I have a spring-boot application that needs to:
I\
mvn spring-boot:run
includes provided
dependencies when it's creating the classpath. It sounds like IntelliJ IDEA does not. Without Tomcat on the classpath, Spring Boot's unable to create an embedded servlet container which causes the exception you're seeing. Arguably this is a bug in IntelliJ as, if there's no container to provide the dependency, then it really needs to be on the classpath.
You may be able to fix the problem by overriding the default classpath that IntelliJ uses when running the main method to include the spring-boot-starter-tomcat
dependency.