A Study of Ruxolitinib for Preventing Graft-Versus-Host Disease in People With a Hematologic Malignancy Who Will Receive a Stem Cell Transplant

Inclusion Criteria: * Patients ≥18- years-old at time of consent * Diagnosis: hematologic malignancy in morphologic remission (blasts \<5%, no evidence of extramedullary disease in AML or MDS). Patients with CR with incomplete count recovery (CRp or CRi) or minimal residual disease are allowed. Patients with lymphoma must have a complete or partial response * Donor: related or unrelated 7-8/8 HLA-matched or related haploidentical * Karnofsky score ≥ 70% * Female subjects of childbearing potential (\<50 years old) have a negative serum or urine pregnancy test. Females of childbearing potential are defined as females without prior hysterectomy or who have had any evidence of menses in the past 12 months. °Sexually active females of childbearing potential enrolled in the study must agree to consistently use two forms of accepted methods of contraception during the course of the study and for 3 months after their last dose of the study drug. Effective birth control includes: \*Intrauterine device (IUD) plus one barrier method \*Stable doses of hormonal contraception for at least 3 months (e.g., oral, injectable, implant, transdermal) plus one barrier method \*2 barrier methods. Effective barrier methods are male or female condoms, diaphragms, and spermicides (creams or gel that contain a chemical to kill sperm); or \* A vasectomized partner. * For male subjects who are sexually active and who are partners of females of childbearing potential: Agreement to use two forms of contraception as per above and to not donate sperm during the treatment period and for at least 3 months after the last dose of study drug Exclusion Criteria: * Recipient of CD34+ selected or engineered stem cell graft * Treatment with in vivo T cell depletion (e.g. anti-thymocyte globulin) * Patients with an active secondary malignancy or prior malignancy requiring systemic therapy within the past 5 years. Exceptions include adequately treated localized non-melanoma skin cancer (basal cell carcinoma and squamous cell carcinoma), as well as localized prostate cancer considered low risk and stable under treatment or surveillance. * Severely impaired renal function defined by serum creatinine \> 2mg/dL, renal dialysis requirement. * Use of investigational agent within 14 days pre-HCT * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months * Uncontrolled psychiatric illness * Female patient who is pregnant or breastfeeding * Known allergy or sensitivity to ruxolitinib