not smoothly, concordant to the Hopf link.
Tim Cochran memorial issue, Journal of Knot Theory and its Ramifications, 26(2): 1740002, 2017.
(With Christopher W. Davis) - Shake slice and shake concordant knots. Journal of Topology, 9(3): 861-888, 2016.
(With Tim D. Cochran) - Satellite operators as group actions on knot concordance. Algebraic & Geometric Topology, 16(2): 945–969, 2016.
(With Christopher W. Davis) - Satellite operators with distinct iterates in knot concordance. Proceedings of the AMS, 143(11): 5005-5020, 2015.
- Casson towers and filtrations of the knot concordance group. Algebraic & Geometric Topology, 15(2): 1119–1159, 2015.
- Injectivity of satellite operators in knot concordance. Journal of Topology, 7(4): 948–964, 2014.
(With Tim D. Cochran and Christopher W. Davis) - Slice knots which bound punctured Klein bottles. Algebraic & Geometric Topology, 13(5): 2713-2731, 2013.
Other writing
- Flächen in 4-dimensionalen Räumen (translated from english to german by Christian Kaiser), MPG Jahrbuch 2020
- My PhD thesis (PDF)
- Unofficial errata for Knots and Links by Dale Rolfsen
- Research Statement, Teaching Statement, and Diversity Statement from 2016
- Research Statement and Statement of Teaching Philosophy from 2015
- Research Statement and Statement of Teaching Philosophy from 2014
Expository notes and projects
- Topological manifolds
- Lecture notes from a mini-course on slice knots and knot concordance
- Lecture notes from a mini-course on topological 4-manifolds
- Superslice knots have Alexander polynomial one
PhD students
- Ben Ruppik, postdoc at Düsseldorf
- Hyeonhee Jin (coadvised with Peter Teichner)
Masters students (and position after graduating)
- Didac Violan Aris, PhD student at ICMAT Madrid
- Constanze Schwarz, Risikomanagementberatung KPMG
- Isacco Nonino, PhD student at Glasgow
- Fadi Mezher, PhD student at Copenhagen
- Raphael Floris, PhD student at RWTH Aachen
- Yikai Teng, PhD student at Rutgers Newark
- Agata Sienicka, Data Scientist, Instytut Monitorowania Mediów
- Cara Hobohm
Collaborators
- Paolo Aceto
- Sebastian Baader
- Stefan Behrens
- Corey Bregman
- Tim D. Cochran
- Christopher W. Davis
- Peter Feller
- Stefan Friedl
- Daniel Kasprowski
- Marc Kegel
- Min Hoon Kim
- Alexandra Kjuchukova
- Lukas Lewark
- Marco Marengon
- Duncan McCoy
- Jeffrey Meier
- Allison N. Miller
- Filip Misev
- Matthias Nagel
- Patrick Orson
- JungHwan Park
- Bram Petri
- Wojciech Politarczyk
- Mark Powell
- Jean Raimbault
- Daniel Ruberman
- Sümeyra Sakallı
- Jonathan Spreer
- András Stipsicz
- Peter Teichner
- Em Thompson
- Stephan Tillmann .
Seminars/conferences/special sessions co/organised
- MPIM topology seminar, Autumn 2017 to present (co-organised at various times with Tobias Barthel, David Gay, Viktoriya Ozornova, and Peter Teichner)
- Graduate Research Opportunities for Women@Bonn, March 2023 (co-organised with Pieter Belmans, Yajnaseni Dutta, Ben Heuer, Regula Krapf, Dominique Mattei, and Emanuel Reinecke)
- Graduate Research Opportunities for Women@Bonn, March 2022 (co-organised with Pieter Belmans, Yajnaseni Dutta, Ben Heuer, and Emanuel Reinecke)
- MATRIX-MFO tandem workshop: Invariants and Structures in Low-Dimensional Topology, September 2021 (co-organised with Stefan Friedl Jessica Purcell, and Stephan Tillmann).
