Research
My research lies at the intersection of representation theory, algebraic combinatorics and diagrammatic algebra. I develop combinatorial models that illuminate deep structures in quantum groups and invariant theory. My work has led to new diagrammatic bases, bijective correspondences, and connections to cyclic sieving, with applications ranging from statistical physics to quantum link invariants.
Research gallery
A visual introduction to my research. Select a diagram to jump to its publication entry.
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Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks
Staircase plane partitions and fans of Dyck paths.
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Rotation-invariant web bases from hourglass plabic graphs
Hourglass plabic graphs and web bases.
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Promotion permutations and the Robinson–Schensted correspondence
Shadow lines and the Robinson–Schensted correspondence.
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Promotion permutations for tableaux
Promotion permutations drawn on a disk.
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A Bijectionist’s Toolkit
Bijections intertwining promotion and rotation.
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Skew characters and cyclic sieving
Skew characters and cyclic sieving.
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Promotion on oscillating and alternating tableaux and rotation of matchings and permutations
Promotion of tableaux and rotation of chord diagrams.
Research visits
- UC Berkeley; Christian Gaetz, 23.4.2025 - 29.04.2025
- Collaborate@ICERM , Brown University; 8.5.2023 - 12.5.2023 and 22.1.2024 - 26.1.2024.
- University of Waterloo; Oliver Pechenik, 20.1.2023 - 28.1.2023
- NDSU, Fargo; Jesscia Striker, 9.10.2023 - 15.10.2023
- USC; Joshua P. Swanson, 4.5.2022 - 6.5.2022
- UC Davis; Anne Schilling, Spring term 2022
Publications
- Sam Hopkins, Jesse Kim and Stephan Pfannerer, Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks, Séminaire Lotharingien de Combinatoire, vol. 95B, 2026, Art. 2, 12, Extended abstract, 38th FPSAC, Seattle
- Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker and Joshua P. Swanson, Rotation-invariant web bases from hourglass plabic graphs, Inventiones mathematicae, vol. 243, no. 2, 2026, pp. 703-804
- Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker and Joshua P. Swanson, Web bases in degree two from hourglass plabic graphs, Int. Math. Res. Not. IMRN, no. 13, 2025, Article rnaf189, 24 pages
- Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker and Joshua P. Swanson, Web Bases for Two-Column Tableaux from Hourglass Plabic Graphs, Séminaire Lotharingien de Combinatoire 93B, 2025, 12 pages
- Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker and Joshua P. Swanson, Promotion permutations for tableaux, Combin. Theory, vol. 4, no. 2, 2024, 56 pages
- Joseph Pappe, Stephan Pfannerer, Anne Schilling and Mary Claire Simone, Promotion and growth diagrams for fans of Dyck paths and vacillating tableaux, Journal of Algebra, vol. 655, 2024, pp. 794-842
- Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker and Joshua P. Swanson, An -web basis from hourglass plabic graphs, Séminaire Lotharingien de Combinatoire, vol. 89B, 2023, Art. 9, 12
- Alexander Grosz, Tobias Kietreiber, Stephan Pfannerer and Martin Rubey, A Bijectionist’s Toolkit, Séminaire Lotharingien de Combinatoire 89B, 2023, 9 pages [SageMath documentation]
- Joseph Pappe, Stephan Pfannerer, Anne Schilling and Mary Claire Simone, Promotion for Fans of Dyck Paths, Séminaire Lotharingien de Combinatoire 89B, 2023, 12 pages
- Stephan Pfannerer, A refinement of the Murnaghan–Nakayama rule by descents for border strip tableaux, Combinatorial Theory, vol. 2, no. 2, 2022
- Per Alexandersson, Stephan Pfannerer, Martin Rubey and Joakim Uhlin, Skew characters and cyclic sieving, Forum of Mathematics, Sigma, vol. 9, 2021, e41
- Per Alexandersson, Stephan Pfannerer, Martin Rubey and Joakim Uhlin, Skew Characters and Cyclic Sieving, Séminaire Lotharingien de Combinatoire 85B, 2021, 12 pages
- Stephan Pfannerer, A Refinement of the Murnaghan-Nakayama Rule by Descents for Border Strip Tableaux, Séminaire Lotharingien de Combinatoire 85B, 2021, 12 pages
- Stephan Pfannerer, Martin Rubey and Bruce Westbury, Promotion on oscillating and alternating tableaux and rotation of matchings and permutations, Algebraic Combinatorics, vol. 3, no. 1, 2020, pp. 107–141
- Stephan Pfannerer, Martin Rubey and Bruce W. Westbury, Promotion, Evacuation and Cactus Groups, Séminaire Lotharingien de Combinatoire 78B, 2017, 12 pages
Preprints
- Sam Hopkins, Jesse Kim and Stephan Pfannerer, Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks, preprint, 2026, 23 pages
