Research

Writings

Preprints

3. J. O. Gómez, G. Jasso, and M. Nielsen, Hopfological algebra, revisited, arXiv:2606.19485 [math.RT] (2026) (submitted).
2. G. Jasso and F. Muro, The Derived Auslander–Iyama Correspondence II: Bimodule Calabi–Yau Structures, arXiv:2509.22625 [math.RT] (2025) (submitted).
1. G. Jasso and F. Muro, Obstruction theory for $A$-infinity bimodules, arXiv:2507.17568 [math.AT] (2025) (submitted).

Books

1. G. Jasso, Differential graded categories in the representation theory of finite-dimensional algebras (work in progress, 251 pages).

Publications

17. G. Jasso and F. Muro, The Derived Auslander–Iyama Correspondence, with an appendix by B. Keller, J. Amer. Math. Soc. 40 (2027), no. 1, 1–127.
    Publication · arXiv · MathSciNet
16. G. Jasso, $Q$-shaped derived categories as derived categories of differential graded bimodules, arXiv:2501.08255 [math.RT] (2025) (accepted for publication in Ann. Represent. Theory).
15. G. Jasso, On a theorem of B. Keller on Yoneda algebras of simple modules, C. R. Math. Acad. Sci. Paris 362 (2024), 1449–1453.
    Publication · arXiv · MathSciNet · zbMATH
14. G. Jasso, Derived equivalences of upper-triangular ring spectra via lax limits, C. R. Math. Acad. Sci. Paris 362 (2024), 279–285.
    Publication · arXiv · MathSciNet · zbMATH
13. T. Dyckerhoff, G. Jasso, and Y. Lekili, The symplectic geometry of higher Auslander algebras: symmetric products of disks, Forum Math. Sigma 9 (2021), Paper No. e10, 49.
    Publication · arXiv · MathSciNet · zbMATH
12. T. Dyckerhoff, G. Jasso, and T. Walde, Generalised BGP reflection functors via the Grothendieck construction, Int. Math. Res. Not. IMRN (2021), no. 20, 15733–15745.
    Publication · arXiv · MathSciNet · zbMATH
11. T. Dyckerhoff, G. Jasso, and T. Walde, Simplicial structures in higher Auslander–Reiten theory, Adv. Math. 355 (2019), 106762.
    Publication · arXiv · MathSciNet · zbMATH
    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 replaced by S^{n+1}.

10. G. Jasso and J. Külshammer, Higher Nakayama algebras I: Construction: with an appendix by J. Külshammer and Ch. Psaroudakis and an appendix by S. Kvamme, Adv. Math. 351 (2019), 1139–1200.
    Publication · arXiv · MathSciNet · zbMATH
9. G. Jasso and S. Kvamme, An introduction to higher Auslander-Reiten theory, Bull. Lond. Math. Soc. 51 (2019), no. 1, 1–24.
   Publication · arXiv · MathSciNet · zbMATH
8. L. Demonet, O. Iyama, and G. Jasso, $\tau$-tilting finite algebras, bricks, and $g$-vectors, Int. Math. Res. Not. IMRN (2019), no. 3, 852–892.
   Publication · arXiv · MathSciNet · zbMATH
   Note:

   Over an algebraically closed field of characteristic 0, statements (b) and (c) in Theorem 1.7 (implied by statement (a), but not conversely) were shown by Derksen and Fei in Proposition 6.1 of their article General presentations of algebras.

7. O. Iyama and G. Jasso, Higher Auslander correspondence for dualizing $R$-varieties, Algebr. Represent. Theory 20 (2017), no. 2, 335–354.
   Publication · arXiv · MathSciNet · zbMATH
6. G. Jasso, $n$-abelian and $n$-exact categories, Math. Z. 283 (2016), no. 3-4, 703–759.
   Publication · arXiv · MathSciNet · zbMATH
   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; see Section 8 in Kvamme’s paper for the correct statement in the non-weakly-idempotent-complete case.

