the $1.049 billion jury verdict tossed out based on the jury foreman's undisclosed legal skirmish with Seagate nearly 20 years ago.
The foreman had worked for Seagate, a technology company in which Samsung owns a small stake, and wound up declaring bankruptcy after a court battle with his former employer.
Samsung hopes to convince Koh that the juror's experience influenced the August verdict, in what amounted to misconduct strong enough to have the outcome overturned.
Samsung also called for Apple lawyers to reveal whether they knew that aspect of the juror's past -- and opted not to share it in court.
In a filing late last week, Apple attorney Mark Selwyn said that the legal team had not been aware of the juror's history with Seagate and argued that deliberations were not tainted by misconduct.
The "lawsuit with Seagate nearly two decades ago is irrelevant to any issue raised by Samsung's post-trial motions," Selwyn contended in the filing.
Koh will hear from both sides in her San Jose, California courtroom, but legal experts caution that the hurdle for overturning a verdict based on jury deliberations is dauntingly high.
The hearing agenda also includes a motion by Apple for an injunction banning US sales of Samsung smartphone models said to contain patented technology at issue in the trial.
Apple asked Koh to ban eight Samsung mobile phones in the US market in the days after its August victory in the patent suit against the South Korean electronics giant.
The request includes phones being sold by AT&T, Verizon and T-Mobile to US customers that were found to have infringed on Apple's patents from its iconic iPhone.
Apple asked the court to ban some of the newer 4G phones from Samsung's Galaxy line as well as the Droid Charge sold through Verizon.
The phones include the Galaxy S 4G, Galaxy S2 AT&T model, Galaxy S2 Skyrocket, Galaxy S2 T-Mobile model, Galaxy S2 Epic 4G, Galaxy S Showcase, Droid Charge and Galaxy Prevail.
Along with Samsung motions to reduce or dismiss charges, Koh is expected to consider Apple's request for "punitive" damages, which could triple the award.
In August, the jury decided that Samsung should pay Apple $1.049 billion in damages for illegally copying iPhone and iPad features, in one of the biggest patent cases in decades -- a verdict that could have huge market repercussions.
Samsung has depicted the verdict as "a loss" for consumers and contended that Apple had "manipulated" the patent system.
The jury decided the case with over 700 separate claims in less than three days of deliberations.
Samsung had steadfastly denied the charges by Apple, claiming it developed its devices independently. It unsuccessfully argued that Apple infringed on its wireless patents.