Inclusion Criteria:

          -  Patients must have clinically and radiographically suspected and previously untreated
             International Federation of Gynecologic and Obstetrics (FIGO) stage III or IV
             epithelial ovarian, primary peritoneal or fallopian tube cancer, high grade, for whom
             the plan of management will include neoadjuvant chemotherapy (NACT) with interval
             tumor reductive surgery (TRS) who have undergone biopsies for histologic confirmation

          -  Institutional confirmation of Mullerian epithelial adenocarcinoma on core biopsy (not
             cytology or fine needle aspiration) or laparoscopic biopsy; (for phase II of the study
             formalin-fixed paraffin-embedded [FFPE] tissue should be available for laboratory
             analysis); patients with the following histologic epithelial cell types are eligible:
             high grade serous carcinoma, high grade endometrioid carcinoma, clear cell carcinoma,
             or a combination of these

          -  All patients must have measurable disease as defined by Response Evaluation Criteria
             In Solid Tumors (RECIST) 1.1; measurable disease is defined as at least one lesion
             that can be accurately measured in at least one dimension (longest diameter to be
             recorded); each lesion must be >= 10 mm when measured by computed tomography (CT),
             magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or >= 20 mm
             when measured by chest x-ray; lymph nodes must be >= 15 mm in short axis when measured
             by CT or MRI

          -  Appropriate stage for study entry based on the following diagnostic workup:

               -  History/physical examination within 28 days prior to registration

               -  Radiographic imaging of the chest, abdomen and pelvis within 28 days prior to
                  registration documenting disease consistent with FIGO stage III or IV disease

               -  Further protocol-specific assessments

          -  Eastern Cooperative Oncology Group (ECOG)/Karnofsky performance status of 0, 1, or 2
             within 28 days prior to registration

          -  Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl; this ANC cannot
             have been induced by granulocyte colony stimulating factors (within 14 days prior to
             registration)

          -  Platelets greater than or equal to 100,000/mcl (within 14 days prior to registration)

          -  Hemoglobin greater than 9.0 mg/dl (transfusions are permitted to achieve baseline
             hemoglobin level) (within 14 days prior to registration)

          -  Estimated creatinine clearance (CrCl) >= 50 mL/min according to the Cockcroft-Gault
             formula (within 14 days prior to registration)

          -  Bilirubin =< 1.5 x upper limit of normal (ULN) (within 14 days prior to registration)

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 3 x ULN (within
             14 days prior to registration)

          -  Alkaline phosphatase =< 2.5 x ULN (within 14 days prior to registration)

          -  Neurologic function: neuropathy (sensory and motor) less than or equal to Common
             Terminology Criteria for Adverse Events (CTCAE) grade 1

          -  Ability to swallow and retain oral medication

          -  The patient must provide study-specific informed consent prior to study entry

          -  BRCA testing results (i.e., comprehensive BRCA1 and BRCA2 sequencing, including
             assessment of gene rearrangements) must be submitted for all patients enrolled to
             Amendment 7 and subsequent amendments; BRCA testing results are optional for all
             patients enrolled prior to Amendment 7; due to the long acceptance of germline BRCA
             testing through Myriad, Myriad testing reports will be accepted without additional
             documentation; if testing for germline BRCA is done by other organizations, in
             addition to the testing report, documentation from a qualified medical professional
             (e.g., ovarian cancer specialty physician involved in the field, high risk genetics
             physician, genetics counselor) detailing the laboratory results is required; please
             retain a copy of all reports (positive, variants of unknown significance [VUS], or
             negative)

        Exclusion Criteria:

          -  Patients with suspected non-gynecologic malignancy, such as gastrointestinal

          -  Patients with a history of other invasive malignancies, with the exception of
             non-melanoma skin cancer and other specific malignancies are excluded if there is any
             evidence of other malignancy being present within the last three years (2 years for
             breast cancer); patients are also excluded if their previous cancer treatment
             contraindicates this protocol therapy