5. P. A. Bergh, G. Jasso, and M. Thaule, Higher $n$-angulations from local rings, J. Lond. Math. Soc. (2) 93 (2016), no. 1, 123–142.
   Publication · arXiv · MathSciNet · zbMATH
4. G. Jasso, $\tau^2$-stable tilting complexes over weighted projective lines, Adv. Math. 273 (2015), 1–31.
   Publication · arXiv · MathSciNet · zbMATH
   Errata:

   The first sentence on page 23 should read ‘… all semistable sheaves of a fixed slope …’ This has no bearing on the argument since the only thing that is used is that every indecomposable rigid sheaf lies in an exceptional tube.

3. G. Jasso, Reduction of $\tau$-tilting modules and torsion pairs, Int. Math. Res. Not. IMRN (2015), no. 16, 7190–7237.
   Publication · arXiv · MathSciNet · zbMATH
2. G. Jasso, The extended affine Lie algebra associated with a connected non-negative unit form, J. Algebra 409 (2014), 148–161.
   Publication · arXiv · MathSciNet · zbMATH
1. M. Barot, Ch. Geiss, and G. Jasso, Tubular cluster algebras II: Exponential growth, J. Pure Appl. Algebra 217 (2013), no. 10, 1825–1837.
   Publication · arXiv · MathSciNet · zbMATH

Proceedings, extended abstracts and other writings

15. G. Jasso, Stable $\infty$-categories for representation theorists, arXiv:2603.14970 [math.RT] (2026) (submitted).
    Note:

    Invited contribution to the proceedings of the 10th conference on Advances in Representation Theory of Algebras (ARTA X)

14. G. Jasso, H. Krause, and S. Schroll, Rickard’s derived Morita theory: Review and outlook, J. Lond. Math. Soc. (2) 113 (2026), no. 6, Paper No. e70577.
    Publication · arXiv · MathSciNet
    Note:

    Contribution to the 100th anniversary volume of the J. Lond. Math. Soc.

13. G. Jasso and F. Muro, Minimal $A_\infty$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects, arXiv:2508.18852 [math.RT] (2025).
    Note:

    Contribution to the proceedings of the XXI International Conference on Representations of Algebras (ICRA 21).

12. G. Jasso, Brackets, trees and the Borromean rings, Snapshots of modern mathematics from Oberwolfach (2025), no. 7.
    Publication
11. G. Jasso, Universal Massey Products in Representation Theory of Algebras, Oberwolfach Rep. 21 (2024), no. 2, 1148–1150.
    Publication · MathSciNet · zbMATH · PDF
    Note:

    Abstracts from the workshop held April 14–19, 2024, Organized by Bernhard Keller, Henning Krause, Wendy Lowen and Andrea Solotar

10. G. Jasso, Derived Endomorphism Algebras in Higher Auslander–Reiten Theory, Oberwolfach Rep. 20 (2023), no. 1, 409–412.
    Publication · MathSciNet · zbMATH · PDF
    Note:

    Abstracts from the workshop held February 12–18, 2023, Organized by Claire Amiot, William Crawley-Boevey, Osamu Iyama and Jan Schröer

    Errata:

    In point (2) of the second theorem, the degree 0 part of B must be basic self-injective.

9. G. Jasso, B. Keller, and F. Muro, The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence, Triangulated Categories in Representation Theory and Beyond, Abel Symp. 17, Springer, Cham, 2024, pp. 105–140.
   Publication · arXiv · MathSciNet · zbMATH
8. G. Jasso, The symplectic geometry of higher Auslander algebras, an overview, Oberwolfach Rep. 17 (2020), no. 1, 190–192.
   Publication · MathSciNet · zbMATH · PDF
   Note:

   Abstracts from the workshop held January 19–25, 2020, Organized by Claire Amiot, William Crawley-Boevey, Osamu Iyama and Henning Krause

