Every summer, SLMath organizes several summer graduate schools (usually two weeks each), some of which are held at SLMath and others at partner institutions around the world. Attending one of these schools can be a very motivating and exciting experience for a student; participants have often said that it was the first experience where they felt like real mathematicians, interacting with other students and mathematicians in their field.
See more information on the SLMath summer graduate schools site.