Biserial algebras via subalgebras and the path algebra of $D_4$
Julian Külshammer. (2011). "Biserial algebras via subalgebras and the path algebra of D4." Journal of Algebra. 331(1).
CV
Education
- Diploma in Mathematics (Second Subject: Computer Science) at the University of Bonn, Germany, December 2009
- Ph.D in Mathematics at the University of Kiel, Germany, May 2012
Work experience
- October 2007 – September 2009: Student assistant
- University of Bonn, Germany
- December 2009 – September 2012: Scientific Assistant
- University of Kiel, Germany
- October 2012 – March 2016: Scientific Assistant
- University of Stuttgart, Germany
- April 2016 – March 2018: DFG Postdoc
- University of Stuttgart, Germany
- April 2018 – August 2018: Scientific Assistant
- University of Stuttgart, Germany
- September 2018 – today: Senior lecturer/Associate professor
- Uppsala University, Sweden
- Parental leave 100%: January–August 2021
- Docent title (roughly equivalent to German habilitation): 31.05.2022. Docent lecture slides on Catalan combinatorics
- Parental leave 50%: September 2022–June 2023
Academic distinctions
- International Conference on Representations of Algebras (ICRA) 2018 Award
Research grants
- January 2025 – December 2028: VR project grant “Quivers, exact categories, and A-infinity algebras”
- Total: 4080000 SEK
Publications
Representation type of Frobenius–Lusztig kernels
Julian Külshammer (2013). "Representation type of Frobenius-Lusztig kernels." The Quarterly Journal of Mathematics. 64(2).
Auslander–Reiten theory of Frobenius–Lusztig kernels
Julian Külshammer (2013). "Auslander--Reiten theory of Frobenius--Lusztig kernels." Bulletin of the London Mathematical Society. 45(6).
Auslander–Reiten theory of small half quantum groups
Julian Külshammer (2014). "Auslander--Reiten theory of small half quantum groups." Proceedings of the American Mathematical Society. 142(4).
Quasi-hereditary algebras, exact Borel subalgebras, A∞-algebras and boxes
Steffen Koenig, Julian Külshammer, and Sergiy Ovsienko (2014). "Quasi-hereditary algebras, exact Borel subalgebras, $A_\infty$-algebras and boxes." Advances in Mathematics. 262.
In the bocs seat: Quasi-hereditary algebras and representation type
Julian Külshammer (2017). "In the bocs seat: Quasi-hereditary algebras and representation type." In: Representation theory--current trends and perspectives (EMS Series of Congress Reports).
Pro-species of algebras I: Basic Properties
Julian Külshammer (2017). "Pro-species of algebras I: Basic Properties." Algebras and Representation Theory. 20.
Nakayama-type phenomena in higher Auslander–Reiten theory
Gustavo Jasso and Julian Külshammer (2018). "Nakayama-type phenomena in higher Auslander--Reiten theory." In: Contemporary Mathematics. 705.
Ringel duality as an instance of Koszul duality
Agnieszka Bodzenta and Julian Külshammer (2018). "Ringel duality as an instance of Koszul duality." Journal of Algebra. 506.
Derived invariance of support varieties
Julian Külshammer, Chrysostomos Psaroudakis, and Øystein Skartsæterhagen (2019). "Derived Invariance of support varieties." Proceedings of the American Mathematical Society. 147.
Higher Nakayama algebras I: Construction
Gustavo Jasso and Julian Külshammer (2019). "Higher Nakayama algebras I: Construction." Advances in Mathematics. 351.
From quasi-hereditary algebras with exact Borel subalgebras to directed bocses
Tomasz Brzeziński, Steffen Koenig, and Julian Külshammer (2020). "From quasi-hereditary algebras with exact Borel subalgebras to directed bocses." Bulletin of the London Mathematical Society. 52(2).
A functorial approach to monomorphism categories of species I
Nan Gao, Julian Külshammer, Sondre Kvamme, and Chrysostomos Psaroudakis (2022). "A functorial approach to monomorphism categories of species I." Communications in Contemporary Mathematics. 24.
Uniqueness of exact Borel subalgebras and bocses
Julian Külshammer and Vanessa Miemietz (2023). "Uniqueness of exact Borel subalgebras and bocses." Preprint, arXiv: 2109.03586, to appear in: Memoirs of the AMS.
Towards bound quivers for exact categories
Julian Külshammer (2023). "Towards bound quivers for exact categories." In: Preprint, survey for Proceedings of ICRA 2022.
A functorial approach to monomorphism categories of species II: Indecomposables
Nan Gao, Julian Külshammer, Sondre Kvamme, and Chrysostomos Psaroudakis (2024). "A functorial approach to monomorphism categories of species II:Indecomposables." Proc. LMS. 129 (4).
