Brown University will provide me with the supplies I need for my future, but will allow me to design it my way.
I kind of agree with Grace. You need to be a little more specific. What kind of supplies/resources does Brown uniquely offer that will help you pursue your goals?
Having my service projects be a big influence on my life, the Swearer Center is an ideal place to work with others and take action.
Small grammar error. "Having my ... life" is describing you, not the Center, so it should instead say
"Having ... life, I can work with others and take action in the ideal environment of the Swearer Center."
Also, you should mention what about the Center makes it ideal.
Hope that helped.