JOHN R. GIBSON, Circuit Judge.
Samuel Davis appeals from a judgment of the United States District Court for the Western District of New York (H. Kenneth Schroeder, Jr., Magistrate Judge), granting summary judgment for appellees and dismissing his 42 U.S.C. § 1983 complaint, and from interlocutory orders (Carol E. Heckman, Magistrate Judge) denying Davis’s preliminary injunction motion and motion to file a supplemental complaint. Davis filed a complaint against New York State, Governor Pataki, the New York State Department of Correctional Services (“the Department”), Glenn S. Goord, its commissioner, the Attica Correctional Facility (“Attica”), Walter R. Kelly, its superintendent,2 Corrections Sergeant Stachewicz, and Corrections Officers McDonald, Christen, and Barone, and their successors, in their individual and official capacities, alleging that defendants violated his Eighth Amendment right to be free from cruel and unusual punishment by exposing him to high levels of secondhand smoke. He also alleged that defendants retaliated against him for engaging in constitutionally protected activity. The district court denied his motions for preliminary injunctive relief and to file an amended complaint, and granted summary judgment for defendants. For the reasons set forth below, we affirm in pari, vacate in part, and remand for further proceedings.
I. BACKGROUND
Davis has been incarcerated at Attica since 1993. Liberally construing his fro se complaint, Davis had been concerned, throughout his incarceration, about his exposure to excessive levels of second-hand smoke while housed in various housing “blocks.” He ultimately filed an inmate grievance in February 1999, complaining that he needed to minimize his exposure to the smoke-laden air by opening the window across from his cell, but Stachewicz, McDonald and Barone told him not to open the window, and threatened to move him out of the honor block, where he was housed at the time, if he opened the window. These concerns were also expressed in a letter to Goord, which was carbon copied to Kelly.
The grievance was dismissed in March 1999, because Davis had been moved out of the honor block by that time. Davis attempted to appeal. In April 1999, Davis was informed that the grievance was not appealable, because it had been dismissed rather than denied. He was further informed that he could request a review of the dismissal, but that the only review available was by the same supervisor who conducted the original investigation into the complaint, and this supervisor had no intention of reopening the complaint.
Davis filed a complaint in the United States District Court for the Western District of New York in April 1999, alleging that defendants violated his Eighth Amendment right to be free from cruel and unusual punishment by forcing him to be exposed to excessive levels of secondhand smoke on a daily basis, because he was housed in an area where a majority of the inmates smoked frequently, the venti[96]*96lation was inadequate, and he was prevented from opening the window. Davis claimed that these conditions jeopardized his current and future health. He claimed to suffer from dizziness, blackouts, congestion, difficulty breathing, watery eyes, and other respiratory problems, as a result of his exposure to smoke. Davis also alleged that Pataki, Goord and Kelly acted with deliberate indifference to his rights as a non-smoker because they failed to implement policies to protect non-smokers’ health, failed to train and supervise officers regarding the rights of non-smoking inmates, and failed to remedy the problem after it was brought to their attention. He further alleged that Staehewicz, Christen, McDonald and Barone retaliated against him, through harassment and threats, for complaining about violations of the Eighth and Fourteenth Amendments. Davis alleged that McDonald harassed and intimidated him, threatened to inflict physical harm, physically assaulted and vei-bally abused him, and that Goord and Kelly had been deliberately indifferent to this misconduct. Davis sought declaratory and in-junctive relief, as well as monetary damages.
In July 1999, Davis moved for a preliminary injunction and temporary restraining order enjoining named and unnamed defendants from “assaulting, harassing, intimidating, threatening and verbally abusing” him in retaliation for exercising his constitutional rights. Davis alleged that he would suffer irreparable harm without the injunction, because the civilian employees who administered his prison work program and other Corrections officers had begun to retaliate against him because of his complaints about excessive secondhand smoke exposure. Davis alleged that a Corrections Sergeant filed a false misconduct report regarding an altercation with a fellow inmate, and that he was found guilty of the charges after a biased and procedurally defective hearing, resulting in thirty days of “keeplock” and loss of his assigned work program. Davis also filed a motion for leave to file a supplemental complaint, raising essentially the same allegations as in the motion for preliminary injunctive relief, and seeking to add Attica supervisory staff and the parties involved in the misconduct report and hearing as defendants.
