By Jim Finkle and Aaron Pressman

BOSTON, May 23 (Reuters) - Facebook Chief Operating Officer Sheryl Sandberg spoke to Harvard University students in her first public appearance since the company's disappointing initial public offering, but refrained from addressing the controversy around its messy, glitch-plagued debut.

Instead, Sandberg urged students graduating this week from Harvard's business school to work for fast-growing companies, communicate honestly and address inequality in the workplace.

"We need to acknowledge openly that gender remains at issue at the highest levels," she told a crowd of students and their families assembled Wednesday afternoon on a lawn outside the business school library alongside Boston's Charles River. Only about 16 percent of the highest corporate jobs are held by women, the same level as a decade ago, she noted.

Sandberg, who visited her alma mater with her parents and two children, only once made reference to the IPO in her speech. After urging the graduates to use Facebook to stay in touch, she said: "We're public now, so could you please click on an ad or two while you're there."

Asked before and after the speech to comment on the IPO, Sandberg said she was not speaking to the media.

She told the crowd that she sometimes gets anxious: "When things are unresolved, I get a tad anxious," said the 42-year-old who became one of Harvard's wealthiest alumni after the IPO. "People have never accused me of being too calm."

She chatted and posed for photos with dozens of students after the speech. Several said they had accepted jobs with Facebook. "I'll see you over the summer," she said to one of them.

Facebook shares closed on Wednesday at $32 a share, 16 percent below the price at the IPO last week. The deal was beset by computer glitches at the Nasdaq market and lower-than-expected demand from investors.

Facebook and lead underwriter Morgan Stanley were sued by shareholders on Wednesday who claimed they hid the social networking company's weakened growth forecasts ahead of its $16 billion initial public offering.

Sandberg received an undergraduate degree from Harvard in 1991 and an MBA from the business school in 1995.

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