Ganetespib in Combination With Paclitaxel, Carboplatin, and Radiation Therapy in Treating Patients With Stage II-III Esophageal Cancer

Inclusion Criteria: * Histologically documented adenocarcinoma or squamous cell carcinoma of the cervical esophagus, thoracic esophagus, or gastroesophageal junction * Stage II or III esophageal carcinoma according to the American Joint Committee on Cancer (AJCC) 7th edition staging * Esophagogastroduodenoscopy (EGD) with endoscopic ultrasound (EUS) +/- biopsy at M.D. Anderson are required to confirm staging * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Patients should have no contraindications for chemotherapy or radiation, and should receive either definitive chemoradiation therapy or preoperative chemoradiation therapy * Patients must have received baseline FDG-PET/CT +/- CT with contrast within 1 month +/- 2 weeks prior to study entry, and should have no contraindications to PET or CT imaging * Women of child-bearing potential and men must agree to adequate contraception (hormonal or barrier method of birth control; abstinence) during and up to 30 days after discontinuing treatment * Women of child-bearing potential must have a negative serum pregnancy test within 14 days of study entry; 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 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * White blood cells (WBC) \>= 2500 cells/ul * Hemoglobin \>= 9 g/dL * Platelets \>= 100x10\^9/L * Albumin \>= 2.5 g/dL * Serum bilirubin =\< 1.5x institutional upper limit of normal (ULN) * Total bilirubin =\< 1.5 x institutional ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x institutional ULN * Serum creatinine =\< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault formula) \>= 50 mL/min OR 24-hour urine creatinine clearance \>= 50 mL/min * Prothrombin time (PT)/international normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.5 x institutional ULN * Baseline screening corrected QT (QTc) \< 470 ms is eligible Exclusion Criteria: * Prior radiation to the chest or abdomen * Previous or concomitant malignancy - EXCEPTIONS: patients with curatively treated carcinoma in situ of the cervix, basal cell of the skin, transitional cell carcinoma of the bladder, or early stage cancers at non-overlapping sites with no evidence of disease for \>= 3 years * No induction chemotherapy * Pregnant or breast-feeding females; patients who become pregnant during active therapy will be immediately removed from the study * Uncontrolled intercurrent illness or serious medical conditions including, but not limited to: * Clinically significant, uncontrolled, major cardiac, respiratory, renal, hepatic, gastrointestinal, or hematologic disease * Active uncontrolled infection * Symptomatic congestive heart failure, unstable angina, or cardiac dysrhythmia not controlled by pacer device * No myocardial infarction within 3 months of registration * Symptomatic inflammatory bowel disease with uncontrolled diarrhea * Major cardiac-related diseases, medications, or laboratory abnormalities including the following: a) clinically unstable cardiac disease, including unstable atrial fibrillation, symptomatic bradycardia, unstable congestive heart failure, active myocardial ischemia, or indwelling temporary pacemaker, b) ventricular tachycardia or a supraventricular tachycardia that requires treatment with a class Ia antiarrhythmic drug (eg, quinidine, procainamide, disopyramide) or class III antiarrhythmic drug (eg, sotalol, amiodarone, dofetilide); use of other antiarrhythmic drugs is permitted; c) use of medications that have been linked to the occurrence of torsades de pointes, d) second- or third-degree atrioventricular (AV) block unless treated with a permanent pacemaker, e) complete left bundle branch block (LBBB), f) history of long QT Syndrome or a family member with this condition, g) if baseline QTc \> 470 ms, average of triplicate electrocardiogram (ECG) recordings is necessary; if average value of QTc is \> 470 ms, patient is ineligible for the study; h) serum potassium, magnesium, and calcium levels outside the laboratory's reference range * Known immediate or delayed hypersensitivity reaction to carboplatin, paclitaxel, polysorbate 80, or any other component of the formulation * Any major surgery, extensive radiotherapy, chemotherapy with delayed toxicity, biologic therapy, or immunotherapy within 21 days prior to study registration, and/or daily or weekly chemotherapy without the potential for delayed toxicity within 14 days prior to registration * Use of other investigational drugs within 28 days (or five half-lives, whichever is shorter; with a minimum of 14 days from the last dose) either preceding the first dose of ganetespib or during the study period * Current use of a prohibited medication; the following medications or non-drug therapies are prohibited: a) other anti-cancer therapy while on study treatment, b) the concurrent use of all herbal supplements is prohibited during the study (including, but not limited to, St. John's wort, kava, ephedra \[ma huang\], gingko biloba, dehydroepiandrosterone \[DHEA\], yohimbe, saw palmetto, or ginseng) * Known human immunodeficiency virus (HIV), active hepatitis B virus (HBV), or active hepatitis C virus (HCV) infection (with the exception of chronic or cleared HBC and HCV infection, which will be allowed)