Zoom link = https://wwu.zoom.us/j/62084376529?pwd=ajZnNndIdGdpNWVleFVsdk9ibFRuZz09 Meeting ID: 620 8437 6529, Passcode: 831811 Abstract: Let $u$ be the small quantum group associated to a semisimple Lie algebra $g$ and a primitive root of unity of degree $l$. The Hochschild cohomology $HH^*(u)$, also known as the derived center of $u$, has a rich structure and carries a natural action of the Lie algebra $g$. This action arises from the Ginzburg-Kumar identification of $HH^*(u)$ with the Hopf algebra cohomology of $u$ with values in $u^{ad}$, the adjoint module. On the other hand, we have a geometric description of blocks of $HH^*(u_q)$ in terms of certain sheaf cohomology over the Springer resolution, which also carries a natural $g$-action. We show that these actions coincide on the derived center of $u_q$. When restricted to the center $HH^0(u)$, these actions also coincide with the adjoint action of $U(g)$ on $z(u)$ via the Frobenius pullback of the $l$-th divided powers of the generators. As an illustration I will discuss the example of $g = sl_2$.