SoSe18 S4A2
Graduate Seminar on Representation Theory

τ-tilitng theory and related topics

Meeting time Fridays 12:15–13:45, room 1.008

Dr. Gustavo Jasso




The class of τ-tilting modules was introduced by Adachi, Iyama and Reiten in [1] as a completion of the class of tilting modules with respect to mutations. In this seminar we will introduce this class of modules and study their relationship with other important classes of objects in representation theory of finite dimensional algebras such as torsion classes, bricks, wide subcategories, stability conditions, etc..


Solid background in representation theory of finite dimensional algebras, Auslander–Reiten theory, basic homological algebra, triangulated categories (in particular the bounded derived category and the bounded homotopy category of projectives for a finite dimensional algebra).

  1. Assem, Ibrahim and Simson, Daniel and Skowroński, Andrzej. Elements of the representation theory of associative algebras. Vol. 1. London Mathematical Society Student Texts, Cambridge University Press, Cambridge 65 (2006): x+458
  2. Happel, Dieter. Triangulated categories in the representation theory of finite-dimensional algebras. London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge 119 (1988): x+208
Organisational meeting Friday 13.04 @ 12:00, room 1.008
Date Speaker Topic References
13.04 Gustavo Overview and distribution of the talks  
20.04   No seminar  
27.04 Gustavo Introduction to τ-tilting theory [1], [2]
04.05 Felix S. τ-titling finite algebras and g-vectors [3]
11.05   No seminar  
18.05 Jan-Paul τ-tilting modules over gentle algebras [4]
25.05   No seminar  
01.06 Gustavo τ-tilting reduction [5]
08.06   No seminar  
15.06 Calvin Lattice theory of torsion classes [6], [7]
22.06   No seminar  
29.06 Apolonia τ-tilting theory and stability conditions [8], [9]
06.07 Jan τ-tilting modules and semibricks [10], [3]
13.06   No seminar  
17.06   No seminar  
  1. Adachi, Takahide and Iyama, Osamu and Reiten, Idun. τ-tilting theory. Compos. Math. 150 (3) (2014): 415–452
  2. Aihara, Takuma and Iyama, Osamu. Silting mutation in triangulated categories. J. Lond. Math. Soc. (2) 85 (3) (2012): 633–668
  3. Demonet, Laurent and Iyama, Osamu and Jasso, Gustavo. τ-Tilting Finite Algebras, Bricks, and g-Vectors. Int. Math. Res. Not. IMRN (00) (2017): 1–41
  4. Palu, Yann and Pilaud, Vincent and Plamondon, Pierre-Guy. Non-kissing complexes and tau-tilting for gentle algebras. (2017)
  5. Jasso, Gustavo. Reduction of τ-tilting modules and torsion pairs. Int. Math. Res. Not. IMRN (16) (2015): 7190–7237
  6. Iyama, Osamu and Reiten, Idun and Thomas, Hugh and Todorov, Gordana. Lattice structure of torsion classes for path algebras. Bull. Lond. Math. Soc. 47 (4) (2015): 639–650
  7. Demonet, Laurent and Iyama, Osamu and Reading, Nathan and Reiten, Idun and Thomas, Hugh. Lattice theory of torsion classes. (2017)
  8. Brüstle, Thomas and Smith, David and Treffinger, Hipolito. Stability conditions, τ-tilting Theory and Maximal Green Sequences. (2017)
  9. Thomas, Hugh. Stability, shards, and preprojective algebras. (2017)
  10. Asai, Sota. Semibricks. (2016)