Mathematical Insitute
Faculty of Mathematics and Natural Sciences
University of Cologne
Contact
Visiting and postal address
Mathematical Institute
University of Cologne
Weyertal 86-90
D-50931 Cologne
Germany
Building 162, office 1.14
Telephone number: +49 221 470 3715
Office hours: by appointment
Secretrary: Ms. Leah Manzanilla
E-mail address
In order to ensure that your messages are read, please contact me only through the following e-mail address:
gjasso[at]math.uni-koeln.de
Any other institutional e-mail addresses of mine have been or will be closed.
PGP key fingerprint
I sign all outgoing e-mail messages using PGP.
My public key fingerprint is the following:
7527 92FC FE23 2132 1A9A 62C1 F655 F8F8 B671 FC89
Download public key (keys.openpgp.com) | What is PGP?
About me
Pronouns: he / him
I am a mathematician. My research interests include the following topics:
- Representation theory of quivers and algebras
- Homological and homotopical algebra, higher category theory
- Cluster algebras and their categorifications
Academical profiles
arXiv.org | Google Scholar | MathSciNet | ORCID | Web of Science | zbMATH Open
Open positions
You are welcome to inquire about upcoming advertisements of positions in the Algebra and Representation Theory Group, but please note that applications are handled through official channels.
Please do not send me unsolicited application materials. For security reasons, I will not open unsolicited files.
Curriculum vitae
Download my abridged CV (comprehensive CV available upon request).
Including my student years, I have been affiliated to the following institutions during my academical career:
Since 2024-08-15 Universitätsprofessor für Algebra (W2) at the Faculty of Mathematics and Natural Sciences of the University of Cologne.
2023-01-01 – 2024-08-01 My research was supported by a Research project grant within natural and engineering sciences from the Swedish Research Council (Vetenskapsrådet).
2022-10-15 11th Award for Encouragement of Alumni and Students (“Hida Award”), Alumni Association of the Graduate School of Mathematics, Nagoya University.
2022-03-01 – 2024-08-14 Senior Lecturer at the Centre for Mathematical Sciences (Faculty of Science) of Lund University.
2018-08-13 International Conference on Representations of Algebras (ICRA) Award 2018 (a second prize was awarded to Julian Külshammer).
2017-10-01 – 2022-02-28 Akademischer Rat auf Zeit at the Mathematisches Institut of the Rheinische Friedrich-Wilhelms-Universität Bonn working in the research group of Prof. Dr. Jan Schröer.
2014-10-01 – 2017-09-30 Hausdorff Postdoc at the Hausdorff Center for Mathematics of the Rheinische Friedrich-Wilhelms-Universität Bonn under the mentorship of Prof. Dr. Jan Schröer.
2011-10-01 – 2014-09-29 Ph.D student at the Graduate School of Mathematics of Nagoya University under the supervision of Prof. Dr. Osamu Iyama.
2005-08-15 – 2011-09-14 B.Sc. and M.Sc. student at the Facultad de Ciencias (B.Sc.) and the Instituto de Matemáticas (M.Sc.) of the Universidad Nacional Autónoma de México under the supervision of Michael Barot (B.Sc. and M.Sc. thesis advisor) and Prof. Dr. Christof Geiß (M.Sc. thesis unofficial second advisor).
1987-03-18 Born in Guadalajara, Jalisco, Mexico.
Remark
My full (legal) name, formed according to the Spanish Naming Customs (used also in Mexico), is Gustavo Jasso Ahuja. Note, however, that I do not utilise my second last name in any professional context.
Activities
Cologne Algebra and Representation Theory Group
I am a member of the Algebra and Representation Theory Group at the University of Cologne. Visit the link to learn about our activities.
Learning seminar
Together with Bernhard Keller (Université Paris Cité) I organise an online Learning Seminar on Higher Category Theory and its Applications to Algebra and Geometry. At the moment this is private seminar; if you are interested in participating please contact either Bernhard or myself by e-mail.