The parties consented to have a magistrate judge handle all proceedings, pursuant to 28 U.S.C. § 636(c). The magistrate judge denied Davis’s motion for a preliminary injunction and temporary restraining order, finding that Davis failed to show that he would suffer irreparable harm because he had no liberty interest in his work assignment or in the privileges lost while in keeplock, and that Davis would not likely succeed on the merits because he could not show that defendants had a retaliatory motive. See Davis v. State of New York, No. 99-CV-307, 1999 WL 1390253 (W.D.N.Y. Sept.29, 1999). The magistrate judge also denied Davis’s motion to amend his complaint, holding that Davis’s new allegations failed to state a claim upon which relief could be granted. See Davis v. State of New York, No. 99-CV-307, 1999 WL 1390247 (W.D.N.Y. Dec.14, 1999).
In September 1999, Davis wrote to Superintendent Herbert, with a carbon copy to Goord, complaining about his medical problems due to second-hand smoke exposure, and requesting placement in a cell with an individual window. According to Davis’s letter, the only housing blocks at Attica that have individual windows in each cell are blocks C and E. Davis explained that on February 28, 1999, he was transferred from the honor block to the C block due to his respiratory problems. Thereafter, he was moved to the B block from June 18 until July 13, and was finally [97]*97transferred to the A block on July 21, where he remained on the waiting list to be assigned to work programs that would require him to be housed in blocks C or E.
In July 2000, Davis moved for summary judgment. He argued that he had demonstrated that his Eighth Amendment rights were violated when defendants knowingly caused him and other non-smoking inmates to be exposed involuntarily to excessive levels of second-hand smoke without adequate ventilation, jeopardizing his current and future health. Davis further contended that he had demonstrated that he was harassed, intimidated, and threatened for exercising his constitutional rights, and that such retaliation was in violation of the Eighth Amendment.
Defendants filed a cross-motion for summary judgment, arguing that Davis’s Eighth Amendment rights were not violated because he did not meet the two-pronged test for establishing an Eighth Amendment claim based on second-hand smoke exposure. Defendants noted that, pursuant to Helling v. McKinney, 509 U.S. 25, 113 S.Ct. 2475, 125 L.Ed.2d 22 (1993), where the harm is allegedly due to secondhand smoke, the plaintiff must meet the objective prong by showing serious harm resulting from exposure to unreasonably high levels of smoke. In addition, defendants noted that, pursuant to Farmer v. Brennan, 511 U.S. 825, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994), the plaintiff must satisfy the subjective prong of the test by showing that prison officials acted with deliberate indifference to inmate health or safety.
Defendants contended that Davis did not submit evidence to establish serious injuries due to second-hand smoke, or that he was exposed to a sufficiently high level of smoke to result in serious injury. In support of them argument that Davis had no serious injuries, defendants submitted the affidavit of Dr. Takos, the health services director of Attica. According to Takos, Davis only complained of smoke-related symptoms once, in February 1999. Takos asserted that Davis’s congestion was due to a deviated septum, which Davis had refused to get corrected. In Takos’s opinion, there was no medical evidence that Davis exhibited intolerance to smoke, or had a condition that warranted housing in a smoke-free environment. Davis had also complained to health services about experiencing blackouts, but the Takos affidavit states that the ambulatory health records had a notation July 9, 1998 that Davis complained that said episodes occurred while laughing. A request for consultation of that date recites that there were two such episodes in the past two weeks “following ‘laughing episodes.’ ” These particular entries contain no mention of exposure to second-hand smoke.