7. G. Jasso, Higher Auslander algebras of type $A$ and the higher Waldhausen $S$-constructions, Representation theory and beyond (J. Šťovíček and J. Trlifaj, eds.), Contemp. Math. 758, Amer. Math. Soc., Providence, RI, 2020, pp. 249–265.
   Publication · arXiv · MathSciNet · zbMATH
6. G. Jasso and J. Külshammer, Nakayama-type phenomena in higher Auslander-Reiten theory, Representations of algebras (G. J. Leuschke, F. Bleher, R. Schiffler, and D. Zacharia, eds.), Contemp. Math. 705, Amer. Math. Soc., Providence, RI, 2018, pp. 79–98.
   Publication · arXiv · MathSciNet · zbMATH
5. G. Jasso, Spherical objects in higher Auslander–Reiten theory (joint work with J. Külshammer), Oberwolfach Rep. 14 (2017), no. 1, 621–622.
   Publication · MathSciNet · zbMATH · PDF
4. G. Jasso and J. Külshammer, The naive approach for constructing the derived category of a $d$-abelian category fails, arXiv:1604.03473 [math.RT] (2016) (not intended for publication).
3. G. Jasso, Reduction of $\tau$-tilting modules and torsion classes, Proceedings of the 16th Workshop on Representation Theory of Algebraic Groups and Quantum Groups, 2013, pp. 157–160.
   PDF
2. G. Jasso, Cluster-tilted algebras of canonical type and quivers with potential, Proceedings of the 45th Symposium on Ring Theory and Representation Theory, 2012, pp. 61–68.
   Publication · PDF
1. G. Jasso, Cluster-tilted algebras of canonical type and graded quivers with potential, Proceedings of the 15th Workshop on Representation Theory of Algebraic Groups and Quantum Groups, 2012, pp. 13–18.
   PDF

Theses and dissertations

3. G. Jasso, On $\tau$-tilting theory and higher Auslander–Reiten theory, Doctoral dissertation, Nagoya University, 2014.
   Publication
   Note:

   comprises publications [3], [4] and [6]

2. G. Jasso, El crecimiento de un álgebra de conglomerados de tipo tubular, Master's thesis, Universidad Nacional Autónoma de México, 2011.
   Publication
   Note:

   comprises part of publication [1]

1. G. Jasso, Álgebras de Lie de tipo extendido y formas cuadráticas, Bachelor's thesis, Universidad Nacional Autónoma de México, 2010.
   Publication
   Note:

   comprises publication [2]

Co-authors

Michael Barot · Petter A. Bergh · Xiaofa Chen · Laurent Demonet · Tobias Dyckerhoff · Christof Geiß · Juan Omar Gómez · Norihiro Hanihara · Osamu Iyama · Bernhard Keller · Henning Krause · Julian Külshammer · Sondre Kvamme · Yankı Lekili · Fernando Muro · Marius Nielsen · Yann Palu · Sibylle Schroll · Marius Thaule · Tashi Walde

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Activities

Monday Seminar on Higher Structures

Our research group meets every Monday 10:00-11:30 during the lecture period to hold informal discussions led by one of the participants on topics related to higher structures, or to present our ongoing research. For more information please see the course catalogue.

Learning seminar on Higher Category Theory

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 a private seminar; if you are interested in participating, please contact either Bernhard or me by e-mail.

FDLIST

Since May 2021, I have been one of 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 the representation theory of finite-dimensional algebras.

Past events

1. ARTA X: Advances in Representation Theory of Algebras
2. Parallel session on 'Homological Algebra' at the 29th Nordic Congress of Mathematicians with EMS
3. XIX International Conference on Representation Theory of Algebras (Online)
4. Junior Trimester Program (JTP) on 'New trends in representation theory'
5. Hausdorff Summer School on Stability Conditions in Representation Theory
6. Workshop: A-infinity structures in geometry and representation theory
7. Spring school: Cluster Algebras in Mathematical Physics (CAMP)

FD Seminar

I was one of 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.

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