# Geometry and topology of symplectic resolutions

@article{Kaledin2006GeometryAT, title={Geometry and topology of symplectic resolutions}, author={Dmitri Kaledin}, journal={arXiv: Algebraic Geometry}, year={2006} }

This is an overview of math.AG/0310186, math.AG/0309290, math.AG/0501247, math.AG/0401002 and math.AG/0504584 written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005.

#### 27 Citations

Enumerative geometry and geometric representation theory

- Mathematics, Physics
- 2017

This is an introduction to: (1) the enumerative geometry of rational curves in equivariant symplectic resolutions, and (2) its relation to the structures of geometric representation theory. Written… Expand

Quantum cohomology of the Springer resolution

- Mathematics, Physics
- 2009

Let G denote a complex, semisimple, simply-connected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine… Expand

Elliptic stable envelopes

- Mathematics, Physics
- 2016

We construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of arXiv:1211.1287. We apply them to… Expand

Rational Cherednik Algebras

- Mathematics
- 2011

We survey a number of results about the rational Cherednik algebra’s representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification… Expand

Stable Bases of the Springer Resolution and Representation Theory

- Mathematics
- 2017

In this note, we collect basic facts about Maulik and Okounkov's stable bases for the Springer resolution, focusing on their relations to representations of Lie algebras over complex numbers and… Expand

Symplectic resolutions of character varieties

- Mathematics
- 2019

In this article, we consider the $G$-character variety of a compact Riemann surface of genus $g > 0$, when $G$ is $\mathrm{SL}(n,\mathbb{C})$ or $\mathrm{GL}(n,\mathbb{C})$. We show that these… Expand

Microlocalization of rational Cherednik algebras

- Mathematics
- 2007

We construct a microlocalization of the rational Cherednik algebras H of type Sn. This is achieved by a quantization of the Hilbert scheme Hilb C2 of n points in C2. We then prove the equivalence of… Expand

Wall-crossings and a categorification of K-theory stable bases of the Springer resolution

- Mathematics
- Compositio Mathematica
- 2021

We compare the
$K$
-theory stable bases of the Springer resolution associated to different affine Weyl alcoves. We prove that (up to relabelling) the change of alcoves operators are given… Expand

Elliptic stable envelope for Hilbert scheme of points in the plane

- Mathematics, Physics
- 2018

We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the… Expand

Stable Basis and Quantum Cohomology of Cotangent Bundles of Flag Varieties

- Mathematics
- 2017

Stable Basis and Quantum Cohomology of Cotangent Bundles of Flag Varieties

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Representation theory and complex geometry

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Preface.- Chapter 0. Introduction.- Chapter 1. Symplectic Geometry.- Chapter 2. Mosaic.- Chapter 3. Complex Semisimple Groups.- Chapter 4. Springer Theory.- Chapter 5. Equivariant K-Theory.- Chapter… Expand