Defendants also asserted that the exposure to second-hand smoke was not substantial. They claimed that Davis’s complaint focused only on the time period during which Davis, housed in a single cell honor block, was not allowed to have the window open. Although there were no non-smoking units at Attica, defendants claimed that Davis should have asked to transfer within the honor block if the smoke in his area was bothering him, and that the transfer would have been granted.
Defendants also argued they did not act with deliberate indifference to the effects of tobacco smoke or Davis’s health. They cited Attica’s smoking policy, which prohibits smoking in common areas but permits smoking in residential areas, as evidence of their good faith. They also noted that a new smoking policy was being phased in, and effective in June 2001, it was “contemplated” that smoking would not be permitted inside any of the Depart-[98]*98merit’s buildings. In addition, defendants claimed that prison officials did not act with deliberate indifference by requiring Davis to keep his window closed, because other inmates complained they were cold, and ordering Davis to shut the window protected Davis from the wrath of other inmates.
In the remainder of their summary judgment brief, defendants argued that: (1) Pataki, Goord, and Kelly were not personally involved in the alleged constitutional violations, so they could not be liable in the § 1983 action; (2) Davis could not establish the retaliation claim; (3) Davis’s physical assault, harassment, and intimidation claims should be dismissed because the alleged conduct did not rise to the level of a constitutional violation; (4) the court lacked subject matter jurisdiction over the claims against agencies of the State of New York and individual defendants in their official capacities, by virtue of the Eleventh Amendment; and (5) the defendants have qualified immunity from liability because the right to be free from second-hand smoke is not clearly established, and the defendants’ actions were reasonable because (a) the Department had a smoking policy that complied with the New York Clean Air Act, and also accounted for the unique nature of the prison environment, in which it is not reasonable to prohibit smoking entirely or have separate, non-smoking housing units, and (b) there is no case law supporting an Eighth Amendment violation based on secondhand smoke exposure where an inmate is housed in a single cell.
In opposition to defendants’ summary judgment motion, Davis argued that defendants did not dispute that he had been exposed, in his open cell with only bars as barriers, to the second-hand smoke of chain smokers in surrounding cells, without adequate ventilation. Davis asserted that the evidence, viewed in the light most favorable to him, afforded a rational basis for a factfinder to conclude that his confinement exposed him to unreasonably high levels of second-hand smoke.
Davis also disputed statements in the Corrections officers’ affidavits regarding the ventilation and degree of smoke in the housing unit, whether the windows were allowed to be kept open on cold days, whether other inmates had complained of being cold, and whether he had always been housed in a single cell. He asserted that from January 1996 to March 1997, he was housed in a double-bunk cell with a cellmate who smoked. Davis also disputed the validity of Dr. Takos’s findings, asserting that he complained of conditions caused by second-hand smoke several times, but not all of the inmates’ complaints become part of their medical record, and Dr. Takos is not a specialist in such conditions. Davis attacked the viability of the new smoking policy, asserting that it is not effective or enforceable, because officers and inmates continue to smoke inside.
The magistrate judge granted defendants’ summary judgment motion as to Governor Pataki based on his lack of personal involvement, then denied Davis’s summary judgment motion, and granted summary judgment for defendants. The magistrate judge concluded that, although the Supreme Court held in Helling that an inmate could state an Eighth Amendment claim for cruel and unusual punishment by showing unreasonable exposure to secondhand smoke, Davis failed to provide evidence that was sufficient to prove, as a matter of law, that he was exposed to unreasonably high levels of second-hand smoke, or that there were material issues of triable fact regarding his exposure.
