We survey the basics of homological algebra in exact categories in the sense of Quillen. All
diagram lemmas are proved directly from the axioms, notably the five lemma, the 3× 3 …

The cluster category associated with a finite-dimensional hereditary algebra was introduced
in [21](and in [26] for the An case). It serves in the representation-theoretic approach to …

We study the interaction between geometric operations on stacks and algebraic operations
on their categories of sheaves. We work in the general setting of derived algebraic …

The purpose of this work is to prove the existence of an algebraic moduli classifying objects
in a given triangulated category. To any dg-category T (over some base ring k), we define a …

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on
compact Riemann surfaces can be identified with spaces of stability conditions on a class of …

Derived algebraic geometry Page 1 EMS Surv. Math. Sci. 1 (2014), 153–240 DOI 10.4171/EMSS/4
EMS Surveys in Mathematical Sciences c European Mathematical Society Derived algebraic …

We develop a geometric approach to A-infinity algebras and A-infinity categories based on
the notion of formal scheme in the category of graded vector spaces. The geometric …

We define and investigate deformed n-Calabi–Yau completions of homologically smooth
differential graded (= dg) categories. Important examples are: deformed preprojective …

We show that Derksen–Weyman–Zelevinsky's mutations of quivers with potential yield
equivalences of suitable 3-Calabi–Yau triangulated categories. Our approach is related to …

We construct a family of 3d quantum field theories $\mathcal T_ {n, k}^ A $ that conjecturally
provide a physical realization--and derived generalization--of non-semisimple mathematical …