Research

Writings

Preprints

J. O. Gómez, G. Jasso, and M. Nielsen, Hopfological algebra, revisited, arXiv:2606.19485 [math.RT] (2026) (submitted).
G. Jasso and F. Muro, The derived auslander–iyama correspondence II: Bimodule calabi–yau structures, arXiv:2509.22625 [math.RT] (2025) (submitted).
G. Jasso and F. Muro, Obstruction theory for $A$ -infinity bimodules, arXiv:2507.17568 [math.AT] (2025) (submitted).

Books

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

Publications

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: The Derived Auslander–Iyama Correspondence, with an appendix by b. Keller arXiv: The Derived Auslander–Iyama Correspondence, with an appendix by b. Keller MathSciNet: The Derived Auslander–Iyama Correspondence, with an appendix by b. Keller
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).
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: On a theorem of B. Keller on Yoneda algebras of simple modules arXiv: On a theorem of B. Keller on Yoneda algebras of simple modules MathSciNet: On a theorem of B. Keller on Yoneda algebras of simple modules zbMATH: On a theorem of B. Keller on Yoneda algebras of simple modules
G. Jasso, Derived equivalences of upper-triangular ring spectra via lax limits, C. R. Math. Acad. Sci. Paris 362 (2024), 279–285.
Publication: Derived equivalences of upper-triangular ring spectra via lax limits arXiv: Derived equivalences of upper-triangular ring spectra via lax limits MathSciNet: Derived equivalences of upper-triangular ring spectra via lax limits zbMATH: Derived equivalences of upper-triangular ring spectra via lax limits
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: The symplectic geometry of higher Auslander algebras: Symmetric products of disks arXiv: The symplectic geometry of higher Auslander algebras: Symmetric products of disks MathSciNet: The symplectic geometry of higher Auslander algebras: Symmetric products of disks zbMATH: The symplectic geometry of higher Auslander algebras: Symmetric products of disks
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: Generalised BGP reflection functors via the Grothendieck construction arXiv: Generalised BGP reflection functors via the Grothendieck construction MathSciNet: Generalised BGP reflection functors via the Grothendieck construction zbMATH: Generalised BGP reflection functors via the Grothendieck construction
T. Dyckerhoff, G. Jasso, and T. Walde, Simplicial structures in higher Auslander–Reiten theory, Adv. Math. 355 (2019), 106762.
Publication: Simplicial structures in higher Auslander–Reiten theory arXiv: Simplicial structures in higher Auslander–Reiten theory MathSciNet: Simplicial structures in higher Auslander–Reiten theory zbMATH: Simplicial structures in higher Auslander–Reiten theory
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}.
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: Higher Nakayama algebras I: Construction: With an appendix by j. Külshammer and ch. Psaroudakis and an appendix by s. Kvamme arXiv: Higher Nakayama algebras I: Construction: With an appendix by j. Külshammer and ch. Psaroudakis and an appendix by s. Kvamme MathSciNet: Higher Nakayama algebras I: Construction: With an appendix by j. Külshammer and ch. Psaroudakis and an appendix by s. Kvamme zbMATH: Higher Nakayama algebras I: Construction: With an appendix by j. Külshammer and ch. Psaroudakis and an appendix by s. Kvamme
G. Jasso and S. Kvamme, An introduction to higher Auslander-Reiten theory, Bull. Lond. Math. Soc. 51 (2019), no. 1, 1–24.
Publication: An introduction to higher Auslander-Reiten theory arXiv: An introduction to higher Auslander-Reiten theory MathSciNet: An introduction to higher Auslander-Reiten theory zbMATH: An introduction to higher Auslander-Reiten theory
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: τ-tilting finite algebras, bricks, and g-vectors arXiv: τ-tilting finite algebras, bricks, and g-vectors MathSciNet: τ-tilting finite algebras, bricks, and g-vectors zbMATH: τ-tilting finite algebras, bricks, and g-vectors
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.
O. Iyama and G. Jasso, Higher Auslander correspondence for dualizing $R$ -varieties, Algebr. Represent. Theory 20 (2017), no. 2, 335–354.
Publication: Higher Auslander correspondence for dualizing R-varieties arXiv: Higher Auslander correspondence for dualizing R-varieties MathSciNet: Higher Auslander correspondence for dualizing R-varieties zbMATH: Higher Auslander correspondence for dualizing R-varieties
G. Jasso, $n$ -abelian and $n$ -exact categories, Math. Z. 283 (2016), no. 3-4, 703–759.
Publication: n-abelian and n-exact categories arXiv: n-abelian and n-exact categories MathSciNet: n-abelian and n-exact categories zbMATH: n-abelian and n-exact categories
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.
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: Higher n-angulations from local rings arXiv: Higher n-angulations from local rings MathSciNet: Higher n-angulations from local rings zbMATH: Higher n-angulations from local rings
G. Jasso, $\tau^2$ -stable tilting complexes over weighted projective lines, Adv. Math. 273 (2015), 1–31.
Publication: τ2-stable tilting complexes over weighted projective lines arXiv: τ2-stable tilting complexes over weighted projective lines MathSciNet: τ2-stable tilting complexes over weighted projective lines zbMATH: τ2-stable tilting complexes over weighted projective lines
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.
G. Jasso, Reduction of $\tau$ -tilting modules and torsion pairs, Int. Math. Res. Not. IMRN (2015), no. 16, 7190–7237.
Publication: Reduction of τ-tilting modules and torsion pairs arXiv: Reduction of τ-tilting modules and torsion pairs MathSciNet: Reduction of τ-tilting modules and torsion pairs zbMATH: Reduction of τ-tilting modules and torsion pairs
G. Jasso, The extended affine Lie algebra associated with a connected non-negative unit form, J. Algebra 409 (2014), 148–161.
Publication: The extended affine Lie algebra associated with a connected non-negative unit form arXiv: The extended affine Lie algebra associated with a connected non-negative unit form MathSciNet: The extended affine Lie algebra associated with a connected non-negative unit form zbMATH: The extended affine Lie algebra associated with a connected non-negative unit form
M. Barot, Ch. Geiss, and G. Jasso, Tubular cluster algebras II: Exponential growth, J. Pure Appl. Algebra 217 (2013), no. 10, 1825–1837.
Publication: Tubular cluster algebras II: Exponential growth arXiv: Tubular cluster algebras II: Exponential growth MathSciNet: Tubular cluster algebras II: Exponential growth zbMATH: Tubular cluster algebras II: Exponential growth