FDLIST
Since May 2021, I am one for the maintainers of the FDLIST, an information list that provides a forum for the exchange of information, ideas, problems and questions, which are related to representation theory of finite-dimensional algebras.
FD Seminar
I was one for the organisers of the FD Seminar, an online seminar on representation theory of quivers and finite-dimensional algebras. The seminar ran from May 2020 until May 2024.
The recordings of most talks that took place at the FD Seminar can be streamed from the seminar’s BigBlueButton Server (account required).
Research group
Ph.D. students
- Marvin Plogmann (since January 2024).
- Jan Henrik Thomm (since October 2022).
Visitors
- Dr. Norihiro Hanihara, Jan 2025 (Kyushu)
- David T. Nkansah, Sep-Dec 2024 (Aarhus)
- Prof. Dr. Catharina Stroppel, May 2024 (Bonn)
- Prof. Dr. Bernhard Keller, Oct 2023 (Paris)
- Sebastian H. Martensen, Oct 2023 (Trondheim)
Writings
Preprints
- Jasso, G., Muro, F., The Derived Auslander–Iyama Correspondence, with an appendix by B. Keller. arXiv:2208.14413 [math.RT] (submitted)
Publications
- Jasso, G., On a theorem of B. Keller on Yoneda algebras of simple modules. arXiv:2402.14004 [math.RT] (Accepted for publication in C. R. Math. Acad. Sci. Paris)
- Jasso, G., Derived equivalences of upper-triangular ring spectra via lax limits. C. R. Math. Acad. Sci. Paris, Volume 362 (2024), 279-285.
Publication | arXiv | MathSciNet - Dyckerhoff, T., Jasso, G., Lekili, Y., The symplectic geometry of higher Auslander algebras: symmetric products of disks. Forum Math. Sigma, Volume 9 (2021), Paper No. e10, 49.
Publication | arXiv | MathSciNet - Dyckerhoff, T., Jasso, G., Walde, T., Generalised BGP reflection functors via the Grothendieck construction. Int. Math. Res. Not. IMRN (2021), Issue 20, 15733-15745.
Publication | arXiv | MathSciNet - Dyckerhoff, T., Jasso, G., Walde, T., Simplicial structures in higher Auslander–Reiten theory. Adv. Math., Volume 355 (2019), 106762.
Publication | arXiv | MathSciNet
Errata: In 1.10 and 1.11 the endomorphism algebras should be their opposites. In the line after 1.14 'right' should be 'left'. In the proof of Prop. 1.17, '(left)' should be '(right)' and the factors of the tensor product should be commuted. In Remark 2.29, the symbol S_{m}^{n+1} should be be replaced by S^{n+1}. - Jasso, G., Külshammer, J., Higher Nakayama algebras I: Construction, with an appendix by J. Külshammer and Ch. Psaroudakis and an appendix by S. Kvamme. Adv. Math., Volume 351 (2019), 1139-1200.
Publication | arXiv | MathSciNet - Jasso, G., Kvamme, S., An introduction to higher Auslander-Reiten theory. Bull. Lond. Math. Soc., Volume 51 (2019), Issue 1, 1-24.
Publication | arXiv | MathSciNet - Demonet, L., Iyama, O., Jasso, G., τ-tilting finite algebras, bricks, and g-vectors. Int. Math. Res. Not. IMRN (2019), Issue 3, 852-892.
Publication | arXiv | MathSciNet - Iyama, O., Jasso, G., Higher Auslander correspondence for dualizing R-varieties. Algebr. Represent. Theory, Volume 20 (2017), Issue 2, 335-354.
Publication | arXiv | MathSciNet - Jasso, G., n-abelian and n-exact categories. Math. Z., Volume 283 (2016), Issue 3-4, 703-759.
Publication | arXiv | MathSciNet
Errata: (S. Kvamme) In Lemma 3.22, the adverbs 'contravariantly' and 'covariantly' should be exchanged in items (vi) and (vii). In Theorem 4.14 the ambient additive category should be assumed to be weakly idempotent complete so that the class Y is closed under weak isomorphisms. - Bergh, P. A., Jasso, G., Thaule, M., Higher n-angulations from local rings. J. Lond. Math. Soc. (2), Volume 93 (2016), Issue 1, 123-142.