The magistrate judge’s conclusion was based on the following “facts”: (1) Davis’s [99]*99complaint only specified three instances when his window was closed against his will; (2) the time period relevant to the complaint was very limited, spanning from October 1998 to February 1999;3 (3) Davis was ordered to stop opening the window less than two months before he was transferred out of the housing block; (4) Davis had applied for and was voluntarily placed in the honor block; (5) Davis did not request to be transferred to a less smoky cell, even though requests to transfer within the honor block were liberally accommodated; (6) Davis occupied a private cell during the relevant time period; (7) a mechanical ventilation system drew air out of Davis’s cell; and (8) Davis’s medical records show only one reference to his complaint about smoke-related symptoms, and the symptoms were actually related to a previous condition. Based on these facts, and Davis’s failure to come forward with enough credible evidence to support a jury verdict in his favor, the magistrate judge disposed of the motions without addressing the other arguments raised by the parties, or the retaliation claim.
II. DISCUSSION
A. Justiciability and mootness
We first consider whether Davis’s claim for permanent injunctive relief is justiciable, or whether the claim is moot, as Davis was transferred to a different housing block, and Attica implemented a new smoking policy. Under Article III, section 2 of the Constitution, federal courts lack jurisdiction to decide questions that cannot affect the rights of litigants in the case before them. See DeFunis v. Odegaard, 416 U.S. 312, 316, 94 S.Ct. 1704, 40 L.Ed.2d 164 (1974) (per curiam) (citing North Carolina v. Rice, 404 U.S. 244, 246, 92 S.Ct. 402, 30 L.Ed.2d 413 (1971)); Bragger v. Trinity Capital Enterprise Corp., 30 F.3d 14, 16 (2d Cir.1994). A case is moot when “it can be said with assurance that there is no reasonable expectation that the alleged violation will recur, [and] interim relief or events have completely and irrevocably eradicated the effects of the alleged violation.” Associated Gen. Contractors of Conn. v. City of New Haven, 41 F.3d 62, 66-67 (2d Cir.1994) (quoting County of Los Angeles v. Davis, 440 U.S. 625, 631, 99 S.Ct. 1379, 59 L.Ed.2d 642 (1979)).
Here, Davis’s claim for injunctive relief is not moot because Davis indicates that his problems with second-hand smoke are ongoing. Despite defendants’ contention that Davis does not complain of ongoing exposure to excessive amounts of secondhand smoke, the most recent information on record indicates that Davis is housed in a block without individual cell windows, in conditions similar to those he experienced prior to being transferred out of the honor block. Moreover, although defendants have implemented a new, restrictive smoking policy, Davis asserts that the policy is not being enforced, and that inmates and Corrections officers are still smoking inside. Therefore, Davis’s claim for permanent injunctive relief is not moot, and we may consider these issues.
B. Summary judgment
We review orders granting summary judgment de novo and determine whether [100]*100the district court properly concluded that there was no genuine issue as to any material fact and the moving party was entitled to judgment as a matter of law. See Cronin v. Aetna Life Ins. Co., 46 F.3d 196, 202-03 (2d Cir.1995). Pursuant to Fed.R.Civ.P. 56(c), the district court must consider all “pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits,” in determining whether there is a genuine issue of material fact. The district court is required to resolve all ambiguities and draw all factual inferences in favor of the non-movant. See Cronin, 46 F.3d at 202. However, reliance upon conclusory statements or mere allegations is not sufficient to defeat a summary judgment motion. See Ying Jing Gan v. City of New York, 996 F.2d 522, 532-33 (2d Cir.1993); Fed.R.Civ.P. 56(e). The nonmoving party must “go beyond the pleadings, and by [his or] her own affidavits, or by the ‘depositions, answers to interrogatories, and admissions on file,’ designate ‘specific facts showing that there is a genuine issue for trial.’ ” Celotex Corp. v. Catrett, 477 U.S. 317, 324, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986) (quoting Fed.R.Civ.P. 56(e)).