- Stephan Pfannerer, Super Major Index Cyclic Sieving, preprint, 2026, 9 pages
- Stephan Pfannerer and Joshua P. Swanson, Promotion permutations and the Robinson–Schensted correspondence, preprint, 2025, 16 pages
Presentations
- Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks, 38th FPSAC, University of Washington, Seattle, USA (Talk), 2026-07
- Bridging Crystals and Webs Through Growth Rules, Workshop on Cluster Algebras, Webs, and Canonical Bases, BIRS, Banff, Canada (Talk), 2026-03
- Rotation-invariant web bases from hourglass plabic graphs, Algebraic and enumerative combinatorics seminar, University of Waterloo (Talk), 2026-03
- Clasped Webs, Trip Permutations, and Promotion on Tableaux, Workshop on Webs in Algebra, Geometry, Topology and Combinatorics, ICERM, Providence, USA (Talk), 2025-12
- Promotion permutations and related constructions, Research seminar (Talk), University of Michigan, 2025-09
- Web Bases for Two-Column Tableaux from Hourglass Plabic Graphs, 37th FPSAC, Hokkaido University, Sapporo, Japan (Poster), 2025-07
- Growth rules for -webs, Canadian Discrete and Algorithmic Mathematics conference, Ottawa (Talk), 2025-05
- Super Major Index Cyclic Sieving, Research seminar (Talk), UC Berkeley, 2025-04
- Rotation-invariant web bases from hourglass plabic graphs, Research seminar (Talk), UC San Diego, 2025-04
- Super Major Index Cyclic Sieving, Research seminar (Talk), USC, 2025-04
- Non-crossing partitions and webs, Recent Perspectives on Non-crossing Partitions (Workshop), ESI Wien (Talk), 2025-02
- A mystery group action and the mystery statistic, William Tutte Colloquium, University of Waterloo (Talk), 2025-01
- Rotation-invariant web bases from hourglass plabic graphs, The Applied Algebra Seminar, York University (Talk), 2024-12
- Descents for Border Strip Tableaux, Algebraic and enumerative combinatorics seminar, University of Waterloo (Talk), 2024-11
- An -web basis from hourglass plabic graphs, International Conference on Enumerative Combinatorics and Applications, Virtual (Talk), 2023-09
- An -web basis from hourglass plabic graphs, EUROCOMB'23, Prague, Czech Republic (Poster), 2023-08
- An -web basis from hourglass plabic graphs, 35th FPSAC, UC Davis, California, USA (Poster), 2023-07
- Promotion and growth diagrams for fans of Dyck paths and vacillating tableaux, 35th FPSAC, UC Davis, California, USA (Poster), 2023-07
- The bijectionist’s toolkit, 35th FPSAC, UC Davis, California, USA (Software Demo), 2023-07
- An web basis, AG Diskrete Mathematik, TU Wien (Talk), 2023-01
- An web basis from hourglass plabic graphs, Algebraic Combinatorics meets Combinatorial Algebra, University of Waterloo, CA (Talk), 2023-01
- Descents for border strip tableaux, Algebra and Discrete Mathematics Seminar, NDSU (Talk), 2022-10
- A mystery group action: An implicit cyclic sieving phenomenon for standard Young tableaux, Summer School in Algebraic Combinatorics, Kraków, Poland (Talk), 2022-07
- Rotation and Promotion, Algebra and Discrete Mathematics Seminar, UC Davis (Talk), 2022-04
- Invariant Tensors and Chord Diagrams, Graduate Student Combinatorics Conference, UC San Diego, USA (Online Talk), 2022-03
- Rotation and Promotion, Graduate Online Combinatorics Colloquium (Online Talk), 2022-02
- Rotation and Promotion, AG Diskrete Mathematik, Universität Wien (Talk), 2022-01
- Skew characters and cyclic sieving, 33rd FPSAC, Bar Ilan University, Ramat Gan, Israel (Poster), 2022-01
- A refinement of the Murnaghan–Nakayama rule by descents for border strip tableaux, 33rd FPSAC, Bar Ilan University, Ramat Gan, Israel (Poster), 2022-01
- A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux, AG Diskrete Mathematik, Universität Wien (Talk), 2021-10
- A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux, AlCoVE Virtual Expedition, Hosted by Univ. of Waterloo, Canada (Online Poster), 2021-06
- A mystery group action: An implicit cyclic sieving phenomenon for standard Young tableaux, Graduate Student Combinatorics Conference, Univ. of Minnesota (Online Talk), 2021-04
- Standard young tableaux and the representation theory of the symmetric group, PhD Colloquium of the Vienna School of Mathematics, Universität Wien (Online Talk), 2020-12
- A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux, 85th Séminaire Lotharingien de Combinatorics, Strobl (Talk), 2020-09
- A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux, Graduate Online Combinatorics Colloquium (Online Talk), 2020-08
- Promotion on oscillating and alternating tableaux and rotation of matchings and permutations, 82nd Séminaire Lotharingien de Combinatorie, Curia, Portugal (Talk), 2019-04
- Promotion on oscillating and alternating tableaux and rotation of matchings and permutations, AG Diskrete Mathematik, TU Wien (Talk), 2019-01
- Promotion, Evacuation and Cactus Groups, 29th FPSAC, London, United Kingdom (Poster), 2017-07