I. Determine frequency of patients who do not receive surgery within 6 weeks of completing cycle 3 therapy for reasons other than non-response, disease progression, or medical contraindications. (Phase I) II. Determine if continuation of ruxolitinib as maintenance therapy in participants who complete 6 cycles of standard chemotherapy in combination with ruxolitinib and have not experienced unacceptable toxicity or disease progression is safe and tolerable. (Phase I) III. Determine the impact of ruxolitinib in combination with chemotherapy on progression-free survival as a function of proposed exploratory biomarkers - ALDH+ CD133+ (possibly also CD24+ CK19+) co-staining by AQUA immunofluorescence (IF); ratio of tumor expression of CD8:FOXP3 by immunohistochemistry (IHC); and tumor CD3, CD4, TAI-1, HLA class I and II, CD68 expression by IHC in archived tumor tissue and serum C-reactive protein (CRP) and IL-6 levels in pre-treatment serum. (Phase II) IV. Investigate the prognostic significance of exploratory laboratory parameters in terms of both progression-free survival and overall survival in women receiving conventional chemotherapy alone. (Phase II) V. Determine whether treatment with ruxolitinib in combination with conventional chemotherapy is associated with total gross resection rate at time of interval cytoreductive surgery. (Phase II) VI. Determine whether treatment with ruxolitinib in combination with conventional chemotherapy is associated with complete pathologic response defined at interval cytoreductive surgery. (Phase II) VII. Demonstrate whether treatment with ruxolitinib in combination with conventional chemotherapy results in an improvement in overall survival in primary management of epithelial ovarian, fallopian tube, or primary peritoneal carcinoma. (Phase II)