Study Of Ruxolitinib (INCB018424) With Preoperative Chemotherapy For Triple Negative Inflammatory Breast Cancer

Inclusion Criteria: * Participants must have histologically confirmed invasive breast cancer. All histologic subtypes are eligible. * Patients must have known ER, PR, and HER2 status defined as triple-negative breast cancer (TNBC), defined as: --ER and PR \<10% by immunohistochemistry, and HER2-negative ( as per ASCO/CAP guidelines, defined as IHC 0 or 1+, or FISH ratio \<2.0 or HER2 copy number \<6.0). * Patients must have the clinical diagnosis of inflammatory breast cancer, involving an intact breast. * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of ruxolitinib in participants \<18 years of age, children are excluded from this study. * ECOG performance status 0 or 1. * Participants must have normal organ and marrow function as defined below: * Leukocytes ≥ 3,000/mm3 * Absolute neutrophil count ≥ 1,500/mm3 * Platelets ≥ 100,000/mm3 * Bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) * AST (SGOT)/ALT (SGPT) \< 2.5 X institutional upper limit of normal * Creatinine ≤1.5 x institutional upper limit of normal OR creatinine clearance \> 60 mL/min/1.73 m2 for subjects with creatinine levels above institutional normal * Patients with evidence of extensive nodal involvement are allowed. Extensive nodal involvement is defined as metastatic disease involving any nodal region outside of the involved breast. * Patients with minimal metastatic disease involvement in bone or viscera are allowed. Minimal metastatic disease is defined as: evidence of metastatic involvement as demonstrated by imaging only, not amenable to biopsy confirmation. * Both men and women are allowed. * The effects of ruxolitinib on the developing human fetus are unknown. For this reason women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry until completion of chemotherapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent document. * LVEF \> 50% calculated by echocardiogram (ECHO) or MUGA * Patients may have bilateral breast cancer so long as one breast meets criteria for inflammatory breast cancer, and neither breast cancer has received prior therapy Exclusion Criteria: * Participants may not be receiving any other investigational agents. * Participants with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ruxolitinib. * Participants receiving any medications or substances that are potent inhibitors of CYP3A4, including grapefruit juice are ineligible. Participants receiving fluconazole are also ineligible. (Please refer to Appendix B for the full list of potent inhibitors and washout periods). * Chronic corticosteroid use in excess of the equivalent of prednisone 10 mg once daily. * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because paclitaxel, doxorubicin, and cyclophosphamide have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued if the mother is treated on study. These potential risks may also apply to other agents used in this study. * Individuals with a history of a different malignancy are ineligible except for the following circumstances. Individuals with a history of other malignancies are eligible if they have been disease-free for at least 3 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 3 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin. * Known HIV-positive individuals on combination antiretroviral therapy are eligible so long as they meet all other criteria. Known HIV-positive individuals who are not on combination antiretroviral therapy are not eligible because these individuals are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * Clinically significant malabsorption syndrome. * Patients may not have received paclitaxel, doxorubicin, or cyclophosphamide as anti-neoplastic therapy. * Patients with prior radiation to the affected breast.