SUMMARY ORDER

Plaintiff-Appellant Mark Sargent appeals from a December 9, 2013 order of the United States District Court for the District of Connecticut (Arterton, J.) denying Sargent’s motion for a preliminary injunction and dismissing his case in its entirety. We assume the parties’ familiarity with the underlying facts, procedural history, and issues on appeal.

The district court denied Sargent’s motion for a preliminary injunction and dismissed Sargent’s complaint on two alternative grounds: first, that the district court was required to abstain from exercising jurisdiction under Younger v. Harris, 401 U.S. 37, 91 S.Ct. 746, 27 L.Ed.2d 669 (1971); and second, that the defendants were entitled to immunity from all of Sargent’s claims. On appeal, Sargent challenges only the first of these determinations and fails to raise any meaningful argument addressing the defendants’ immunity to suit. “We regard as waived any challenges ... to adverse decisions that are undiscussed.” Lore v. City of Syracuse, 670 F.3d 127, 149 (2d Cir. 2012); see also Jackler v. Byrne, 658 F.3d 225, 233 (2d Cir. 2011) (“[The plaintiffs] brief on appeal contains no argument that any ruling other than the dismissal of his First Amendment retaliation claims was incorrect, and we thus regard all of his other claims as abandoned.”). Accordingly, we find that Sargent has abandoned his claim that the district court erred in finding his action barred by the defendants’ immunity, and we may affirm the district court’s dismissal of the complaint on this ground alone.

Nonetheless, we also find that the district court correctly concluded that immunity bars Sargent’s claims against the defendants here. The Eleventh Amendment bars suits by private persons against state governments unless the state waives its sovereign immunity or Congress abrogates it by appropriate legislation. See Virginia Office for Prot. & Advocacy v. Stewart, — U.S. -, 131 S.Ct. 1632, 1638, 179 L.Ed.2d 675 (2011). State sovereign immunity under the Eleventh Amendment extends to actions against the state’s agencies and instrumentalities, see Regents of the Univ. of California v. Doe, 519 U.S. 425, 429, 117 S.Ct. 900, 137 L.Ed.2d 55 (1997), and “applies to a suit seeking an injunction,” Cory v. White, 457 U.S. 85, 91, 102 S.Ct. 2325, 72 L.Ed.2d 694 (1982). Here, the district court correctly found that the Judicial Branch of the State of Connecticut, one of the defendants in this action, is a department of the state and thus shares in its sovereign immunity. See Conn. Gen.Stat. § 51-la. Moreover, there is no indication that the state has waived its immunity, and it is well established that Congress did not abrogate state sovereign immunity in enacting 42 U.S.C. § 1983, under which all of Sargent’s claims were brought. See Quern v. Jordan, 440 U.S. 332, 345, 99 S.Ct. 1139, 59 L.Ed.2d 358 (1979). Therefore, the district court correctly found that the Eleventh Amendment bars Sargent’s suit against the Judicial Branch of the State of Connecticut.

*53 With respect to Judge Emons, the other defendant in these proceedings, the Federal Courts Improvement Act of 1996 amended section 1983 to provide “that in any action brought against a judicial officer for an act or omission taken in such officer’s judicial capacity, injunctive relief shall not be granted unless a declaratory decree was violated or declaratory relief was unavailable.” Federal Courts Improvement Act of 1996, § 309(c), Pub.L. No. 104-317, 110 Stat. 3847, 3853 (1996) (amending 42 U.S.C. § 1983). Claims for injunctive relief under section 1983 against judges acting in their official capacity are therefore barred by absolute judicial immunity as long as declaratory relief remains available, the judge did not exceed her jurisdiction, and the plaintiff does not allege that a declaratory judgment was violated. See Montero v. Travis, 171 F.3d 757, 761 (2d Cir. 1999) (per curiam). Here, Sargent sued Judge Emons solely in her judicial capacity in adjudicating Sargent’s custody dispute. And, as the district court found, Sargent has not alleged that Judge Emons acted in violation of any declaratory decree or in excess of her jurisdiction. See Conn. Gen.Stat. § 46b-56(a) (granting continuing jurisdiction to the Connecticut Superior Court over custody matters). Nor has Sargent claimed that declaratory relief is unavailable. The district court therefore correctly found that Sargent’s injunctive claims against Judge Emons under section 1983 are barred by the doctrine of judicial immunity.

Accordingly, we conclude that the district court was correct in finding that immunity bars Sargent’s claims, a finding that required denial of Sargent’s motion for a preliminary injunction and dismissal of this action, and so we need not reach the question of whether abstention was required on the facts of this case. We have considered Sargent’s remaining arguments and find them to be without merit. For the reasons stated herein, the judgment of the district court is AFFIRMED.