Contact


Professor Markus Szymik
School of Mathematical and Physical Sciences
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
United Kingdom

m.szymik@sheffield.ac.uk

Publications

In this section you can find out about the papers (and the book) that I have written (with the indicated co-authors).
The publications may differ from the preprint versions; please refer to the former in the interest of accuracy.
The manuscripts are often under revision; some links may sometimes be broken.


Manuscripts

Thompson's quandle
Arxiv

Homological stability fails for the Cremona groups
Arxiv

Artin-Schreier quandles of involutions in absolute Galois groups
Arxiv

The homotopy types of free racks and quandles
(with T. Lawson)
Arxiv

The homology of permutation racks
(with V. Lebed)
Arxiv - HAL

The stable homotopy theory of vortices on Riemann surfaces
Arxiv

Published or Accepted Papers

Groups, conjugation and powers
(with T. Vik)
Involve (to appear)
Arxiv

Preludes to the Eilenberg-Moore and the Leray-Serre spectral sequences
(with F. Neumann)
Doc. Math. 29 (2024) 1319–1339
Link - Arxiv

Generalizations of Loday's assembly maps for Lawvere's algebraic theories
(with A.M. Bohmann)
J. Inst. Math. Jussieu 23 (2024) 811–837
Link - Arxiv

Boolean algebras, Morita invariance, and the algebraic K-theory of Lawvere theories
(with A.M. Bohmann)
Math. Proc. Cambridge Philos. Soc. 175 (2023) 253–270
Link - Arxiv

Spaces of knotted circles and exotic smooth structures
(with G. Arone)
Canad. J. Math. 74 (2022) 1-23
Link - Arxiv

Adams operations and symmetries of representation categories
(with E. Meir)
Indiana Univ. Math. J. 70 (2021) 501-523
Link - Arxiv

The third Milgram-Priddy class lifts
J. Algebra 547 (2020) 173-178
Link - Arxiv

The homology of the Higman-Thompson groups
(with N. Wahl)
Invent. Math. 216 (2019) 445-518
Link - Arxiv

The rational stable homology of mapping class groups of universal nil-manifolds
Ann. Inst. Fourier 69 (2019) 783-803
Link - Arxiv

Alexander-Beck modules detect the unknot
Fund. Math. 246 (2019) 89-108
Link - Arxiv

Quandle cohomology is a Quillen cohomology
Trans. Amer. Math. Soc. 371 (2019) 5823-5839
Link - Arxiv

String bordism and chromatic characteristics
Homotopy Theory: Tools and Applications. Contemp. Math. 729 (2019) 239-254
Link - Arxiv

Homotopy coherent centers versus centers of homotopy categories
New Directions in Homotopy Theory. Contemp. Math. 707 (2018) 121-142
Link - Arxiv

Permutations, power operations, and the center of the category of racks
Comm. Algebra 46 (2018) 230-240
Link - Arxiv

Spectral sequences for Hochschild cohomology and graded centers of derived categories
(with F. Neumann)
Selecta Math. 23 (2017) 1997-2018
Link - Arxiv

Frobenius and the derived centers of algebraic theories
(with W.G. Dwyer)
Math. Z. 285 (2017) 1181-1203
Link - Arxiv

Brauer spaces for commutative rings and structured ring spectra
Manifolds and K-theory. Contemp. Math. 682 (2017) 189-208
Link - Arxiv

A non-trivial ghost kernel for complex projective spaces with symmetries
Publ. Res. Inst. Math. Sci. 52 (2016) 249-270
Link - Arxiv

Drinfeld centers for bicategories
(with E. Meir)
Doc. Math. 20 (2015) 707-735
Link - Arxiv

Homotopies and the universal fixed point property
Order 32 (2015) 301-311
Link - Arxiv

Commutative S-algebras of prime characteristics and applications to unoriented bordism
Algebr. Geom. Topol. 14 (2014) 3717-3743
Link - Arxiv

Twisted homological stability for extensions and automorphism groups of free nilpotent groups
J. K-Theory 14 (2014) 185-201
Link - Arxiv

The chromatic filtration of the Burnside category
Math. Proc. Cambridge Philos. Soc. (2013) 287-302
Link - Arxiv

Bauer-Furuta invariants and Galois symmetries
Q. J. Math. 63 (2012) 1033-1054
Link - Arxiv

Brauer groups for commutative S-algebras
(with A. Baker and B. Richter)
J. Pure Appl. Algebra 216 (2012) 2361-2376
Link - Arxiv

Crystals and derived local moduli for ordinary K3 surfaces
Adv. Math. 228 (2011) 1-21
Link - Arxiv

The Brauer group of Burnside rings
J. Algebra 324 (2010) 2589-2593
Link - Arxiv

Characteristic cohomotopy classes for families of 4-manifolds
Forum Math. 22 (2010) 509-523
Link - Arxiv

K3 spectra
Bull. Lond. Math. Soc. 42 (2010) 137-148
Link - Arxiv

Stable diffeomorphism groups of 4-manifolds
Math. Res. Lett. 15 (2008) 1003-1016
Link - Arxiv

Equivariant stable stems for prime order groups
J. Homotopy Relat. Struct. 2 (2007) 141-162
Link - Arxiv

