Apostolos
Beligiannis
Professor
Ph.D., University of Ioannina
Greece (1995)
Curriculum
Vitae
Contact Information:
Department of Mathematics,
University of Ioannina,
GR - 45110 Ioannina, Greece.
Office: 409 δ' (4th floor), Math. Department Building
Email: abeligia at uoi.gr (new)
abeligia at cc.uoi.gr
(old)
Phone: +30 26510 08227
Fax: +30 26510 08203.
Research
Interests
- Representation Theory of Artin Algebras
- Ring and Module Theory
- Homological Algebra and Triangulated Categories
- Torsion Theories and (Cluster) Tilting
- Stable Homotopy Theory
- Homotopical Algebra:
- Quillen's Closed Model Categories
- Abstract Homotopy Theory
- Non-Commutative (Algebraic) Geometry
- Category Theory
-
Homological/Homotopical Aspects of Functional Analysis
- Applications of Homological Algebra and Representation Theory
to Algebraic Geometry
Profiles
E-Books
Seminar [Section of Algebra and
Geometry]
Seminar [Department]
Published
Papers
- A. Beligiannis: ''Stable
Categories
of Abelian Categories'', Ph.D., University of
Ioannina, Greece, (1995), 285 pages (in Greek).
- A. Beligiannis and N.
Marmaridis: ''On Left Derived Categories
of a Stable Category'', pdf,
Proc. ICRA VI, Carlton-Ottawa Math. Lect. Note Series, No
14, (1992), 31 pages.
- A. Beligiannis and N. Marmaridis:
''Left Triangulated Categories Arising From
Contravariantly Finite Subcategories'', pdf,
Communications in Algebra 22
(1994), pp. 5021-5036.
- A. Beligiannis and N. Marmaridis:
''Grothendieck Groups Arising From Contravariantly Finite
Subcategories'', pdf,
Communications in Algebra 24,
(1996), pp. 4415-4438.
- A. Beligiannis, N. Marmaridis and I. Assem:
''Right Triangulated Categories with Right
Semi-equivalences'', pdf, Algebras
and Modules II, (Geiranger 1996), CMS Conf. Proc. 24, Amer. Math. Soc.,
Providence, RI (1998), pp. 17-37.
- A. Beligiannis: ''Relative
Homological Algebra and Purity in Triangulated Categories'',
pdf,
Journal of Algebra 227,
(2000), pp. 268- 361.
- A. Beligiannis: ''On the Relative
Homology of Cleft Extensions of Rings and Abelian Categories'',
pdf,
Journal of Pure and Applied Algebra, 150, (2000), pp. 237-299.
- A. Beligiannis: ''Cleft Extensions of
Abelian Categories and Applications to Ring Theory'',
pdf,
Communications in Algebra 28,
(2000), pp. 4503-4546.
- A. Beligiannis: ''The Homological
Theory of Contravariantly Finite Subcategories: Gorenstein
Categories, Auslander-Buchweitz Contexts and
(Co-)Stabilization'' pdf,
Communications in Algebra 28,
(2000), pp. 4547-4596.
- A. Beligiannis: ''On the Freyd
Categories of an Additive Category'', pdf,
Homology, Homotopy and Applications Vol. 2, No.11 (2000),
pp. 147-185.
- A. Beligiannis: ''Homotopy Theory of
Modules and Gorenstein Rings'',
pdf,
Mathematica Scandinavica 89,
(2001), pp. 5-45.
- A. Beligiannis: ''Stable
Equivalences and Stable Grothendieck Groups'',
pdf,
Communications in Algebra 30,
(2002), pp. 205-236.
- A. Beligiannis: ''Purity and Almost
Split Morphisms in Abstract Homotopy Categories: A Unified
Approach via Brown Representability'', pdf,
Algebras and Representation Theory 5, (2002), pp. 483-525.
- A. Beligiannis and H.
Krause: ''Realizing Maps Between Modules
over Tate Cohomology Rings'', pdf, Beitrage
Algebra Geom. Vol. 44,
No. 2, (2003), pp. 451-466.
- A. Beligiannis: ''Auslander-Reiten
Triangles, Ziegler Spectra and Gorenstein Rings'',
pdf,
K-Theory 32, (2004),
1-82.
- A. Beligiannis: ''Cohen-Macaulay Modules,
(Co)Torsion Pairs and Virtually Gorenstein Algebras'',
pdf, Journal
of Algebra Vol. 288,
No.1, (2005), pp. 137-211.
- A. Beligiannis and I. Reiten:
''Homological and Homotopical Aspects of Torsion Theories'',
pdf,
Memoirs of the American Mathematical Society, Vol. 188, (2007), 207 pp.