Publication | arXiv | MathSciNet - Jasso, G., τ²-stable tilting complexes over weighted projective lines. Adv. Math., Volume 273 (2015), 1-31.
Publication | arXiv | MathSciNet - Jasso, G., Reduction of τ-tilting modules and torsion pairs. Int. Math. Res. Not. IMRN (2015), Issue 16, 7190-7237.
Publication | arXiv | MathSciNet - Jasso, G., The extended affine Lie algebra associated with a connected non-negative unit form. J. Algebra, Volume 409 (2014), 148-161.
Publication | arXiv | MathSciNet - Barot, M., Geiss, Ch., Jasso, G., Tubular cluster algebras II: Exponential growth. J. Pure Appl. Algebra, Volume 217 (2013), Issue 10, 1825-1837.
Publication | arXiv | MathSciNet
Remarks
- My Ph.D. thesis comprises articles [3-4] and [6].
- My master’s thesis comprises part of article [1].
- My bachelor’s thesis comprises article [2].
Proceedings, extended abstracts and other writings
- Jasso, G., Universal Massey Products in Representation Theory of Algebras. In: Keller, B., Krause, H., Lowen, W., Solotar, A., (.eds), Hochschild (Co)Homology and Applications: Abstracts from the workshop held April 14–19, 2024, Oberwolfach Rep. (to appear).
Publication | PDF - Jasso, G., Derived Endomorphism Algebras in Higher Auslander–Reiten Theory. In: Amiot, C., Crawley-Boevey, W., Iyama, O., Schröer, J., (.eds), Representation theory of quivers and finite-dimensional algebras: Abstracts from the workshop held January 12–18, 2023, Oberwolfach Rep. (to appear).
Publication | PDF
Errata: In point (2) of the second theorem, the degree 0 part of B must be basic self-injective. - Jasso, G., Keller, B., Muro, F., The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence. In: Bergh, P. A., Oppermann, S., Solberg, Øyvind, (.eds), Triangulated categories in representation theory and beyond. The Abel Symposium 2022, Abel Symposia, Springer Cham (2024) 105-140.
Publication | arXiv - Jasso, G., The symplectic geometry of higher Auslander algebras, an overview. In: Amiot, C., Crawley-Boevey, W., Iyama, O., Krause, H., (.eds), Representation theory of quivers and finite dimensional algebras: Abstracts from the workshop held January 19–25, 2020, Oberwolfach Rep. 17 (2020) 143-230.
Publication | PDF - Jasso, G., Higher Auslander algebras of type A and the higher Waldhausen S-constructions. In: Šťovíček, J., Trlifaj, J., (.eds), Representation theory and beyond, Contemp. Math. 758, Amer. Math. Soc., Providence, RI (2020) 249-265.
Publication | arXiv - Jasso, G., Külshammer, J., Nakayama-type phenomena in higher Auslander-Reiten theory. In: Leuschke, G. J., Bleher, F., Schiffler, R., Zacharia, D., (.eds), Representations of algebras, Contemp. Math. 705, Amer. Math. Soc., Providence, RI (2018) 79-98.
Publication | arXiv - Jasso, G., Spherical objects in higher Auslander–Reiten theory (joint work with J. Külshammer). In: Crawley-Boevey, W., Iyama, O., Krause, H., (.eds), Representation Theory of Quivers and Finite Dimensional Algebras: Abstracts from the workshop held February 19–25, 2017, Oberwolfach Rep. 14 (2017) 591-681.
Publication | PDF - Jasso, G., Külshammer, J., The naive approach for constructing the derived category of a d-abelian category fails. arXiv:1604.03473 [math.RT] (not intended for publication)
- Jasso, G., Reduction of τ-tilting modules and torsion classes. In: Proceedings of the 16th Workshop on Representation Theory of Algebraic Groups and Quantum Groups (2013) 157-160.