Talks
An alternative characterisation of biserial algebras
Seminar talk at University of Paderborn, Paderborn, Germany
Auslander–Reiten theory for small quantum groups
Contributed talk at ICRA XIV, Tokyo, Japan
Biserial algebras via $D_4$-subalgebras
Seminar talk at Bielefeld University, Bielefeld, Germany
Invariant support varieties and AR-theory of quantum groups
Contributed talk at Schwerpunkttagung 2011, Münster, Germany
Skew group algebras and the Auslander–Reiten theory of half-quantum groups
Contributed talk at Doktorandentagung Darstellungstheorie, Bonn, Germany
The quiver of the Frobenius–Lusztig kernel for $SL_2$
Seminar talk at University of Bochum, Bochum, Germany
Representation type of Frobenius–Lusztig kernels
Contributed talk at Representation Theory Days 2011, Hannover, Germany
Auslander–Reiten theory of Frobenius–Lusztig kernels
Seminar talk at University of Stuttgart, Stuttgart, Germany
Representation type and Auslander–Reiten theory of Frobenius–Lusztig kernels
Contributed talk at ICRA XV, Bielefeld, Germany
Exact Borel subalgebras via A-infinity categories
Seminar talk at University of Münster, Münster, Germany
Quasi-hereditary algebras, A-infinity algebras and boxes
Plenary talk at MFO, Oberwolfach, Germany
Quasi-hereditary algebras, A-infinity algebras and boxes
Contributed talk at DFG-priority program SPP1388, Soltau, Germany
In the box seat: Quasi-hereditary algebras
Plenary talk at ICRA XVI, Sanya, China
Representation type, boxes, and Schur algebras
Plenary talk at Schwerpunkttagung 2015, Bad Honnef, Germany
Representation theory of (generalised) species
Seminar talk at University of Kiel, Kiel, Germany
Boxes and tame Schur algebras
Seminar talk at University of Bonn, Bonn, Germany
Boxes and filtered representation type of Schur algebras
Invited talk at AMS-EMS-SPM joint meeting, Porto, Portugal
Bocses and quasi-hereditary algebras
Seminar talk at University of East Anglia, Norwich, United Kingdom
Higher Nakayama algebras
Contributed talk at Representation theory days 2015, Stuttgart, Germany
Analogues of Nakayama algebras in higher Auslander–Reiten theory
Seminar talk at NTNU, Trondheim, Norway
Exact Borel subalgebras and representation type
Invited talk at Representation theory conference, Uppsala, Sweden
Higher Nakayama algebras
Plenary talk at ICRA XVII, Syracuse, USA
On a higher cluster category of type A∞$
Seminar talk at University of Bonn, Bonn, Germany
Quasi-hereditary algebras and directed corings
Seminar talk at MPIM Bonn, Bonn, Germany
Spherical objects in higher Auslander–Reiten theory
Seminar talk at Bielefeld University, Bielefeld, Germany
Spherical objects and the higher cluster category of the cyclic apeirotope
Seminar talk at University of Münster, Münster, Germany
Higher Nakayama algebras
Plenary talk at MFO, Oberwolfach, Germany
Ringel dual bocses and smooth rational surfaces
Seminar talk at University of Cologne, Cologne, Germany
Ringel duality as a special case of Koszul duality
Seminar talk at University of Kaiserslautern, Kaiserslautern, Germany
Ringel duality as a special case of Koszul duality
Invited talk at 20th NWDR workshop, Hannover, Germany
From A-infinity algebras to bocses via Koszul duality
Seminar talk at HIM Bonn, Bonn, Germany
A-infinity structures on Ext-algebras for quasi-hereditary algebras
Contributed talk at Representation Theory Days 2017, Eichstätt, Germany
Bocses — the quivers with relations for quasi-hereditary algebras
Seminar talk at University of Bonn, Bonn, Germany
Pro-species of algebras and monomorphism categories
Seminar talk at Bielefeld University, Bielefeld, Germany
Existence and uniqueness of exact Borel subalgebras
Invited talk at Workshop Tensor Categories, Hopf algebras and quantum groups, University of Marburg, Marburg, Germany
Existence and uniqueness of exact Borel subalgebras
Seminar talk at University of Erlangen--Nürnberg, Erlangen, Germany
Existence and uniqueness of exact Borel subalgebras
Seminar talk at Séminaire d'Algèbre, Paris, France
Understanding quasi-hereditary algebras using A-infinity algebras
Invited talk at Workshop on non-associative algebras and applications, Lancaster University, Lancaster, United Kingdom
A-infinity structures on Ext-algebras of standard modules for quasi-hereditary algebras
Plenary talk at ICRA XVIII, Prague, Czechia
Hopotopy and homology of standardly filtered categories II
Invited talk at Homotopy meets homology, Dublin, Ireland
How to make modules simple using A-infinity algebras (6 talks with 4 problem sessions)
Plenary talk at Summer School: Strong homotopy methods in homological algebra, Nordfjordeid, Norway
Gorenstein homological algebra for generalised species
Seminar talk at University of Thessaloniki, Thessaloniki, Greece
