Metody homotopické teorie ve vychylující teorii

• Název práce v češtině: Metody homotopické teorie ve vychylující teorii
• Název v anglickém jazyce: Homotopy-theoretic methods in tilting theory
• Akademický rok vypsání: 2021/2022
• Typ práce: disertační práce
• Ústav: Katedra algebry (32-KA)
• Vedoucí / školitel: doc. RNDr. Jan Šťovíček, Ph.D.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 05.10.2021
• Datum zadání: 05.10.2021
• Datum potvrzení stud. oddělením: 05.10.2021

Zásady pro vypracování

The aim of the thesis is to study tilting theory, derived equivalences and related topics using tools of stable homotopy theory. One can use various enhancements of triangulated categories such as derivators [1-4] in order to obtain such equivalences which are valid universally (independently of the field of coefficients, for example) for combinatorial reasons. This is expected to considerably generalize results from [5,6], for example. However, the same methods were used to study higher Auslander theory [7] and may apply in silting theory as well [8].

Seznam odborné literatury

[1] M. Groth, J. Šťovíček, Tilting theory via stable homotopy theory. J. Reine Angew. Math. 743 (2018), 29-90.

[2] M. Groth, J. Šťovíček, Abstract tilting theory for quivers and related categories. Ann. K-Theory 3 (2018), no. 1, 71-124.

[3] M. Groth, J. Šťovíček, Abstract representation theory of Dynkin quivers of type A. Adv. Math. 293 (2016), 856-941.

[4] M. Groth, J. Šťovíček, Tilting theory for trees via stable homotopy theory. J. Pure Appl. Algebra 220 (2016), no. 6, 2324-2363.

[5] S. Ladkani, Universal derived equivalences of posets, arXiv:0705.0946.

[6] S. Ladkani, On derived equivalences of lines, rectangles and triangles. J. Lond. Math. Soc. (2) 87 (2013), no. 1, 157-176.

[7] T. Dyckerhoff, G. Jasso, T. Walde, Simplicial structures in higher Auslander-Reiten theory. Adv. Math. 355 (2019), 73 pp.

[8] S. Oppermann, Quivers for silting mutation. Adv. Math. 307 (2017), 684–714.