In Helling, the Supreme Court, identifying both the objective and subjective components of the Eighth Amendment violation, determined that a plaintiff “states a cause of action under the Eighth Amendment by alleging that [prison officials] have, with deliberate indifference, exposed him to levels of ETS that pose an unreasonable risk of serious damage to his future health.”4 Helling, 509 U.S. at 35, 113 S.Ct. 2475. Objectively, a plaintiff must show that “he himself is being exposed to unreasonably high levels of ETS.” Id. “The objective factor not only embraces the scientific and statistical inquiry into the harm caused by ETS, but also ‘whether society considers the risk ... to be so grave that it violates contemporary standards of decency to expose anyone unwillingly to such a risk.’ ” Warren v. Keane, 196 F.3d 330, 333 (2d Cir.1999) (quoting Helling, 509 U.S. at 36, 113 S.Ct. 2475) (emphasis in original). In granting summary judgment in favor of the defendants, the magistrate judge only reached the objective prong, concluding that Davis had failed to produce evidence which would create a genuine issue of fact as to whether Davis had been exposed to unreasonable levels of second-hand smoke.
The magistrate judge evaluated the summary judgment motions as if Davis had only produced evidence indicating that he was exposed to unreasonable levels of second-hand smoke on the three occasions, between October 1998 and February 1999, when he was required to close the window. However, our de novo examination of the record demonstrates that Davis’s evidence encompassed more than the district court identified. For example, Davis indicated that he had previously been housed in a double-bunk cell with a smoker, and he never alleged that the second-hand smoke problem was limited to the times when he was required to shut the window. Instead, he asserted that, during the time he had been at Attica since arriving in June 1993, he had always been housed in areas where the majority of inmates were smokers, and that, in the honor block area, he was surrounded by seven inmates who were chain smokers or frequent smokers, such that “the smell of smoke fills the air and enters] my cell in a manner as though I was myself smoking.” Complaint, Ex. A (letter to Goord). Davis further alleged that the [101]*101smoke caused him to suffer dizziness, difficulty breathing, blackouts, and respiratory problems. These assertions are not mere conclusory allegations, but may be sufficient to create an issue of fact as to the level of smoke to which Davis was exposed and, thus, whether his Eighth Amendment rights were violated. See Warren, 196 F.3d at 333 (rejecting the argument that the Eighth Amendment right to be free from exposure to unreasonable secondhand smoke levels is limited to the facts in Helling, where an inmate was double-celled with an inmate who smoked five packs of cigarettes daily).
We note that it is possible that Davis did not exhaust administrative remedies, pursuant to the Prison Litigation Reform Act (“PLRA”), 42 U.S.C. § 1997e(a), with respect to complaints about excessive second-hand smoke levels prior to, and following, the time period examined by the district court. See Porter v. Nussle, 534 U.S. 516, 532, 122 S.Ct. 983, 152 L.Ed.2d 12 (2002) (holding that “the PLRA’s exhaustion requirement applies to all inmate suits about prison life, whether they involve general circumstances or particular episodes, and whether they allege excessive force or some other wrong”). However, the defendants did not raise the issue of failure to exhaust administrative remedies, nor did the district court cite this as the reason for its narrow construction of Davis’s allegations. Accordingly, we vacate, in part, the district court’s grant of summary judgment for defendants, and remand for the district court to consider in the first instance Davis’s claims relating to the time period between January 1993 and October 1998. The district court should determine (1) whether Davis properly exhausted his administrative remedies with regard to his claims with respect to the defendants’ behavior during this time period, or whether the defendants waived compliance with the exhaustion requirement by failing to raise it, and if so, (2) whether the inclusion of Davis’s claims regarding this time period creates a genuine issue of material fact as to whether Davis was exposed to unreasonable levels of secondhand smoke.