- Jasso, G., Cluster-tilted algebras of canonical type and quivers with potential. In: Proceedings of the 45th Symposium on Ring Theory and Representation Theory (2012) 61-68.
Publication - Jasso, G., Cluster-tilted algebras of canonical type and graded quivers with potential. In: Proceedings of the 15th Workshop on Representation Theory of Algebraic Groups and Quantum Groups (2012) 13-18.
Collaborators
Michael Barot | Petter A. Bergh | Laurent Demonet | Tobias Dyckerhoff | Christof Geiß | Osamu Iyama | Julian Külshammer | Sondre Kvamme | Yankı Lekili | Fernando Muro | Yann Palu | Marius Thaule | Tashi Walde
Resources
Below are the notes/slides from some of my talks and also a poster. Click on the titles to open/download the corresponding PDF file.
- Minimal A-infinity algebras of endomorphisms. XXI International Conference on Representations of Algebras (ICRA). Shanghai Jiao Tong University, China (2024).
- The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence. McKay correspondence, Tilting Theory and Related Topics. Kavli IPMU, Kashiwa, Japan (2023).
- Auslander’s Formula for stable infinity-categories, after Klemenc. Representation theory and non-commutative geometry/ARTIG 3. Paderborn, Germany (2023).
- Exact infinity-categories. Current trends in representation theory, cluster algebras and geometry. CIRM-Luminy, Marseille, France (2023).
- The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence. . Casa Matemática Oaxaca, Mexico (2023).
- Quivers, quivers and more quivers. Maths Student’s Day. Lund, Sweden (2023).
- (Non-)uniqueness of strong DG enhancements. Combinatorial aspects of Representation Theory. Oslo, Norway (2023).
- (Non-)uniqueness of strong DG enhancements. New Directions in Group Theory and Triangulated Categories. Online seminar (2023).
- Brackets, trees and the Borromean rings. Lund Mathematics Colloquium. Lund, Sweden (2022).
- The Donovan-Wemyss Conjecture via the Derived Auslander–Iyama Correspondence. Geometric Representation Theory Seminar. YMSC, Beijing, China (2022).
- The Triangulated Auslander–Iyama Correspondence. Algebra Days in Paris in honor of Bernhard Keller. IHP, Paris, France (2022).
- The Triangulated Auslander–Iyama Correspondence. 28th Nordic Congress of Mathematicians. Helsinki, Finland (2022).
- The Triangulated Auslander–Iyama Correspondence, part I. Abel Symposium 2022, Ålesund, Norway. (2022).
Notes of part II by F. Muro (external link) - La conjectura “optimista” de Lekili y Polishchuk. Coloquio Oaxaqueño de Matemáticas. Oaxaca, Mexico (2022).
- The Triangulated Auslander–Iyama Correspondence. Online Workshop on Higher Dimensional Homological Algebra. IPM-Isfahan, Iran (2022).
- Generalised BGP reflection functors. . Bielefeld, Germany (2021).
- Homotopical algebra in exact (infinity-)categories. 2021 London Mathematical Society Northern Regional Meeting and Conference (A conference in celebration of the work of Bill Crawley-Boevey). Bielefeld, Germany (2021).
- The Waldhausen S-dot construction and the symplectic geometry of surfaces and their symmetric products. Opening Workshop (IRP Higher Homotopical Structures). CRM Barcelona, Spain (2021).
- Universal properties of derived categories, after Lurie. BIREP Seminar. Bielefeld, Germany (2021).
- Deriving a theorem of Ladkani. Flash Talks in Representation Theory at NTNU. Trondheim, Norway (2021).
- Partially wrapped Fukaya categories of symmetric products of marked disks. Winter School: Connections between representation theory and geometry. Bonn, Germany (online event) (2020).
- Stable infinity-categories: localisations and recollements:. ‘Two Weeks of Silting’ Summer School. Stuttgart, Germany (2019).
Exercises - Higher-dimensional Auslander algebras of type A and the higher-dimensional Waldhausen S-constructions. XVIII International Conference on Representations of Algebras (ICRA). Prague, Czech Republic (2018).
