Senior Lecturer (Universitetslektor)

Department of Mathematics

Faculty of Science

Lund University

## About me

Pronouns: he / him

I am a member of the Research Group in Algebra.

My research interests include the following topics:

- Representation theory of quivers and algebras
- Homological and homotopical algebra
- Cluster algebras and their categorifications

Visit my Profile at Lund University’s Research Portal.

**2023-01-01 – 2026-12-31** My research is supported by a Research project grant within natural and engineering sciences from the Swedish Research Council (Vetenskapsrådet).

### Academical profiles

arXiv.org | Google Scholar | MathSciNet | ORCID | Web of Science | zbMATH Open

### Open positions

Open doctoral and postdoctoral/researcher positions at Lund University can be found at the following URL:

https://www.lunduniversity.lu.se/vacancies

You are welcome to inquire about upcoming advertisements of positions in the Algebra group, but please note that applications are handled through the Varbi system (accessible from the previous link).

*Please do not send me unsolicited application materials. For security reasons, I will not open unsolicited files.*

## Contact details

### E-mail address(es)

E-mail sent to any of the following addresses will arrive to the same inbox.

`gustavo.jasso[at]math.lu.se`

`gustavo.jasso_ahuja[at]math.lu.se`

### PGP key fingerprint

`7527 92FC FE23 2132 1A9A 62C1 F655 F8F8 B671 FC89`

Download public PGP key | What is PGP? (external)

### Visiting address

Room MH:406

Centre for Mathematical Sciences Sölvegatan 18, 221 00 Lund, Sweden

## 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:

**2022-10-15** 11th Award for Encouragement of Alumni and Students (“Hida Award”), Alumni Association of the Graduate School of Mathematics, Nagoya University.

**Since 2022-03-01** 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 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 Jan Schröer.

**2011-10-01 – 2014-09-29** Ph.D student at the Graduate School of Mathematics of Nagoya University under the supervision of 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 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

### FD Seminar

I am one for the organisers of the FD Seminar, an online seminar on representation theory of quivers and finite-dimensional algebras.

### 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.

### Network on Silting Theory

I am a member of the Network on Silting Theory, which is funded by the Deutsche Forschungsgemeinschaft, DFG.

### 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.

## Research

### 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.**,. Int. Math. Res. Not. IMRN (2019), Issue 3, 852-892.*τ*-tilting finite algebras, bricks, and*g*-vectors

Publication | arXiv | MathSciNet - Iyama, O.,
**Jasso, G.**,*Higher Auslander correspondence for dualizing*. Algebr. Represent. Theory, Volume 20 (2017), Issue 2, 335-354.*R*-varieties

Publication | arXiv | MathSciNet **Jasso, G.**,. Math. Z., Volume 283 (2016), Issue 3-4, 703-759.*n*-abelian and*n*-exact categories

Publication | arXiv | MathSciNet*Errata:*In Lemma 3.22, the adverbs 'contravariantly' and 'covariantly' should be exchanged in items (vi) and (vii).- Bergh, P. A.,
**Jasso, G.**, Thaule, M.,*Higher*. J. Lond. Math. Soc. (2), Volume 93 (2016), Issue 1, 123-142.*n*-angulations from local rings

Publication | arXiv | MathSciNet **Jasso, G.**,. Adv. Math., Volume 273 (2015), 1-31.*τ²*-stable tilting complexes over weighted projective lines

Publication | arXiv | MathSciNet**Jasso, G.**,*Reduction of*. Int. Math. Res. Not. IMRN (2015), Issue 16, 7190-7237.*τ*-tilting modules and torsion pairs

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*. arXiv:2301.11593 [math.AG] (to appear in the proceedings of the Abel Symposium 2022: Triangulated categories in representation theory and beyond)**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*. In: Šťovíček, J., Trlifaj, J., (.eds), Representation theory and beyond, Contemp. Math. 758 (2020) 249-265.*A*and the higher Waldhausen*S*-constructions

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 (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*. arXiv:1604.03473 [math.RT] (not intended for publication)*d*-abelian category fails**Jasso, G.**,*Reduction of*. In: Proceedings of the 16th Workshop on Representation Theory of Algebraic Groups and Quantum Groups (2013) 157-160.*τ*-tilting modules and torsion classes**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.

- 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

### Teaching activities

You need a LU student account to access the Canvas pages below.

#### Spring Term 2024

#### Fall Term 2023

MATP43 Representation theory of quivers

#### Spring Term 2023

#### Fall Term 2022

### Students

Please contact me by e-mail if you are a student at Lund University and are interested in writing your bachelor’s or master’s thesis under my supervision.

#### Ph.D. students

- Marvin Plogmann (since January 2024).
- Jan Henrik Thomm (since October 2022).

#### Master students

- Eric Dannetun,
*Quotients of triangulated categories*(2024).*Afterwards:*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).*Afterwards:*PhD position with Prof. Dr. Christof Geiss in Odense.

Publication | arXiv - Jan-Paul Lerch,
*Bijections in tau-tilting theory*(2019).*Afterwards:*PhD position with Prof. Dr. Henning Krause in Bielefeld. - Aran Tattar,
*On Gorenstein k-categories*(2018).*Afterwards:*PhD position with Prof. Dr. Sibylle Schroll in Leicester.

##### Remark

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 [1-6] were supervised at the University of Bonn.