Phrases such as the center, the institute, or the new museum are not capitalized. Capitalize official names of bulletins, forms, conventions, conferences, classes, etc. Dr. Johnson will teach Advanced Environmental Geology next semester. He will teach advanced geology. Capitalize when referring to the building.
Capitol building is redundant.
The committee met in the Capitol to discuss capital expenditures. The Capitol is in Austin, which is the capital city of Texas. 20th century, 21st century. Avoid using superscript letters. The Board of Regents' style is to use the term chairman in all references to board positions, even for female members.