Pianist Jeremy Denk is having an exceptionally busy 2011.

After playing an intense schedule in January and February, he accepted two major—and unscheduled—engagements in March when other artists fell ill.

From March 17 to 20, Mr. Denk joined the Los Angeles Philharmonic as a replacement for Martha Argerich ; he had one week and two rehearsals to prepare for his debut with the orchestra. And on Sunday, Mr. Denk makes his solo recital debut at Carnegie Hall's Stern Auditorium—replacing Maurizio Pollini.

"I thought I was going to be on vacation," the 40-year-old said.

Jeremy Denk makes his solo recital debut at Carnegie Hall Sunday. Samantha West

Instead, he'll be onstage playing Charles Ives's "Concord" sonata and Bach's "Goldberg Variations."

"I've been practicing a lot and chilling out," he said. "I just got through the thing last week. I've been trying to see if I can make this work. Then I've been wondering where I could check myself into."

Carnegie Hall's director of artistic planning, Jeremy Geffen, turned to Mr. Denk as a replacement because the pianist was already at the top of the list as someone to showcase; Mr. Denk hit a high mark in his February recital at Zankel Hall, the 599-seat venue within Carnegie Hall. (Stern Auditorium has 2,804 seats.)

"The follow-up to a success like that can often wait several seasons because we schedule so far in advance," Mr. Geffen said. "This was a great opportunity for an artist that we feel very strongly about—and we could use the momentum of his more recent success."

At Zankel in February, Mr. Denk played Ligeti's "Etudes" and the Goldberg Variations. At a previous concert there in 2008, he played Ives's "Concord" and Beethoven's "Hammerklavier."

The upcoming concert on the main stage takes pieces—the Ives and Bach—from the previous appearances. "There is not much time, so it has to be music that I'm already playing. I'm playing the Ives sonata in Houston on Tuesday," he said.

Why is Sunday's concert considered a debut when he has already played at Carnegie Hall? Even the Denk family has asked this question. "My parents joke, 'How many different Carnegie Hall debuts can you have?'" said the pianist.

In classical music, debuts are sliced and diced every which way. A conductor, for example, can have a North American operatic conducting debut—and still be up for a North American orchestral conducting debut.

At Zankel in February, Mr. Denk's concert had a waiting list, which was a good sign to a house in need of filling almost 3,000 seats with less than a week's notice.

"There aren't many people who have the 'Goldberg Variations' ready to go at the drop of a hat," said Mr. Geffen, adding that it is also somewhat rare for an artist to play a second work on a program with the Bach.

Mr. Denk finds that Ives and Bach work well when presented together. "Both are looking for transcendence," he said. "Ives is much more eclectic and schizophrenic. Bach goes for it in a more serene and unruffled way. There is more inward and subtle storytelling."

Mr. Denk, who lives on the Upper West Side, is also something of a stereotype-breaker. Because of preconceptions of classical music, artists can seem set off from popular culture. But this pianist embraced media with his blog Think Denk as far back as 2005.

Although his success is obviously a result of his musical credibility, the blogging has been an asset.

"One thing that the blogging did emphasize was that—in addition to being a pianist of the highest order—he has become a great spokesperson of the art form," said Mr. Geffen. "He is not only witty and insightful, but he approaches people on a level they can identify with."

And though the pianist is a less frequent blogger these days, he could be a model for other artists.

"The blog was a very important part of people's introduction to him," said Mr. Geffen. "With more engagements and success comes less time to express yourself in words."