This is an open-label phase 2 study designed to explore the efficacy and safety of low-dose PTCy-ruxolitinib GVHD prophylaxis in older adults undergoing allogeneic HCT with a matched sibling or unrelated donor with a peripheral blood stem cell graft.

Following reduced intensity conditioning and 8/8-matched peripheral blood transplant on Day 0, all patients will receive a GVHD prophylaxis post-transplant composed of the following: (i) cyclophosphamide administered at 25 mg/kg on Day +3 and +4, (ii) tacrolimus beginning on Day +5 and through Day +180 and administered with a trough target of 5-10 ng/ml through Day +90 and tapered thereafter; (iii) mycophenolate mofetil (MMF) administered at 15 mg/kg thrice daily beginning on Day +5 through Day +35; and (iv) ruxolitinib administered at 5 mg twice daily starting after engraftment (between Days +30 and +60) and continuing through one year post transplant.

Inclusion Criteria:

1. History of hematologic malignancy.

2. Must be in remission:

   • Acute Leukemia, chronic leukemia, or myelodysplasia/myeloproliferative neoplasm (excluding primary myelofibrosis): No circulating blasts and <5% blasts in the bone marrow.
   • Hodgkin and non-Hodgkin lymphomas: Chemo-sensitive disease at time of transplant

3. Patients must have a related or unrelated peripheral blood stem cell donor that is an 8/8 match at HLA-A, -B, -C and -DRB1 at high resolution using DNA-based typing. Unrelated donors must be willing to donate peripheral blood stem cells and meet NMDP criteria for donation.

4. Planned reduced intensity conditioning therapy with fludarabine/melphalan, with total dose of melphalan of 100-140 mg/m^2 IV or fludarabine/busulfan with total dose of busulfan of 6.4 mg/kg IV.

5. Karnofsky Performance Scale of 60 or greater.

6. Male participants must agree to abstinence or to use of barrier contraception during the entire study period.

7. Female participants of childbearing potential will require a negative pregnancy test and should agree to practice two effective methods of contraception during the entire study period.

8. Ability to understand a written informed consent document, and the willingness to sign it.

Exclusion Criteria:

1. Prior allogeneic HCT or Chimeric antigen receptor (CAR) -T cell therapy.
2. Patients with liver dysfunction evidenced by bilirubin ≥2x upper limit normal (ULN), except for a history of Gilbert syndrome.
3. Patients with renal impairment defined by creatinine<2mg/dL.
4. Patients with cardiac dysfunction defined by a left ventricular ejection fraction ≤45%.
5. Patients with pulmonary dysfunction defined by a forced expiratory volume in the first second (FEV1) or diffusing capacity for carbon monoxide (DLCO) (corrected for hemoglobin) ≤50% of predicted.
6. Patients with a chronic or active infection requiring systemic treatment during and after transplant.
7. Presence of other active malignant disease diagnosed within 12 months, except for adequately treated non-melanoma skin cancer, adequately treated melanoma grade 2 or less, or cervical intraepithelial neoplasia. Active malignancy is malignancy receiving treatment.
8. Pregnant or lactating subjects.