McKay correspondence, Tilting theory and related topics

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3d McKay correspondence and 5d SCFTs

$(1,2)$-symmetric subgroups of SL$(4,\mathbb{C})$

(Derived) Deformations of Crepant Curves

An example of crepant resolution in characteristic 2 and its duality

Birational geometry of quiver moduli through Cox rings

Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories

Combinatorial actions on quivers and geometric interpretations

Cotilting complexes over commutative noetherian rings

Distribution of bricks and one-parameter families of stable modules

Exceptional surfaces in 3-folds and derived symmetries

Explicit examples of trihedral G-Hilbert schemes

F-blowups of quotient singularities and toric singularities

Hilbert schemes and the Le Bruyn-Procesi theorem

Hyperpolygon spaces and their crepant resolutions

Invariant theory of skew polynomial algebras

L-genera and applications

McKay correspondence and perverse schobers

McKay correspondence for Hilb^n(C^3), categorical DT theory and geometric Langlands

Mutations of noncommutative crepant resolutions in geometric invariant theory

Nc resolutions of finite dimensional commutative algebras via smooth surface blow-ups

Non-commutative crepant resolutions of a special family of stable set rings

On derived McKay correspondence between non-commutative deformations

On recent developments in quasi-hereditary structures

Projective crepant resolutions of toric cDV singularities and dimer combinatorics

Reflexive modules and Auslander-Gorenstein rings

Spherical objects in dimension two and three

TF equivalence, silting theory and canonical decompositions

The Donovan-Wemyss Conjecture via the Derived Auslander-Iyama Correspondence

The E10 diagram, symmetric polytopes and Enriques surfaces

The Euler characteristic of the Fujiki-Oka resolution via continued fractions

The invariant Hilbert scheme of the Cox realization

Tilting theory and g-fans

Towards derived Reid’s recipe for dimer models

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