A Study of Varlilumab and IMA950 Vaccine Plus Poly-ICLC in Patients With WHO Grade II Low-Grade Glioma (LGG)

Inclusion Criteria: * Patients must be \>= 18 years old. * Pathological criteria - Participants must have a newly diagnosed or recurrent WHO grade II astrocytoma, oligoastrocytoma or oligodendroglioma that has been histologically confirmed by prior biopsy or surgical resection. If the pathological diagnosis ws made outside of University of California, San Francisco (UCSF), the pathology must be reviewed and confirmed at UCSF. * Patients must be positive for HLA-A2 based on flow-cytometry or genotyping * Before enrollment, patients must show non-enhancing T2-FLAIR lesions lesions that are amenable to surgical resection. Surgical resection of at least 0.3 grams of tumor is expected to ensure adequate evaluation of the study endpoints * Prior radiation therapy (RT) after the initial diagnosis will be allowed but there must be at least 6 months from the completion of RT (or radiosurgery) to signed informed consent. * Prior chemotherapy and any systemic molecularly targeted anti-tumor therapy will be allowed, and there must be at least 28 days from the last temodar chemotherapy, 42 days for nitrosourea; at least 14 days from the last dose for chemotherapy regimens given continuously or on a weekly basis with limited potential for delayed toxicity. * Patients must have a Karnofsky performance status (KPS) of \>= 70%. * Off or low dose (\<= 4 mg/day by Decadron) corticosteroid at least two weeks before the first pre-surgical vaccine * Adequate organ function within 28 days of study registration including: 1) Adequate bone marrow reserve: absolute neutrophil (segmented and bands) count (ANC) \>=1.0 x 10\^9/L, absolute lymphocyte count \>=4.0 x 10\^8/L, platelets \>=100 x 10\^9/L; hemoglobin \>=8 g/dL; 2) Hepatic: - Total bilirubin \<= 1.5 x upper limit of normal (ULN) and Serum glutamic pyruvic transaminase(SGPT)/ (alanine aminotransferase (ALT)) \<=2.5 x upper limit of normal (ULN), and 3) Renal: Normal serum creatinine or creatinine clearance \>=60 ml/min/1.73 m\^2 * Must be free of systemic infection. Subjects with active infections (whether or not they require antibiotic therapy) may be eligible after complete resolution of the infection. Subjects on antibiotic therapy must be off antibiotics for at least 7 days before beginning treatment. * Sexually active females of child bearing potential must agree to use adequate contraception (diaphragm, birth control pills, injections, intrauterine device (IUD), surgical sterilization, subcutaneous implants, or abstinence, etc.) for the duration of the vaccination period. Sexually active males must agree to use barrier contraceptive for the duration of the vaccination period. * Women of child-bearing potential and men must agree to use adequate contraception (ex. Hormonal or barrier method of birth control or abstinence) prior to study entry and for the duration of study participation (until one month after the last vaccine) since the effects of the current regimen on the developing human fetus are unknown. 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 * Patient must sign an informed consent document indicating that they are aware of the investigational nature of this study, which includes an authorization for the release of their protected health information Exclusion Criteria: * Presence of gliomatosis cerebri, cranial or spinal leptomeningeal metastatic disease * Presence of T1 Gadolinium (Gd)-enhancing lesions (on MRI) suggestive of high-grade glioma * Pathological diagnosis for the resected tumor demonstrates transformation to higher grade (i.e. WHO grade III or IV) gliomas. If a patient is diagnosed as HGG upon resection after receiving the pre-surgical treatment, the patient will be withdrawn from the study and considered for therapeutic options for HGG (trials for HGG or standard of care). The tumor tissue of such a case would be brought to the lab before the pathological diagnosis is made; and thus would be processed before the lab is informed of the final HGG diagnosis. Because HGG tissue may still reflect the vaccine effects, we will evaluate the tumor tissue to help us develop future approaches for HGG. * Pregnant women are excluded from this study because IMA950 and poly-ICLC are drugs with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with IMA950 plus poly-ICLC (IMA950-poly-ICLC hereafter) vaccine, breastfeeding should be discontinued if the mother is treated with IMA950- poly-ICLC vaccine * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection (e.g. active or chronic hepatitis B and C), symptomatic congestive heart failure, unstable angina pectoris, or psychiatric illness/social situations that would limit compliance with study requirements * History or current status of immune system abnormalities such as hyperimmunity (e.g., autoimmune diseases) that needed to be treated by systemic therapy, such as immuno-suppressants and hypoimmunity (e.g., myelodysplastic disorders, marrow failures, AIDS, transplant immunosuppression). * Any isolated laboratory abnormality suggestive of a serious autoimmune disease (e.g. hypothyroidism): Antinuclear antibody, thyroid-stimulating hormone (TSH), free thyroxine (FT4), rheumatoid factor * Any condition that could potentially alter immune function (AIDS, multiple sclerosis, diabetes, renal failure) * Receiving ongoing treatment with immunosuppressive drugs or dexamethasone \> 4mg * Use of any of the following concurrent treatment or medications: * radiation therapy * chemotherapy * interferon (e.g. Intron-A) * allergy desensitization injections * growth factors (e.g. Procrit, Aranesp, Neulasta) * Interleukins (e.g. Proleukin) * any investigational therapeutic medication * Prior cancer diagnosis except the following: * squamous cell cancer of the skin without known metastasis * basal cell cancer of the skin without known metastasis * carcinoma in situ of the breast (DCIS or LCIS) * carcinoma in situ of the cervix * Any other acute or chronic medical or psychiatric condition or laboratory abnormality that could increase the risk associated with trial participation or trial drug administration or could interfere with the interpretation of trial results and, in the judgment of the investigator, would make the patient inappropriate for entry into the trial. * Participants with known addiction to any drugs