- A. Beligiannis and H.
Krause: "Thick Subcategories and Virtually
Gorenstein Algebras", pdf,
Illinois Journal of Mathematics, Vol. 52, No. 2, (2008), pp. 551-562.
- A. Beligiannis: ''On Algebras of Finite
Cohen-Macaulay Type'', pdf,
Advances in Mathematics 226, No.2, (2011), pp.
1973-2019.
- A. Beligiannis: ''Rigid Objects,
Triangulated Subfactors and Abelian
Localizations'', pdf,
Mathematische Zeitschrift, Vol. 274, No. 3, (2013),
pp. 841-883.
- A. Beligiannis: ''Relative Homology,
Higher Cluster Tilting Theory, and Categorified
Auslander-Iyama Correspondence'', pdf, Journal
of Algebra, Vol. 444, No. 3, (2015), pp. 367-503.
Preprints
- A. Beligiannis: "Tilting Theory in
Abelian Categories and Related Homological and Homotopical
Structures'', preprint, University of
Ioannina, Greece, (2010), 175 pages.
- A. Beligiannis: "Variations on a
Theme of Auslander-Tachikawa: Abelian Resolving
Subcategories and Auslander's Formula'',
preprint, University of Ioannina, Greece, (2019), 130 pages.
Oberwolfach
Reports
- A. Beligiannis: ''Cohen-Macaulay
modules and virtually Gorenstein algebras'', pdf,
Oberwolfach Reports, Volume 2, Issue 1, (2005), 340-342.
- A. Beligiannis: ''A Note on Virtually
Gorenstein Algebras", pdf,
Oberwolfach Reports, Volume 3, Issue 1, (2006), 469-471.
- A. Beligiannis: ''Relative Homology
and Higher Cluster Tilting Theory'', pdf,
Oberwolfach Reports, Volume 8, Issue 1, (2011), 534-537.
Preprints in
Preparation - Work in Progress
- A. Beligiannis: ''Relative Homology,
Tilting Objects and Freyd's Generating Hypothesis'',
preprint in preparation.
- A. Beligiannis: ''Representations of
Exact Categories'', preprint in preparation.
Notes - Unpublished Papers
- A. Beligiannis: ''Some Ghost Lemmas'',
pdf,
notes for the Conference "The
Representation Dimension of Artin Algebras", 1 May -
4 May, 2008, Bielefeld, Germany.
- A. Beligiannis: ''Torsionless Modules'',
pdf,
notes for the Conference "The
Representation Dimension of Artin Algebras", 1 May -
4 May, 2008, Bielefeld, Germany.
- A. Beligiannis: ''Relative Homology
and (Strong) Cluster Tilting Subcategories'',
notes for the Conference "Cluster
Algebras and Quiver Representations", 29 June - 1
July, 2010, Tehran, Iran.
People
Journals
Dave
Benson's List of Journals
Preprints - Free
Online Papers
Conferences and
Meetings
- 4th
Panhellenic Conference on Algebra and Number Theory,
University of Patras, May 30 - June 2 2002.
- Algebra
Conference, Venezia, Italy: June 3 - 8, 2002.
- Conference
on Representation Theory of Algebras and Related Topics (ICRA
X), Fields Institute, Toronto: July 15 - August 10, 2002.
- International
Congress
of
Mathematicians 2002, Beijing, China: August 20 - 28, 2002.
- International
Conference on Algebra, (Satellite Conference of ICM 2002).
- Noncommutative
Geometry and Rings, University of Almeria, Spain:
September 2 - 8, 2002.
- Twenty
Years of Tilting Theory, Fraueninsel, Germany:
November 18 - 22, 2002.
- Workshop
on representations of finite dimensional algebras,
Warwick, UK: December, 8-14, 2003.
- International
Algebraic Conference, Moscow, 26 May-2June 2004.
- Representation
Theory and its Applications, Uppsala, Sweden: 22-27 June
2004.
- Summer
school:
Interactions between homotopy theory and algebra,
University of Chicago, USA: July 26 through August 6, 2004.
- ICRA XI (Workshop
and Conference), Mexico, August 11 - 20, 2004.
- Non
commutative artinian algebras, representations and
cohomologies, IRM, Luminy, France: September 13-17,
2004.
- Perspectives
in Mathematics: Algebras and Representations, Conference
dedicated to the 60th birthday of Claus Michael Ringel,
Bielefeld, 4-5 February, 2005.
- Representation
Theory of Finite-Dimensional Algebras, Oberwolfach,
Germany, February 06-12, 2005.
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