- AMS Special Session on Women in Topology, Joint Mathematics Meetings, January 2020 (co-organised with Jocelyn Bell, Rochy Flint, and Candice Price)
- Workshop on 4-manifolds, MPIM, September 2019 (co-organised with David Gay Jeffrey Meier, and Peter Teichner)
- Four manifolds: Confluence of high and low dimensions, Fields Institute, July 2019 (co-organised with Ian Hambleton, Alexander Kupers, and Mark Powell)
- Workshop on smooth concordance classes of topologically slice knots, American Institute for Mathematics, June 2019 (co-organised with Shelly Harvey and JungHwan Park)
- Special session on the topology of 3- and 4-manifolds,, AWM research symposium, April 2019 (co-organised with Allison N. Miller)
- AMS Special Session on Women in Topology, Joint Mathematics Meetings, January 2019 (co-organised with Jocelyn Bell, Rosemary Guzman, and Candice Price)
- AMS Special Session on Women in Topology, Joint Mathematics Meetings, January 2017 (co-organised with Jocelyn Bell, Eleanor Ollhoff, and Candice Price)
- Conference on 4-manifolds and knot concordance at MPIM, October 2016 (co-organised with Christopher Davis, Peter Feller, Min Hoon Kim, Jeffrey Meier, Allison Miller, Mark Powell, and Peter Teichner) Problem list
- EveryTopic Seminar, Fall 2015 and Spring 2016 (co-organised with Carl Wang Erickson), and Spring 2017, (co-organised with McKee Krumpak and Konstantin Matveev)
- Spectral Sequences Learning Seminar, Fall 2014
- Heegaard-Floer computationar, Spring 2014
- 4-manifolds seminar, Spring 2014
- Characteristic classes seminar, following Milnor & Stasheff's Characteristic Classes, Summer 2012
- Knot invariants seminar, Summer 2011
Some slides and videos
- Counterexamples in 4-manifold topology, Columbia geometry and topology seminar, March 4, 2022
- Welche Form hat unser Universum, Mathenacht aus Bonn und Münster, November 26, 2021
- Embedding surfaces in 4-manifolds, Nearly Carbon Neutral Geometry and Topology Conference, plenary talk, June 22, 2021
- Knoten in der Mathematik, Bonner Matheclub, June 5, 2021
- A surface embedding theorem, Regensburg low-dimensional geometry and topology seminar, June 1, 2021. Slides
- On 1-shake slice knots, ARC lightning talks, April 20, 2021
- How to disprove the triangulation conjecture, Bonn-Berkeley surfaces in 4-manifolds seminar, March 2, 2021
- Filtrations of the knot concordance group, Building bridges seminar, February 17, 2021
- Isotopy and equivalence of knots in 3-manifolds, Joint Math Meetings, January 8, 2021
- Embedding surfaces in 4-manifolds, Tech topology conference, December 5, 2020
- Embedding surfaces in 4-manifolds, UNC AWM lecture series, October 26, 2020.
- Embedding surfaces in 4-manifolds, CIRGET geometry and topology seminar, October 23, 2020.
- Geometrically transverse spheres in 4-manifolds, Workshop on Unifying 4-dimensional knot theory, Banff International Research Station, November 6, 2019.
- (Yet another proof that) Alexander polynomial one knots are topologically slice, London Mathematical Society Durham Symposium, Pseudoholomorphic Curves and Gauge Theory in Low-Dimensional Topology, Durham University, August 19, 2019.
- Knots, four dimensions, and fractals, Bowdoin College, February 6, 2017.
- 4-dimensional analogues of Dehn's lemma, Joint Mathematics Meetings, January 5, 2017.
- Satellite operations and fractal structures on knot concordance, Topology in dimension 3.5: a conference in memory of Tim Cochran, Rice University, June 2, 2016.
- Satellite operations and knot concordance, Colloquium, San Francisco State University, February 18, 2016.
- Knots, four dimensions, and fractals, Mathematics Adventures & Diversions, Lafayette College, February 2, 2016.
- Is the set of knots a fractal?, Colloquium, SUNY Geneseo, January 29, 2016.
- Shake slice and shake concordant knots, Joint Mathematics Meetings, January 6, 2016.
- A new family of links topologically, but not smoothly, concordant to the Hopf link, CMS Winter Meeting, Montreal, QC, December 5, 2015.
- Satellite operators as group actions on knot concordance, AWM Research Symposium Poster Session, University of Maryland, College Park, April 11, 2015.
- Casson towers and filtrations of the smooth knot concordance group, PhD Defense, Rice University, April 8, 2014.
- Satellite operators on knots, and fractals, STEM colloquium, University of Wisconsin-Eau Claire, March 7, 2014.
- The fractal nature of the knot concordance group, Joint Mathematics Meetings, January 18, 2014.
- Satellite operators as group actions on knot concordance, AMS Central Sectional Meeting, Washington University at St. Louis, October 20, 2013.
- Casson towers and filtrations of the smooth knot concordance group, AMS Central Sectional Meeting, Washington University at St. Louis, October 19, 2013.
- There exist infinitely many unknotted winding number one satellite operators on knot concordance, 2013 Lehigh University Geometry and Topology Conference, Lehigh University, May 25, 2013.
- A friendly introduction to knots in three and four dimensions, Mathematics Department Colloquium, SUNY Geneseo, April 25, 2013.
- Slice knots which bound Klein bottles, AMS Central Sectional Meeting, University of Akron, October 20, 2012.