**Background:**

There are two lists of open problems about Cherednik or Symplectic Reflection Algebras from 2007: Ian Gordon's Problems, Chapter 9 in Symplectic Reflection Algebras, and Ginzburg & Etingof's list given at a workshop in 2007 here.

Gordon titled these "Problems for next year". Now, more than years later, some of them are certainly solved. For example

**2) in 1 or 0.1 in 2:** Aspherical locus, conjugation-invariant functions $c$ for which $U_{1,c}$ and $H_{1,c}$ are Morita equivalent. There were characterized by a theorem of Bezrukavikov and Etingof in this paper as precisely those for which $U_{1,c}$ has finite homological dimension. Those aspherical values were then characterized in this paper by Dunkl and Griffeth.

**6) in 1:** Derived equivalences of the category $\mathcal{O}_c$ and $\mathcal{O}_{c'}$ where $c-c'$ is an integer conjugation-invariant function on the set of relections. This conjecture by Rouquier was settled in a recent paper by Losev.

My **questions** are:

*A) Which of the questions posted in 1 or 2 still remain open?*

(Or even questions from the original paper, Chapter 17).

I am particularly interested in the following ones:

**1) in 1:** Has there been progress in studying symplectic reflection algebras for symplectic reflection groups that are neither complex nor wreath products?

**3) in 1 or 0.4 in 2:** Is the Bernstein inequality for finitely generated $H_{1,c}$-modules that the Gelfand-Kirillov dimension is at least $1/2$ that of the reflection representation still open?

**8) in 1:** Is $\mathcal{O}_c$ Koszul?

**Disclaimer:** Due to my unfamiliarity with this vast field, I may be picking out the wrong ones or being imprecise in my review on things that are now proved. Apologies for that. Thank you!