A stable approach to the equivariant Hopf theorem
Topology Appl. 154 (2007) 2323-2332
Link - Arxiv

Software

A new Kenzo module for computing the Eilenberg-Moore spectral sequence
(with A. Romero and J. Rubio and F. Sergeraert)
ACM Commun. Comput. Algebra 54 (2020) 57-60
Link

Textbook

A Basic Course in Topology
(with G. Laures)
Birkhäuser, Heidelberg, 2025
Link

Grundkurs Topologie
(with G. Laures)
Spektrum Akademischer Verlag, Heidelberg, 2009
2., überarbeitete Auflage, Springer Spektrum, Heidelberg, 2015
3., überarbeitete Auflage, Springer Spektrum, Heidelberg, 2023
Link

Editing

Category Theory at Work in Computational Mathematics and Theoretical Informatics
(edited with K. Ebrahimi-Fard, G. Fløystad, H. Gylterud, H. Munthe-Kaas, C. Riener, and U. Wolter)
Springer (to appear)

Equivariant Topology and Derived Algebra
(edited with S. Balchin, D. Barnes, and M. Kędziorek)
Cambridge University Press, 2021
Link

Topological Data Analysis
(edited with N. Baas, G. Carlsson, G. Quick, and M. Thaule)
The Abel symposium 2018
Springer, 2020
Link


Seminars and Conferences

In this section you can learn about the presentations that I give and the conferences that I organise.


Organisation

Biracks and biquandles — an ARTIN meeting
Leeds, 16–19 December 2024

Yorkshire and Midlands Category Theory Seminar (YaMCATS)
Leeds, Manchester, and Sheffield, 2024

36th British Topology Meeting with Early Careers Researchers' Conference
Sheffield, 5-8 September 2023

Category Theory at Work in Computational Mathematics and Theoretical Informatics
Bergen, 26-30 June 2023

Effectively Teaching Mathematics as a Postgraduate
Sheffield, 25 May 2023

Equivariant Topology and Derived Algebra
Trondheim, Jul 29-Aug 2, 2019

Knots and Braids in Norway
Trondheim, May 13-17, 2019

Abelsymposium 2018: Topological Data Analysis
Geiranger, Jun 4-8, 2018

Topology and Applications
Trondheim, Nov 30-Dec 2, 2016


Talks

Bochum, 27 Jun 2024
Topology Seminar

Warwick, 25 Apr 2024
TTT Meeting

Southampton, 22 April 2024
Topology Seminar

Amiens, 20 March 2024
Journées de topologie algébrique, géométrique et quantique

Trondheim, 28 Feb 2024
NTNU Topology Seminar

Luminy/Marseille, 13-17 Nov 2023
Symmetry, Stability, and Interactions with Computation

Aalborg, 3-7 July 2023
29th Nordic Congress of Mathematicians

Leeds, 19 June 2023
Yorkshire and Midlands Category Theory Seminar

Lancaster, 28 Apr 2023
Functor Categories for Groups - Groups and Topology

Aberdeen, Nov 30, 2022
Algebra Seminar

Belfast, Nov 7, 2022
MSRC Colloquium

Tromsø, Sep 2, 2022
Nasjonalt Matematikermøte

Tromsø, Aug 30, 2022
Lie-Størmer Days

Warwick, May 10, 2022
Warwick Algebraic Topology Seminar

Ankara (via Zoom), Nov 15, 2021
Bilkent University Topology Seminar

Leicester (via Zoom), Jun 3, 2021
LAGOON - Leicester Algebra & Geometry Open Online Seminar

Bergen (via Zoom), Apr 22, 2021
Fundamental Interactions Between Algebra and Computation

Berlin (via Zoom), Apr 20, 2021
Forschungsseminar Geometrie und Topologie

Regensburg (via Zoom), Apr 15, 2021
Seminar in Homotopy Theory and Related Areas

Oberwolfach (via Zoom), Apr 7, 2021
Arbeitsgemeinschaft

Marburg (via Zoom), Mar 24, 2021
Algebraic Topology for Amateurs

University of Tromsø (via Zoom), Jan 15, 2021
Mørketidens Mattemøte

Bochum (via Zoom), Jul 7, 2020
Oberseminar Topologie

Queen's University Belfast (via Zoom), June 15, 2020
Online Algebraic Topology Seminar

Leicester, Nov 19-22, 2019
Topological Methods in Group Representation Theory

Caen, Oct 21-23, 2019
Journée Normandes de Topologie

Regensburg, Jul 19, 2019
SFB-Seminar

The Fields Institute, Toronto, Jul 8-12, 2019
Four Manifolds: Confluence of High and Low Dimensions

Leeds, Jul 1-4, 2019
Loops in Leeds

Copenhagen, Jun 24-28, 2019
10 years with SYM in Copenhagen

Oxford, Jun 20, 2019
Topology Seminar

Bielefeld, May 23, 2019
Mathematisches Kolloquium

Bochum, May 10-11, 2019
NRW Topology Meeting

Stockholm, Mar 19, 2019
Topology Seminar


Outreach

Trondheim, Sep 3, 2019
Birralee International School Trondheim
On Learning Mathematics

Trondheim, Mar 18, 2018
Study Group at Galleri KiT
Badiou - Inaesthetics - Topology