          -  Patients who have received prior chemotherapy for any abdominal or pelvic tumor within
             the last three years are excluded; patients may have received prior adjuvant
             chemotherapy and radiotherapy for localized breast cancer, provided that it was
             completed more than 2 years prior to registration, the patient remains free of
             recurrent or metastatic disease and hormonal therapy has been discontinued

          -  Patients who have received prior radiotherapy to any portion of the abdominal cavity
             or pelvis or thoracic cavity within the last three years are excluded; prior radiation
             for localized cancer of the head and neck or skin is permitted, provided that it was
             completed more than three years prior to registration, and the patient remains free of
             recurrent or metastatic disease

          -  Patients who have received any targeted therapy (including but not limited to
             vaccines, antibodies, tyrosine kinase inhibitors) or hormonal therapy for management
             of their epithelial ovarian, fallopian tube or peritoneal primary cancer

          -  Patients with mucinous carcinoma, low grade endometrioid carcinoma, low grade serous
             carcinoma or carcinosarcoma

          -  Patients with synchronous primary endometrial cancer, or a past history of primary
             endometrial cancer, unless all of the following conditions are met: stage not greater
             than I-A, grade 1 or 2, no more than superficial myometrial invasion, without vascular
             or lymphatic invasion; no poorly differentiated subtypes, including serous, clear cell
             or other FIGO grade 3 lesions

          -  Severe, active co-morbidity defined as follows:

               -  Chronic or current active infectious disease requiring systemic antibiotics,
                  antifungal or antiviral treatment

               -  Known brain or central nervous system metastases or history of uncontrolled
                  seizures

               -  Clinically significant cardiac disease including unstable angina, acute
                  myocardial infarction within 6 months from enrollment, New York Heart Association
                  class III or IV congestive heart failure, and serious arrhythmia requiring
                  medication (this does not include asymptomatic atrial fibrillation with
                  controlled ventricular rate)

               -  Partial or complete gastrointestinal obstruction

          -  Patients who are not candidates for major abdominal surgery due to known medical
             comorbidities

          -  Patients with any condition that in the judgment of the investigator would jeopardize
             safety or patient compliance with the protocol

          -  Patients who are unwilling to be transfused with blood components

          -  Concurrent anticancer therapy (e.g. chemotherapy, radiation therapy, biologic therapy,
             immunotherapy, hormonal therapy, investigational therapy)

          -  Receipt of an investigational study drug for any indication within 30 days or 5
             half-lives (whichever is longer) prior to day 1 of protocol therapy

          -  Patients who, in the opinion of the investigator, are unable or unlikely to comply
             with the dosing schedule and study evaluations

          -  Patients who are pregnant or nursing; the effects of ruxolitinib on the developing
             human fetus are unknown; for this reason, women of child-bearing potential (WOCBP)
             must agree to use adequate contraception (hormonal or barrier method of birth control;
             abstinence) prior to study entry and for the duration of study participation; WOCBP
             must have a screening negative serum or urine pregnancy test within 14 days of
             registration; a second pregnancy test must be done within 24 hours prior to the start
             of the first cycle of study treatment; women must not be breastfeeding

               -  Women who are not of childbearing potential (i.e., who are postmenopausal or
                  surgically sterile) do not require contraception

               -  Women of childbearing potential (WOCBP) is defined as any female who has
                  experienced menarche and who has not undergone surgical sterilization
                  (hysterectomy and/or bilateral oophorectomy) or who is not postmenopausal;
                  menopause is defined clinically as 12 month amenorrhea in a woman over 45 in the
                  absence of other biological or physiological causes; in addition, women under the
                  age of 55 must have a documented serum follicle stimulating hormone (FSH) level
                  greater than 40mIU/mL

          -  Known history of human immunodeficiency virus (HIV), hepatitis B, or hepatitis C
             infection or known history of tuberculosis; (This exclusion criterion is necessary
             because the treatments involved in this protocol may be immunosuppressive)