Buparlisib (BKM120) In Patients With Recurrent/Refractory Primary Central Nervous System Lymphoma (PCNSL) and Recurrent/Refractory Secondary Central Nervous System Lymphoma (SCNSL)

Inclusion Criteria: * Participants must be able to understand and be willing to sign a written informed consent document. * Subjects must be at least 18 years of age on the day of consenting to the study. * Histologically documented PCNSL or SCNSL. Patients with SCNSL need to have cytology or tissue biopsy documenting lymphomatous involvement of the CNS * Patients must have relapsed/refractory PCNSL or relapsed/refractory SCNSL * All patients need to have received at least one prior CNS directed therapy. There is no restriction on the number of recurrences. * Patients with parenchymal lesions must have unequivocal evidence of disease progression on imaging (MRI of the brain or head CT) 21 days prior to study registration. For patients with leptomeningeal disease only, CSF cytology must document lymphoma cells and/or imaging findings consistent with CSF disease 21 days prior to study registration. * Participants must have a Karnofsky performance status (KPS) of ≥ 50. * Participants must have adequate bone marrow and organ function shown by: Absolute neutrophil count (ANC) ≥ 1.5x 109/L * Platelets ≥ 100 x 109/L and no platelet transfusion within the past 14 days prior to study registration * Hemoglobin (Hgb) ≥ 9 g/dL and no red blood cell (RBC) transfusion within the past 14 days prior to study registration * International Normalized Ratio (INR) ≤ 1.5 * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 1.5 times the ULN. * Serum bilirubin ≤ upper limit of normal; or total bilirubin ≤ 2.0x the ULN with direct bilirubin within the normal range in patients with well documented Gilbert Syndrome. * Participants must be able to take oral medication. * Patients must be able to tolerate MRI scans. * Patients must be able to tolerate lumbar puncture and/or Ommaya taps. * Participants must have recovered to grade 1 toxicity from prior therapy. * Participates must be able to submit 20 unstained slides from the initial tissue diagnosis for confirmation of diagnosis and correlative studies * Life expectancy of \> 3 months (in the opinion of the investigator) Note: Prior autologous stem cell transplant as well as radiation to the CNS is NOT an exclusion criterion. Prior allogenic stem cell transplant IS an exclusion criterion. Exclusion Criteria: * Patients with SCNSL actively receiving treatment for extra-CNS disease are excluded. Patient should have complete resolution of their systemic disease not requiring additional systemic therapy (e.g. maintenance rituximab or decadron). * The patient has received prior treatment with a PI3K inhibitor, AKT inhibitor, or mTOR inhibitor (e.g. rapamycin, MK2206, perifosine, etc.). * Patient is concurrently using other approved or investigational antineoplastic agents * Patient has received chemotherapy or targeted anticancer therapy, monoclonal antibodies ≤ 4 weeks or 5 half-lives, whichever is shorter, or 6 weeks for nitrosourea or mitomycin-C prior to starting the study drug, or the patient has not recovered side the side effects of such therapy * Patient who has received wide field radiotherapy ≤ 4 weeks or limited field radiation for palliation ≤ 2 weeks prior to starting study drug or who have not recovered to grade 1 or better from related side effects of such therapy (except alopecia) * Patient requires more than 8 mg of dexamethasone daily or the equivalent * Patient is taking an enzyme inducing anti-epileptic drug (EIAED), including phenobarbital, phenytoin, fosphenytoin, primidone, carbamazepine, oxcarbazepine, eslicarbazepine, rufinamide, and felbamate. Participates must be off of any EIAED for a least two weeks prior to starting the study drug * Patient is taking a drug known to be a strong inhibitor or inducers of the isoenzyme CYP3A. Participants must be off a strong CYP3A inhibitors and inducers for at least two weeks prior to starting the study drug. * Patient is taking a drug with known risk to promote QT prolongation and Torsade de Pointes Patient is currently using herbal preparations or medications. Participants should stop using herbal medications 7 days prior to the first dose of the study drug. * Patient is using warfarin or any other Coumadin-derivative anticoagulant. Patients must be off Coumadin-derivative anticoagulants for at least seven days prior to starting the study drug. Low molecular weight heparin is allowed * Patient has a history of allergic reactions to compounds of similar chemical or biological composition to buparlisib * Patient has an uncontrolled intercurrent illness, including, but not limited to, ongoing or active infection, chronic liver disease, chronic renal disease, pancreatitis, chronic pulmonary disease, or psychiatric illness or social situations that would limit compliance with the study requirements * Patient has acute viral hepatitis or a history of chronic or active HBV or HCV infection * Patient has an active concurrent malignancy requiring active therapy. * Patient is known to have human immunodeficiency virus (HIV) infection * Patient has any severe psychiatric disease that would interfere with participation in the trial as determined by the study investigator * Patient has ≥ CTCAE grade 3 anxiety * Patient has ≥ CTCAE grade 2 diarrhea Patient has a score ≥12 on the PHQ-9 questionnaire * Patient selects a response of "1, 2 or 3" to question number 9 on the PHQ-9-questionaire regarding potential for suicidal thoughts or ideation (independent of the total score of the PHQ-9). * Patient has a GAD-7 mood scale score ≥15. * Patient has a medically documented history of or active major depressive episode, bipolar disorder (I or II), obsessive-compulsive disorder, schizophrenia, a history of suicidal attempt or ideation, or homicidal ideation (e.g. risk of doing harm to self or others). * Patient has active cardiac disease or cardiac dysfunction including any of the following: * Left ventricular ejection fraction (LVEF) ,50% as determined by Multiple Gated Acquisition (MUGA) scan or echocardiogram (ECHO) * QTc\>480msec on screening ECG (using the QTcF formula) * Angina pectoris that requires the use of anti-anginal medications * Ventricular arrhythmias except for benign premature ventricular contractions * Supraventricular and nodal arrhythmias requiring a pacemaker or not controlled with medication * Conduction abnormality requiring a pacemaker * Valvular disease with documented compromise in cardiac function * Symptomatic pericarditis * Myocardial infarction within the last 6 months, documented by persistent elevated cardiac enzymes or persistent regional wall motion abnormalities on assessment of left ventricular ejection fraction function * History of documented congestive heart failure (New York Heart Association functional classification III-IV) * Documented cardiomyopathy * Congenital long QT syndrome * Patient is currently receiving treatment with QT prolonging medication known to have a risk to induce Torsades de Pointes, and the treatment cannot be discontinued or switched to a different medication prior to starting study drug. * Patient has impaired gastrointestinal function or gastrointestinal disease affecting absorption of buparlisib (e.g. ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or extensive small bowel resection). * Patient has poorly controlled diabetes mellitus with a glycosylated hemoglobin \>8% or poorly controlled steroid-induced diabetes mellitus with a glycosylated hemoglobin of \>8%. * Patient underwent major systemic surgery ≤ 2 weeks prior to starting the trial treatment or who has not recovered from the side effects of such surgery. * Women who are pregnant or nursing (lactating), where pregnancy is defined as a state of a female after conception until the termination of gestation, confirmed by a positive serum hCG laboratory test of \> 5 mIU/mL. * Patients who have received allogenic stem cell transplants.