Amy Lau, a New York interior designer and a founder of the annual Design Miami fair, whose vernacular was the saturated colors of the American Southwest and whose deep knowledge of modernist objects was the foundation of her work, died on Jan. 17 in Scottsdale, Ariz. She was 56.

The cause was cancer, her family said.

Ms. Lau’s success did not rest on an ability to parse paint colors and match furniture and rugs (although of course she could do both things). Rather, it was her consummate talent for choosing important pieces — for example, a sofa designed by Vladimir Kagan, a sculpture by Anish Kapoor, a bronze work by the furniture sculptor Silas Seandel — and crafting warm, striking interiors around them. Those selections were the raison d’être, not the afterthought.

“Designers all begin from some vantage point, and Amy’s was her knowledge of midcentury modern,” Amanda Nisbet, an interior designer in New York and Palm Beach, said in an interview. “But she was also a real supporter of current artists and artisans, and sought out the work of the ones she thought were worthy of her clients’ money.”

Those clients included the media executive and Seagram heir Edgar Bronfman Jr. and his wife, Clarissa; the fashion designer Elie Tahari (Ms. Lau designed his East Hampton boutique); and the real estate developer Craig Robins.

It was Mr. Robins with whom Ms. Lau teamed up in 2005, along with the designer Ambra Medda, to start Design Miami, a collectible-design fair conceived to run in tandem with the annual art fair Art Basel Miami Beach. It has become an important showcase and destination for designers and their clients.

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