Uber CEO Travis Kalanick (left) and Anthony Levandowski Associated Press This week could be pivotal in the case that has pitted two of Silicon Valley's largest tech companies against each other as a federal judge has warned that his decisions on two important matters to the case are "very likely" to be filed this week.

Up in the air are two major decisions: whether Waymo will win a preliminary injunction to ban Uber from using its trade secrets and halting parts of its research, and Uber's argument that the case should not be heard in open courts in the first place.

On Tuesday, Judge William Alsup warned the two companies that his orders are "impending" and are "very likely" to be filed this week.

The filings will mark the first major decisions made in the case since the dispute between the companies kicked off in February when Waymo, the self-driving-car division that spun out of Google in December, accused Uber of stealing its trade secrets and intellectual property and of infringing on patents related to its lidar systems.

#1 — Waymo's bid to halt Uber's research

Since its initial filing, Waymo had filed a preliminary injunction to try to put an emergency stop to Uber's alleged use of its trade secrets and proprietary information.

An Uber self-driving car with Lidar unit on the roof Business Insider/Corey Protin During the court hearing last week, Judge Alsup heard Waymo's claims that Uber had concocted a cover-up scheme and created a shell company to bring on Anthony Levandowski, a former Google engineer accused of downloading 14,000 files and taking them to the ride-hailing company. Uber, on the other hand, has argued that it's not hiding anything, including the Lidar unit that Waymo argues is a blatant violation of its patents.

The arguments related to the Lidar designs and misappropriation of trade secrets happened behind closed doors. But Alsup said during the hearing on Thursday that Waymo still hadn't proved a direct link between any stolen files and the products Uber was working on that would warrant a halt to Uber's self-driving-car research.

"I've already given you lots of time for discovery, and you don't seem to have a smoking gun," Alsup said on Thursday. However, the companies are still trading files and taking depositions of employees so that could change. Uber is planning to hand over the acquisition agreement for Waymo to read for the first time this week.

#2 — The decision that could plunge the case into darkness

While the companies have already openly traded barbs in court related to the preliminary injunction, Uber has also been working on trying to keep the case from ever going to a jury trial.

Uber's lawyers have argued that Google has made its arbitration agreement overly broad when it says they have to arbitrate disputes with anyone as it relates to an individual's employment. Much of Waymo's case is built on the actions taken by Levandowski, the former engineer, starting with when he allegedly downloaded 14,000 files from Google before leaving the company. (As it turns out Google, has itself actually brought a separate case in arbitration against Levandowski, for allegedly trying to poach employees.)

While any disputes between Waymo and Levandowski would have to be bound by the employment contract, Waymo did not sue Levandowski directly; rather, it sued Uber and the companies founded by Levandowski that were acquired by Uber, including Otto. The judge now has to decide whether the overly-broad arbitration agreement covers this case since Levandowski's actions are intrinsically tied to the case — a decision he'll also "likely" make this week."

Regardless of Alsup's decision on the arbitration, the claims of patent infringement would move forward since they don't involve Levandowski's actions. But having that arbitration agreement, a common clause in so many contracts, could mean that the most controversial claims in the high-stakes case could be resolved in secret.