Ideas for a deep learning project?

Hi! I am currently taking a graduate level class in Machine learning at my University. I have a strong background in mathematical optimization(linear, non linear, integer, stochastic) and have in the past worked on projects using SVMs, decision trees, Naive bayes(and its variants). So, I was thinking about doing an implementation based project on deep learning wherein I am able to use some of my optimization knowledge. Could you guys give me some ideas and/or point me to some good resources and data sets? Thanks.