HUD runs the Section 8 housing choice voucher program, which cities rely on to help house the poor. And it enforces the Fair Housing Act, part of the Civil Rights Act of 1968, which makes housing discrimination illegal.

Even in a time of economic expansion, dealing with poverty will be the biggest challenge the next HUD secretary faces, conservative and liberal housing experts agree. The American Enterprise Institute, a conservative research organization, cited housing assistance programs as among those “ripe for reform’’ under Mr. Trump. Since 2000, the number of high-poverty neighborhoods in America has doubled, rising faster in the suburbs, like Ferguson, Mo., than in cities, said Amy Liu, the director of the Metropolitan Policy Program at the left-leaning Brookings Institution in Washington.

“There’s a lot of anxiety now, because this election was about the heartland versus the coastal elites; we’re going to need a HUD secretary who governs both,” Ms. Liu said. “When I think about what HUD is going to have to deal with next, it’s going to be the future of high-poverty neighborhoods, and how to deal with that not only in Baltimore but also Ferguson.”

Mr. Carson’s history and how it translates to HUD

Mr. Carson grew up poor in Detroit and became a celebrated neurosurgeon by the time he was in his 30s — a path that he attributes to his up-from-the-bootstraps philosophy. His admirers praise his rags-to-riches success story. But his critics say a career in medicine is not the right training for someone running a vast federal housing bureaucracy.

“He has a powerful personal story that could connect him to a lot of families that rely on HUD assistance,” Ms. Liu said. “He just needs to use that personal story to listen and empathize — and really learn about the latest innovations in the field.’’