H3.3K27M-specific Peptide Vaccine and Poly ICLC with or without Nivolumab in Treating Patients with Newly Diagnosed HLA-A2 Positive, H3.3K27M Positive Diffuse Intrinsic Pontine Glioma or Other Newly Diagnosed Gliomas

Inclusion Criteria

• Stratum A: Newly diagnosed children (3-21 years old) with DIPG who are positive for the H3.3K27M mutation (positive testing from a Clinical Laboratory Improvement Act [CLIA] laboratory or equivalent laboratory required) that underwent standard radiation therapy
• Stratum B: Newly diagnosed children (3-21 years old) with diagnosis of midline glioma other than DIPG who are positive for the H3.3K27M mutation (positive testing from a CLIA laboratory or equivalent laboratory required) including spinal cord gliomas, that underwent standard radiation therapy
• Stratum C: Newly diagnosed children 3-21 years of age with diagnosis of DIPG or midline glioma other than DIPG (excluding primary spinal cord gliomas) who are positive for the H3.3K27M mutation (positive testing from a CLIA or equivalent laboratory required), that underwent standard radiation therapy
• The patient must test positive for HLA-A*02:01 (positive testing from a CLIA or equivalent laboratory required; only the HLA A*02:01 subtype is eligible; other subtypes are excluded)
• The patient must be either off systemic steroids or be on stable dose of dexamethasone or equivalent (max 0.1 mg/kg/day; maximum 4 mg/day) at time of enrollment
• Patients must not have received any prior chemotherapy, immunotherapy or bone marrow transplant for the treatment of their tumor; prior use of temozolomide during radiation at maximum of the standard pediatric dosing (defined as 90 mg/m^2 /dose continuously during radiation therapy for 42 days) or dexamethasone is allowed
• Patients must have undergone radiation therapy and surgery as part of their standard of care * Stratum A: Radiation therapy must have started within 4 weeks of diagnosis by imaging or surgery, whichever is later * Stratum B: For subjects undergoing surgery for more extensive resection, radiation therapy should be started within 4-6 weeks from surgery * Stratum C: Radiation therapy must have started within 4 weeks of diagnosis by imaging or surgery, whichever is later. For subjects undergoing surgery for more extensive resection, radiation therapy should be started within 4-6 weeks from surgery
• Karnofsky >= 50 for patients >= 16 years of age, and Lansky >= 50 for patients < 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score
• Peripheral absolute neutrophil count (ANC) >= 1000/mm^3
• Platelet count >= 100,000/mm^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
• Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70mL/min/1.73 m^2 or a serum creatinine based on age/gender as follows: * 3 to < 6 years: 0.8 (male and female) * 6 to < 10 years: 1 (male and female) * 10 to < 13 years: 1.2 (male and female) * 13 to < 16 years: 1.5 (male) 1.4 (female) * >= 16 years: 1.7 (male) 1.4 (female)
• Bilirubin (sum of conjugated + unconjugated) =< 1.5 x upper limit of normal (ULN) for age
• Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) =< 110 U/L
• Serum albumin >= 2 g/dL
• Serum lipase =< ULN at baseline
• No evidence of dyspnea at rest, no exercise intolerance due to pulmonary insufficiency, and a pulse oximetry of > 92% while breathing room air
• Patients with seizure disorder may be enrolled if seizure disorder is well controlled
• The effects of the H3.3K27M vaccine and nivolumab on the developing human fetus are unknown. For this reason, females of child-bearing potential and males must agree to use adequate contraception. Adequate methods include: hormonal or barrier method of birth control; or abstinence prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Males treated or enrolled on this protocol must also agree to use adequate contraception prior to the study and for the duration of study participation
• Ability to understand a written informed consent document, and the willingness to sign it. Assent will be obtained when appropriate based on the subjects age

Exclusion Criteria

• Investigational Drugs * Patients who are currently receiving another investigational drug are not eligible * Prior treatment with another investigational drug
• Anti-cancer Agents * Patients who are currently receiving other anti-cancer agents are not eligible * Prior treatment with other anti-cancer agents
• Patients who have received a live / attenuated vaccine within 30 days of first treatment
• Patients with evidence of disseminated or leptomeningeal disease
• Patients with a known disorder that affects their immune system, such as human immunodeficiency virus (HIV), or hepatitis B or C, or an auto-immune disorder requiring systemic cytotoxic or immunosuppressive therapy are not eligible. Note: Patients that are currently using inhaled, intranasal, ocular, topical or other non-oral or non-IV steroids are not necessarily excluded from the study but need to be discussed with the study chair
• Patients with a >= grade 2 hypothyroidism due to history of autoimmunity are not eligible. (Note: Hypothyroidism due to previous irradiation or thyroidectomy will not impact eligibility)
• Patients who have received prior solid organ or bone marrow transplantation are not eligible
• Patients with uncontrolled infection
• Female patients of childbearing potential must not be pregnant or breast-feeding. Female patients of childbearing potential must have a negative serum or urine pregnancy test prior to the start of therapy (as clinically indicated)