Kara Swisher broke the story at AllThingsD, citing unnamed insider sources. Though Yahoo employs around 14,000 people, she noted that thousands of employees could be laid off. The layoffs are apparently the upshot of a series of meetings Thompson held with top management at the end of March. What will Yahoo look like after the layoffs? Swisher described the goal as a drastically slimmed-down organization with a focus on media, advertising and new but unclear ‘future’ initiatives. To that end, the layoffs will mostly affect those employed in the product, research and marketing units of Yah…