سخنرانی‌های تبیینی در نظریه نمایش: سخنرانی‌های ممتاز موریس آسلندر و کنفرانس بین‌المللی، ۲۵-۳۰ آوریل ۲۰۱۲، موسسه اقیانوس‌شناسی وودز هول، پردیس کوئسیت، فالموث، ماساچوست

This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams. Preface 8 Fine and coarse moduli spaces in the representation theory of finite dimensional algebras 10 1. Introduction and notation 10 Acknowledgements 12 2. Affine and projective parametrizations of the Λ-modules of dimension vector d 13 3. Quotient varieties on the geometric market—generalities and representation-theoretic particulars 15 4. Rendering Riemann’s classification philosophy more concrete 17 5. Approach A: King’s adaptation of Mumford stability: Focusing on the objects which are (semi-)stable relative to a weight function 21 6. Approach B. Slicing Λ-mod into strata with fixed top 24 7. Slicing Λ-mod more finely, in terms of radical layerings Representation-theoretically optimal coordinatization of Grass^{T}_{d} 33 8. Problems. Pros and Cons of Approach B 40 References 42 More Representations of Wild Quivers 44 Introduction 44 1. Preliminaries 45 2. Spectral properties of the Coxeter transformations 47 3. Elementary modules 48 4. The regular components 49 5. Partial tilting modules 52 6. The perpendicular category of a rigid regular module 54 7. A functor between categories of regular modules 56 8. Generation of cocones 59 9. Factorisations of morphisms 61 References 62 Phantom Morphisms and Salce’s Lemma 66 1. Introduction 66 2. Preliminaries 68 3. Salce’s Lemma 69 4. The Flat Cover Conjecture 72 5. Phantom Morphisms 74 6. Salce’s Lemma for Ideals 78 7. Subfunctors of Ext 81 8. Examples 83 9. Quasi-Frobenius Rings 87 10. The Powers of the Phantom Ideal 89 References 91 Morita theory, revisited 94 1. Introduction 94 2. Notations 95 3. Morita theory 96 4. The Lambek theorem 100 5. Self-dual idempotents and Morita algebras 102 References 105 Universal deformation rings of group representations, with an application of Brauer’s generalized decomposition numbers 106 1. Introduction 106 2. Mazur’s deformation theory 107 3. Universal deformation rings of modules for finite groups 113 4. Brauer’s generalized decomposition numbers and universal deformation rings 115 References 118 Derived Representation Schemes and Noncommutative Geometry 122 1. Introduction 122 Notation and Conventions 125 2. Model categories 125 3. Representation Schemes 136 4. Cyclic Homology and Higher Trace Maps 143 5. Abelianization of the Representation Functor 152 6. Examples 159 Acknowledgements 167 References 167 Classifying torsion pairs for tame hereditary algebras and tubes 172 Introduction 172 1. Torsion pairs 173 2. Torsion pairs and tilting for finite dimensional algebras 174 3. Big cotilting modules for finite dimensional algebras 176 4. Tubes 179 5. Combinatorial classifications 180 References 186 Problems solved by using degrees of irreducible morphisms 188 Introduction 188 1. Preliminaries and Notation 189 2. On degrees 192 3. Characterizations of the notion of degree 196 4. Composite of irreducible morphisms and the powers of the radical of a module category 201 5. Degrees and finite representation type of an algebra 206 6. On the bound of the radical of a module category 208 References 210 Arc diagram varieties 214 1. Introduction 214 Acknowledgement 215 2. The stratification 215 3. Partially ordered sets 220 4. An algorithmic approach 224 5. Three excursions 228 References 232