- d-homological algebra. Panorama of Mathematics. Bonn, Germany (2015).
- tau-tilting reduction. XV International Conference on Representations of Algebras (ICRA). Bielefeld, Germany (2012).
- The extended affine Lie algebra associated with a connected non-negative unit form. XIV International Conference on Representations of Algebras (ICRA). Tokyo, Japan (2010).
Teaching
Detailed information on my current teaching activities can be found in the course catalogue.
Information on the seminars organised by the Algebra and Representation Theory Group can be found at the following URL:
https://www.mi.uni-koeln.de/RepTheory/
@UzK students: Please write me an e-mail if you are interested in writing a bachelor’s or master’s thesis under my supervision.
Teaching at the University of Cologne (since 2024)
- Summer Semester 2025
Introduction to ∞-category theory - Winter Semester 2024/2025
Homotopy theory of simplicial sets
Teaching at Lund University (2022-2024)
- Spring Term 2024
MATP33 Group and Ring Theory - Fall Term 2023
MATP43 Representation Theory of Quivers and Algebras
MATM35 Number Theory - Spring Term 2023
MATP33 Group and Ring Theory - Fall Term 2022
MATM35 Number Theory
Teaching at the University of Bonn (2016–2021)
- Winter Semester 2021/2022
S4A2 Graduate Seminar on Representation Theory “Tilting theory” (co-organised with Prof. Dr. Jan Schröer) - Summer Semester 2021
V5A2 Selected topics in Algebra “Differential graded categories” - Summer Semester 2019
S4A2 Graduate Seminar on Representation Theory “Triangulated categories in the representation theory of finite-dimensional algebras” - Summer Semester 2018
S4A2 Graduate Seminar on Representation Theory “τ-tilting theory” - Winter Semester 2016/2017
V5A5 Advanced Topics in Representation Theory “Differential graded categories, a representation theoretic approach”
Students
Master students
- Eric Dannetun, Quotients of triangulated categories (2024).
Aftwerwards : PhD position with Dr. Samuel Lundqvist at Stockholm University. - Daniel Falkowski, A note on tensor-triangular geometry (2024).
- Carl-Fredrik Lidgren, t-structures & recollements (2023).
- Martin Böhm, Cluster algebras and knot polynomials (2021).
- Jona Klemenc, The stable hull of exact infinity-categories (2020).
Publication | arXiv - Calvin Pfeifer, Torsion classes and wide subcategories (2020).
Aftwerwards : PhD position with Prof. Dr. Christof Geiss in Odense.
Publication | arXiv - Jan-Paul Lerch, Bijections in tau-tilting theory (2019).
Aftwerwards : PhD position with Prof. Dr. Henning Krause in Bielefeld. - Aran Tattar, On Gorenstein k-categories (2018).
Aftwerwards : PhD position with Prof. Dr. Sibylle Schroll in Leicester.
Remark
- Students [7-8] were supervised at Lund University.
- Students [1-5] were supervised at the University of Bonn.
Bachelor students
- Arthur Faxén, The Barr-Beck Mondadicity Theorem (2024).
- Bror Persson, Introduction to Auslander-Reiten Theory (2024).
- Sebastian Westerlund, Hall algebras (2024).
- Erik Christmansson, Gentle algebras (2024).
- Diego González Pérez, Elements of Abelian categories. The Yoneda Ext and the Baer Sum (2024).
- Yijia Zeng, Frieze patterns (2023).
- Felix Anton Brandt, Decomposition theorems for persistence modules (2021).
- Tanja Helme, Cluster-Algebren und Kettenbrüche (2020).
- George Tyriard, A Morita-theoretic proof of the Dold-Kan correspondence (2020).
- Aaron Wild, Lurie’s differential graded nerve is a right Quillen functor (2020).
- Roman Höffken, Morita Theorie für Ringe und Kategorien (2020).
- Vincent Siebler, The derived category of a gentle algebra (2019).
Remark
- Students [7-12] were supervised at Lund University.
- Students [1-6] were supervised at the University of Bonn.