Carboplatin, Nab-Paclitaxel, Durvalumab Before Surgery and Adjuvant Therapy in Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Previously untreated, histologically proven, surgically resectable primary squamous cell carinoma of the head and neck, stage III or IV (HPV positive or negative non-metastatic disease). SCCHN of unknown primary is excluded. SCCHN of the oral cavity is allowed\*. Unambiguously squamous Epstein-Barr virus (EBV)-negative nasopharynx cancer will be excluded nor will unambiguously squamous cancers of the skull base that are clearly surgically resectable and clearly squamous. Squamous skin cancer occurring in the head/neck region will not be eligible nor will EBV+positive nasopharynx cancer. (\*Note: Induction chemotherapy is not considered standard therapy for SCCHN of the oral cavity and participation on this trial will lead to a delay in time to definitive, potentially curative therapy i.e., surgery). * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Measurable disease as per RECIST 1.1 * Age greater than or equal to 18 at time of study entry * Adequate bone marrow function as demonstrated by: * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm3 * Hgb \> 10 g/dL (use of transfusion to reach this threshold prior to study initiation is acceptable) * Platelet count ≥ 100,000/mm3 * Adequate hepatic and renal function as demonstrated by: * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x upper limit of normal (ULN); * Total serum bilirubin ≤1.5 x ULN * Creatinine clearance (CrCL) \> 40 mL/min as measured via Cockcroft-Gault * Males: Creatinine CL (mL/min) = (Weight (kg) x (140 - Age))/(72 x serum creatinine (mg/dL)) * Females: Creatinine CL (mL/min) = (Weight (kg) x (140 - Age))/(72 x serum creatinine (mg/dL)) x 0.85 * Negative serum β human chorionic gonadotropin (β-hCG) pregnancy test within 72 hours of day 1 of induction chemotherapy in women of child-bearing potential. * All males and females of childbearing potential must agree to use adequate contraception during the study. Adequate contraception is defined as any medically recommended method (or combination of methods) as per standard of care. Females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy or bilateral oophorectomy. See section 4.13 for list of acceptable methods of contraception. * Signed an institutional review board (IRB)-approved informed consent and HIPAA authorization. * Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. * Subjects must agree to allow use of any pre-treatment tissue remaining after definitive diagnosis is made (ie, archival and or fresh tissue) for research purposes. In addition, subjects must consent to allow use of their residual post-operative tissue for research purposes. Exclusion Criteria: * Involvement in the planning and/or conduct of the study (applies to staff at the study site) or previous enrollment in the present study. * Any metastatic disease. * Known history of previous clinical diagnosis of tuberculosis. * History and/or confirmed pneumonitis. * Low-risk HPV+ disease of the oropharynx, defined as meeting all of the following criteria: * Patients with known HPV+ by fluorescence in situ hybridization (FISH) and/or p16 * Smoking history ≤ 10 pack years * Stage T1-2N0-2b, T3N0 * Not considered eligible for any of the chemotherapy agents included in the induction regimen. * Current active hepatic or biliary disease (with exception of patients with Gilbert's syndrome, asymptomatic gallstones, or stable chronic liver disease per investigator assessment). * Major surgery within 28 days prior to day 1 of study treatment from which the patient has not completely recovered. * Receiving any investigational agent currently or within 28 days or 5 half-lives of Day 1 of treatment on this study, whichever is shorter. * Active, serious infection, medical, or psychiatric condition that would represent an inappropriate risk to the patient or would likely compromise achievement of the primary study objective, including unstable angina, serious uncontrolled cardiac arrhythmia, uncontrolled infection, or myocardial infarction ≤ 6 months prior to study entry. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[eg, colitis, Crohn's disease\], diverticulitis with the exception of a prior episode that has resolved or diverticulosis, celiac disease, irritable bowel disease, or other serious gastrointestinal chronic conditions associated with diarrhea; systemic lupus erythematosus; Wegener's syndrome \[granulomatosis with polyangiitis\]; myasthenia gravis;; rheumatoid arthritis; hypophysitis, uveitis; etc) within the past 2 years prior to the start of treatment. \[Note: Subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded\] * Known mean QT interval corrected for heart rate (QTc) ≥470 ms calculated from 3 electrocardiograms (ECGs) using Frediricia's Correction. (Note that ECG is not required for study entry and is not part of study procedures). * Other prior or concomitant malignancies with the exception of: * Non-melanoma skin cancer * In-situ malignancy * Low-risk prostate cancer after curative therapy * Other cancer for which the patient has been disease free for ≥ 5 years before the first dose of study drug and of low potential risk for recurrence. * Any concurrent chemotherapy, investigational product, biologic or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g. hormone replacement therapy) is acceptable. * Current or prior use of immunosuppressive medication within 14 days prior to the first dose of durvalumab. The following are exceptions to this criterion: intranasal, inhaled, topical or local steroid injections (eg. intra-articular injection); steroids as premedication for hypersensitivity reactions; systemic corticosteroid at physiologic doses not to exceed 10mg/day of prednisone or equivalent.\[Note: If systemic corticosteroids are part of the treatment regimen for the indication under study, the systemic corticosteroid is permitted\]. * Known human immunodeficiency virus (HIV), hepatitis C virus (HCV) or evidence of active hepatitis B virus (HBV). * History of hypersensitivity to durvalumab or any excipient. * Receipt of live attenuated vaccination within 30 days prior the first dose of durvalumab \[Note: If a vaccine is part of the treatment regimen for the indication under study, the vaccine is permitted\]. * Female subjects who are pregnant, breast-feeding or female patients of reproductive potential who are not employing an effective method of birth control from starting dose of study medications (Cycle 1 Day 1), including dosing interruptions through 90 days after receipt of the last dose of durvalumab. Refrain from egg cell donation while taking durvalumab and for at least 90 days after the last dose of durvalumab. * Male subjects who are not employing an effective method of birth control from starting dose of study medications (Cycle 1 Day 1), including dosing interruptions through 6 months after receipt of study treatment. Male subjects should agree to refrain from sperm donation while taking study treatment and for at least 6 months after the last dose of nab-paclitaxel and at least 90 days after the last dose of durvalumab. Should a female partner of a male patient become pregnant or suspect she is pregnant while participating in the study, he should inform his treating physician and the female partner should call her physician immediately. * Any previous treatment with a programmed cell death protein 1 (PD-1) or programmed death-ligand 1 (PD-L1) inhibitor, including durvalumab. * History of primary immunodeficiency. * History of organ transplant. * Any condition that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of patient safety or study results (eg, uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active bleeding diatheses or psychiatric illness/social situations that would limit compliance with study requirements or compromise the ability of the subject to give written informed consent). * Patients with known contraindications to radiotherapy including inherited syndromes associated with hypersensitivity to ionizing radiation (e.g., Ataxia Telangiectasia, Nijmegen Breakage Syndrome).