Brief Summary: The purpose of this research study is to determine the rate of local regional control at 2 years when using de-intensified chemoradiotherapy (CRT) in patients with Human Papillomavirus (HPV)-associated head and neck squamous cell carcinoma (HNSCC). Local regional control means no recurrence of the cancer in the head or neck area. Study subjects will be enrolled into 4 groups. Group/treatment will be based on a number of factors, including smoking and drinking history.

Detailed Description: The purpose of this research study is to determine the rate of local regional control at 2 years when using de-intensified chemoradiotherapy (CRT) in patients with Human Papillomavirus (HPV)-associated head and neck squamous cell carcinoma (HNSCC). Local regional control means no recurrence of the cancer in the head or neck area. Study subjects will be enrolled into 4 groups. Group/treatment will be based on a number of factors, including smoking and drinking history. If participants choose to participate, participants will be asked to: * Participate in screening for eligibility, this will include: questions regarding \\medical history, physical exam, blood/urine samples, electrocardiogram, PET/CT and/or CT-MRI of the neck, assessment of tumor, and a questionnaire. * Complete the study regimen including evaluations and follow up visits. Participants may be in this research study for approximately to 5 years after receiving standard of care (SOC) treatment. Depending on the group enrolled in, the treatment will last either 6 weeks (Groups 1-3) or 15 weeks (Group 4.This group will also receive 3 cycles of SOC induction therapy (One cycle = 21 days). Induction therapy is initial chemotherapy delivered prior to radiation or surgery when treating cancer. * Participate in routine types of procedures such as clinical exams, blood and urine tests, and imaging tests to assess tumor. * Consent to storage of research samples. This research study involves chemotherapy and intensity-modulated radiation therapy (IMRT) IMRT is used to safely deliver precise radiation to a tumor while minimizing the dose to surrounding normal tissue. There are no added costs associated with participation. There is no reimbursement for participation. The names of the drugs/interventions involved in this study are: * Cisplatin * Docetaxel (Group 4 only) * Fluorouracil (Group 4 only) * Carboplatin (Group 4 Only) All of the drugs listed above are approved for use by the Food and Drug Administration (FDA), commercially available, and considered standard of care (SOC) for cancer. Serious known side effects that participants may experience include: * Nausea and vomiting * Diarrhea * Fever * Skin irritation, rash * Joint pain