The fellows of the Yale Corporation arrived on campus Thursday and will stay until Saturday, using their time in New Haven to deliberate on the University’s financial health and on designs for the new residential colleges.

The agenda of the Corporation, which is the University’s highest governing body, is kept secret. But University President Richard Levin said in a telephone interview that the fellows will continue to examine financial projects and budget scenarios, as the group has during its other meetings this year.

The Corporation’s discussions about Yale’s finances are expected to yield another update to the community about the University’s financial well-being during the economic recession. Harvard President Drew Faust issued two such letters earlier this week, and Levin said he may follow suit with a letter of his own in the next few weeks.

The Corporation will discuss important questions such as how much to raise tuition in Yale College for next year and how many cuts should be proposed in this year’s annual budget guidelines. The answers to those questions would likely work their way into any letter from Levin.

School of Architecture Dean Robert A.M. Stern ARC ’65 will present renderings of the two new residential colleges to the Corporation. The colleges are to be built on Prospect Street, north of the Grove Street Cemetery, and their price tag could be as high as $600 million. Construction was planned to begin in 2011 and finish in 2013, though the project will now see delays because of the economy, administrators have said.

“We are going to review the designs for the colleges,” Levin said. “They are fabulous designs. Dean Stern has done a tremendous amount of work at this point, and any decision on speeding the project up or slowing it down will really be completely independent of the design. The financial issues and the design issues are completely separate.”

Corporation Senior Fellow Roland Betts ’68 said in a telephone interview that the group will meet in three plenary sessions — where all 16 fellows are present at once — which is more than usual. In addition, regular committees will hold meetings throughout the weekend.

Amid their busy weekend, the Corporation fellows will also find time to meet with representatives of the Yale College Council. YCC President Rich Tao ’10 said his group plans to discuss the addition of academic minors for undergraduates and a proposal for bike-sharing throughout the University with the Corporation.

After its meetings Saturday, the Corporation will adjourn and not meet again until April. Its final meeting of the year will be held after Commencement.