Introduction to quasi-hereditary algebras (2 talks)
Plenary talk at Tilting theory, Singularity categories and noncommutative resolutions, Banff International Research Station, Oaxaca, Mexico
The Auslander–Reiten translation in monomorphism categories
Seminar talk at University of Stuttgart, Germany, Stuttgart, Germany
Dual extensions — bocs perspectives
Seminar talk at University of Stuttgart, Germany, Stuttgart, Germany
Monomorphism categories for generalised species
Plenary talk at ICRA 2020 Research Snapshot, online
Exact categories via A∞-algebras
Seminar talk at Tokyo-Nagoya algebra seminar, online
Uniqueness of exact Borel subalgebras and bocses
Invited talk at A conference in celebration of the work of Bill Crawley-Boevey, online
Nakayama functors and monomorphism categories
Plenary talk at Abel Symposium: Triangulated categories in representation theory and beyond, Ålesund, Norway
Towards bound quivers for exact categories (Lecture Series, 3 talks of 1h each)
Plenary talk at ICRA 2022 Workshop, Montevideo, Uruguay
Existence and uniqueness of exact Borel subalgebras
Invited talk at 28th Nordic Congress of Mathematicians, Helsinki, Finland
Exact Borel subalgebras and (A_n)-combinatorics
Invited talk at Combinatorial aspects of representation theory, Oslo, Norway
Uniqueness of exact Borel subalgebras and bocses (Lecture Series, 3 talks of 1h each)
Plenary talk at Postmodern Ringel duality, bocses and contramodules, Stuttgart, Germany
Auslander–Reiten theory of monomorphism categories
Invited talk at Homological algebra and representation theory, Karlovasi, Greece
Indecomposables in monomorphism categories
Invited talk at University of Stuttgart, Stuttgart, Germany
Classifying submodules: From the Birkhoff problem to topological data analysis
Invited talk at Mälardalen University, Västerås, Sweden
Teaching
As Lecturer
Representation theory of finite dimensional algebras and corings
Summer term 2018
Linear algebra II (for engineering physics and IT engineering)
Fall term 2018 (Period 2)
Elementary number theory
Spring term 2019 (Period 4)
Modules and homological algebra
Fall term 2019 (Periods 1+2)
PhD course in algebra
Fall term 2019 (Periods 1+2)
Linear algebra II (for mathematicians, system engineers, and teachers)
Spring term 2020 (Period 3)
Elementary number theory
Spring term 2020 (Period 4)
Linear algebra II (for engineers)
Fall term 2020 (Period 1)
A-infinity structures in representation theory
Fall term 2021 (Periods 1+2)
Perspectives on Mathematics
Spring term 2023 (Period 3)
Linear Algebra and geometry I (for engineers and chemists)
Fall term 2023 (Period 2)
Representation theory of finite groups
Spring term 2024 (Period 3+4)
Logic and proof techniques I
Spring term 2024 (Period 4)
Linear algebra and geometry I
Autumn term 2024 (Period 1)
Modules and homological algebra
Autumn term 2024 (Period 1+2)
Linear algebra II (for mathematicians, engineers, and teachers)
Spring term 2025 (Period 3)
Logic and proof techniques I
Spring term 2025 (Period 4)
As Teaching Assistant
Logic and discrete structures for computer scientists
Winter term 2007/08
Linear algebra for computer scientists
Summer term 2008
Introduction to representation theory
Winter term 2008/09
Seminar on representation theory
Summer term 2009
Linear algebra I
Winter term 2009/10
Algebra II
Summer term 2010
Algebra I
Winter term 2010/11
Algebra II
Summer term 2011
Mathematics for earth scientists
Winter term 2011/12
Foundations of geometry
Summer term 2012
Topology
Winter term 2012/13
Higher mathematics for engineers II
Summer term 2013
Higher mathematics for engineers I
Winter term 2013/14
Higher mathematics for engineers II
Summer term 2014
Higher mathematics for physicists I
Winter term 2014/15
Higher mathematics for physicists II
Summer term 2015
Linear algebra I
Winter term 2015/16
Linear algebra II (for electrical engineers)
Fall term 2018 (Period 1)
Linear algebra II (for engineering physics and IT engineering)
Fall term 2018 (Period 2)
Several variable calculus (for engineers)
Spring term 2019 (Periods 3+4)
Linear algebra II (for mathematicians)
Spring term 2020 (Period 3)
Linear algebra II (for system engineers)
Spring term 2020 (Period 3)
Several variable calculus (limited version)
Spring term 2020 (Period 4)
Linear algebra II (for engineers)
Fall term 2020 (Period 1)
Algebra II
Spring term 2024 (Period 3)
Linear algebra II (for system engineers)
Spring term 2025 (Period 3)
Logic and proof techniques I
Spring term 2025 (Period 4)
Service
- Programme Coordinator for the Master Programme in Mathematics at Uppsala University (2020–2023)
- Director of Postgraduate Studies in Mathematics at Uppsala University (2024–2026)
- Maintainer of FDLIST
- Organiser of FD Seminar (2020-2024)