Billy Corgan prompts mixed feelings among music listeners. A quizzical figure in front of interviewing journalists and his die-hard fans, the ruling artistic mind and talent behind the Smashing Pumpkins has spent nearly his entire life in some sort of conflict, whether it's with himself, those closest to him, or his own creativity. The group's “Siamese Dream” and “Mellon Collie and the Infinite Sadness” remain two of the best rock albums of the '90s, mixing sprawling guitar distortion and aggressive, brokenhearted vulnerability. Corgan's continued ambition is so often his best friend and worst enemy. The Smashing Pumpkins perform at the National on Tuesday, July 13, at 8 p.m. $45.