Carl Icahn might be down, but he’s not out. The legendary activist investor, 87—who has seen the stock of his investment company,
Icahn Enterprises
plunge after an attack by short-seller Hindenburg Research and a possible federal probe—squares off on Thursday in a proxy fight at
Illumina
the dominant developer of gene-sequencing technology. Illumina has been mired in a messy attempt to buy its former unit, cancer screener Grail.