Proceedings, extended abstracts and other writings

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).
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: Rickard’s derived Morita theory: Review and outlook arXiv: Rickard’s derived Morita theory: Review and outlook MathSciNet: Rickard’s derived Morita theory: Review and outlook
Note:
Contribution to the 100th anniversary volume of the J. Lond. Math. Soc.
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).
G. Jasso, Brackets, trees and the borromean rings, Snapshots of modern mathematics from Oberwolfach (2025), no. 7.
Publication: Brackets, trees and the borromean rings
G. Jasso, Universal massey products in representation theory of algebras, Oberwolfach Rep. 21 (2024), no. 2, 1148–1150.
Publication: Universal massey products in representation theory of algebras MathSciNet: Universal massey products in representation theory of algebras zbMATH: Universal massey products in representation theory of algebras PDF: Universal massey products in representation theory of algebras
Note:
Abstracts from the workshop held April 14–19, 2024, Organized by Bernhard Keller, Henning Krause, Wendy Lowen and Andrea Solotar.
G. Jasso, Derived Endomorphism Algebras in Higher Auslander–Reiten Theory, Oberwolfach Rep. 20 (2023), no. 1, 409–412.
Publication: Derived Endomorphism Algebras in Higher Auslander–Reiten Theory MathSciNet: Derived Endomorphism Algebras in Higher Auslander–Reiten Theory zbMATH: Derived Endomorphism Algebras in Higher Auslander–Reiten Theory PDF: Derived Endomorphism Algebras in Higher Auslander–Reiten Theory
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.
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: The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence arXiv: The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence MathSciNet: The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence zbMATH: The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence
G. Jasso, The symplectic geometry of higher Auslander algebras, an overview, Oberwolfach Rep. 17 (2020), no. 1, 190–192.
Publication: The symplectic geometry of higher Auslander algebras, an overview MathSciNet: The symplectic geometry of higher Auslander algebras, an overview zbMATH: The symplectic geometry of higher Auslander algebras, an overview PDF: The symplectic geometry of higher Auslander algebras, an overview
Note:
Abstracts from the workshop held January 19–25, 2020, Organized by Claire Amiot, William Crawley-Boevey, Osamu Iyama and Henning Krause.
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: Higher Auslander algebras of type A and the higher Waldhausen S-constructions arXiv: Higher Auslander algebras of type A and the higher Waldhausen S-constructions MathSciNet: Higher Auslander algebras of type A and the higher Waldhausen S-constructions zbMATH: Higher Auslander algebras of type A and the higher Waldhausen S-constructions
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: Nakayama-type phenomena in higher Auslander-Reiten theory arXiv: Nakayama-type phenomena in higher Auslander-Reiten theory MathSciNet: Nakayama-type phenomena in higher Auslander-Reiten theory zbMATH: Nakayama-type phenomena in higher Auslander-Reiten theory
G. Jasso, Spherical objects in higher Auslander–Reiten theory (joint work with j. Külshammer), Oberwolfach Rep. 14 (2017), no. 1, 621–622.
Publication: Spherical objects in higher Auslander–Reiten theory (joint work with j. Külshammer)MathSciNet: Spherical objects in higher Auslander–Reiten theory (joint work with j. Külshammer)zbMATH: Spherical objects in higher Auslander–Reiten theory (joint work with j. Külshammer)PDF: Spherical objects in higher Auslander–Reiten theory (joint work with j. Külshammer)
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).
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: Reduction of τ-tilting modules and torsion classes
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: Cluster-tilted algebras of canonical type and quivers with potential PDF: Cluster-tilted algebras of canonical type and quivers with potential
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: Cluster-tilted algebras of canonical type and graded quivers with potential

Theses and dissertations

G. Jasso, On $\tau$ -tilting theory and higher Auslander–Reiten theory, Doctoral dissertation, Nagoya University, 2014.
Publication: On τ-tilting theory and higher Auslander–Reiten theory PDF: On τ-tilting theory and higher Auslander–Reiten theory
Note:
comprises publications [3], [4] and [6].
G. Jasso, El crecimiento de un álgebra de conglomerados de tipo tubular, Master's thesis, Universidad Nacional Autónoma de México, 2011.
PDF: El crecimiento de un álgebra de conglomerados de tipo tubular
Note:
comprises part of publication [1].
G. Jasso, Álgebras de lie afines extendidos y formas cuadráticas, Bachelor's thesis, Universidad Nacional Autónoma de México, 2010.
PDF: Álgebras de lie afines extendidos y formas cuadráticas
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

Activities

Reading Seminar on Higher Structures

Our research group meets every week 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

I am one of the maintainers of the FDLIST (since 2021-05), 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

I was involved in the organisation of the following events:

FD Seminar

I was one of the organisers of the FD Seminar (2020-05 – 2024-05), an online seminar on representation theory of quivers and finite-dimensional algebras.