Extended Abstracts Spring 2015

1. Front Matter

   Pages i-ix

   PDF

2. Homological Algebra on an Adams Algebraic Stack

   • Leovigildo Alonso Tarrío

   Pages 1-5

3. Lyubeznik Numbers of Local Rings and Linear Strands of Graded Ideals

   • Josep Àlvarez Montaner

   Pages 7-13

4. The Heart of a t-Structure Induced by a n-Tilting Module

   • Silvana Bazzoni

   Pages 15-19

5. On Some Local Cohomology Spectral Sequences

   • Alberto F. Boix

   Pages 21-26

6. Homotopy Representations of Classifying Spaces

   • Natàlia Castellana

   Pages 27-33

7. Decomposing Gorenstein Rings as Connected Sums

   • Hariharan Ananthnarayan, Ela Celikbas, Zheng Yang

   Pages 35-39

8. Rigid and Test Modules

   • Olgur Celikbas

   Pages 41-46

9. Tate Homology Beyond Gorenstein Rings

   • Lars Winther Christensen

   Pages 47-51

10. On the Classification of Artin Algebras and the Inverse System of Macaulay

    • Joan Elias

    Pages 53-57

11. Purity in Categories of Sheaves

    • Sergio Estrada

    Pages 59-62

12. Idempotent Functors and Nilpotent Spaces

    • Wojciech Chachólski, Emmanuel Dror Farjoun, Ramón Flores, Jérôme Scherer

    Pages 63-67

13. Decomposition Spaces and Incidence (Co)Algebras

    • Imma Gálvez-Carrillo

    Pages 69-74

14. Cellular Approximations for Fusion Systems

    • Alberto Gavira-Romero

    Pages 75-80

15. Homological Epimorphisms and the Lie Bracket in Hochschild Cohomology

    • Reiner Hermann

    Pages 81-85

16. Gorenstein Projective Precovers

    • Alina Iacob

    Pages 87-90

17. Hochschild Homology on Schemes and Fundamental Class

    • Ana Jeremías López

    Pages 91-95

18. A Remark on Leclerc’s Frobenius Categories

    • Martin Kalck

    Pages 97-101

19. Atom-Molecule Correspondence in Grothendieck Categories

    • Ryo Kanda

    Pages 103-107

20. Proalgebraic Crossed Modules of Quasirational Presentations

    • Andrey Mikhovich

    Pages 109-114

This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)."

Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area.

It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.

• Commutative Algebra
• Homological Algebra
• Triangulated Category
• Matrix Factorizations
• Derived Category
• Singularity Category
• Representation Theory

• Universitat Autònoma de Barcelona, Departament de Matemàtiques Universitat Autònoma de Barcelona, Bellaterra, Spain

  Dolors Herbera, Wolfgang Pitsch

• Universitat de Barcelona, Departament de Matemàtiques i Informàtica, Barcelona, Spain

  Santiago Zarzuela

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