We decline to address whether Davis raised a genuine issue of material fact as to the defendants’ deliberate indifference, as the magistrate judge did not reach the subjective prong of the Eighth Amendment claim. We uphold summary judgment with respect to some of the defendants on alternate grounds. See Johnson v. Nyack Hosp., 964 F.2d 116, 122 (2d Cir.1992). The dismissal of Davis’s claim against Pataki is affirmed, because Davis did not sufficiently allege Pataki’s personal involvement in Attica’s smoking policies. See Moffitt v. Town of Brookfield, 950 F.2d 880, 886 (2d Cir.1991). In addition, the dismissal of Davis’s claims against the State of New York, the Department, and Attica, and Davis’s claims for damages against all of the individual defendants in their official capacities is affirmed, because these claims are barred by the Eleventh Amendment. See Kentucky v. Graham, 473 U.S. 159, 169, 105 S.Ct. 3099, 87 L.Ed.2d 114 (1985) (a claim for damages against state officials in their official capacity is considered to be a claim against the State and is therefore barred by the Eleventh Amendment); Pennhurst State Sch. & Hosp. v. Halderman, 465 U.S. 89, 100, 104 S.Ct. 900, 79 L.Ed.2d 67 (1984) (agencies and departments of the state are entitled to assert the state’s Eleventh Amendment immunity); see also Santiago v. New York State Dep’t of Corr. Servs., 945 F.2d 25, 28 n. 1 (2d Cir.1991) (the Department is an agency of the State, and therefore entitled to assert Eleventh Amendment immunity). However, to the extent that Davis raises genuine issues of material fact as to whether his Eighth [102]*102Amendment rights were violated, the remaining claims for declaratory and injunctive relief and damages against defendants, in their individual capacities, are remanded to the district court for further proceedings. See Hafer v. Melo, 502 U.S. 21, 27-31, 112 S.Ct. 358, 116 L.Ed.2d 301 (1991) (Eleventh Amendment does not bar damages actions against state officials sued in their personal or individual capacities); Kostok v. Thomas, 105 F.3d 65, 69 (2d Cir.1997) (“A federal court may grant prospective injunctive relief only to stop or prevent acts that are illegal under federal law”).
C. Interlocutory orders
Davis also appeals the magistrate judge’s intermediate decisions, which include, in addition to the dismissal of Davis’s claim against Pataki, the denial of Davis’s motion for a preliminary injunction, and the denial of his motion to amend his complaint.5 The latter two motions were based on alleged acts of retaliation surrounding the misconduct report, and the subsequent disciplinary proceeding and punishment.
This Court reviews district court denials of preliminary injunctions and motions to amend a complaint for abuse of discretion. See No Spray Coalition, Inc. v. City of New York, 252 F.3d 148, 150 (2d Cir.2001) (per curiam) (preliminary injunction); Lane Capital Mgmt., Inc. v. Lane Capital Mgmt., Inc., 192 F.3d 337, 343 (2d Cir.1999) (motion to amend complaint). Our review of these orders indicates that it was not an abuse of discretion for the magistrate judge to deny either motion, for substantially the reasons set forth in the orders.
III. CONCLUSION
For the foregoing reasons, we affirm, in part, the magistrate judge’s grant of summary judgment for defendants and the magistrate judge’s dismissal of Davis’s claims against Pataki, the State of New York, the Department, and Attica, and the dismissal of Davis’s damages claims against Goord, Kelly, Stachewicz, Christen, McDonald, and Barone, in their official capacities. However, we reverse the magistrate judge’s grant of summary judgment in all other respects, and remand for further proceedings. On remand, the district court should consider (1) whether Davis properly exhausted his administrative remedies with regard to his claims with respect to the defendants’ behavior between January 1993 and October 1998, or whether the defendants waived compliance with the exhaustion requirement by failing to raise it, and if so, (2) whether the inclusion of Davis’s claims regarding this time period creates a genuine issue of material fact as to whether Davis was exposed to unreasonable levels of second-hand smoke. In addition, on remand the district court may reach the retaliation claims it did not reach earlier. Finally, the district court should consider appointing counsel to assist Davis with the ongoing proceedings.