It's been 201 days of Republican inaction since President Obama nominated Merrick Garland to the Supreme Court, which means that when oral arguments begin for the fall term on Tuesday, they will still be heard by eight justices instead of nine.

Despite the risk of a polarizing case ending in a tie vote, as did the June ruling blocking Obama's plan to allow millions of undocumented immigrants to work, the court has agreed to take on 39 cases so far this term. The docket features important issues, including freedom of religion and speech, insider trading, the death penalty, and racial discrimination.

Here are eight of the key cases to look out for this term, which runs through June of next year.

Separation of church and state is up for interpretation in Trinity Lutheran Church of Columbia v. Pauley. The Missouri Department of Natural Resources denied the church's application in 2012 for a scrap-tire grant program to refurbish its playground, citing the state's constitution, which says, "No money shall ever be taken from the public treasury, directly or indirectly, in aid of any church, sect, or denomination of religion." Alliance Defending Freedom, the conservative group that brought the case, argues that while the Missouri constitution bans public funding for things like devotional training, it does not ban funding for secular activities, such as playgrounds, that are associated with churches. The alliance says the church's rights to equal protection under the law and freedom of religion were violated, going so far as to call the state's action "religious hostility."

The Supreme Court has previously allowed state funding for religious-affiliated organizations such as universities, but not directly for churches.

First Amendment cases are typically polarizing, and the justices have not yet scheduled oral argument for this case. American University law professor and SCOTUSblog contributor Stephen Wermiel wonders whether the justices have avoided slating oral argument because they are split. "That seems likely to be closely divided," he said of the case. "All the briefing is done and ready to go."

A 4-4 tie ruling would affirm the lower court's decision that Missouri is allowed to exclude the church from the program.

The corporate securities industry will be watching Salman v. U.S. very closely as the court is expected to clarify what kind of proof prosecutors need to convict someone of insider trading.

Bassam Salman's lawyers argue that only family love was exchanged when Maher Kara, who worked as a healthcare investment banker at Citigroup in California, passed merger and acquisition information to his brother, who passed it to his brother-in-law, Salman, who made nearly $1 million by trading with the information.

Salman was convicted of conspiracy to commit securities fraud and sentenced to three years in prison in 2014. In a separate case, the Kara brothers pleaded guilty to the same crime and were sentenced to three years of probation.

Salman's lawyers argue that since Kara never sought any monetary benefit from Salman in return for the insider information, this should not count as insider trading.

In 2013, the 2nd Circuit Court ruled in U.S. v. Newman that in order to convict someone of insider trading, prosecutors must prove that the insider benefited in an objective, consequential and valuable way. The 9th Circuit disagreed, counting Salman and Kara's family relationship as a benefit.

Mark Cuban, the billionaire businessman and investor who successfully defended himself against the Securities and Exchange Commission in a 2008 insider trading case, and the libertarian Cato Institute were among those who submitted briefs to the court in support of Salman. They argue that the lower court's view of Salman's actions is too far-reaching, and that decisions about insider trading parameters should be set by Congress, not the court.

But Wayne State University law professor Peter Henning said that insider trading rules have been almost entirely defined by the court: "We have few crimes that are completely derived from judicial opinions, but this is one of them."

Oral argument is scheduled for Oct. 5, and a 4-4 tie would affirm the 9th Circuit Court's ruling that information sharing between relatives is proof of insider trading.

For Jennings v. Rodriguez, the court will decide whether it is legal to lock up immigrants long-term without giving them bail hearings. The ACLU of Southern California sued U.S. Immigration and Customs Enforcement in 2007 on behalf of about 1,000 people, some asylum seekers and some legal immigrants who allegedly committed crimes punishable by deportation, arguing that they had the right to bail hearings. A California court agreed, as did the 9th Circuit Court in 2015, but the U.S. government appealed again.

The Justice Department recently admitted to providing the Supreme Court with incorrect data about the average time immigrants spend in detention in a similar 2003 case; the DOJ said average detention time was four months, when in reality it was more than a year. The Supreme Court ruled in the DOJ's favor then, and this term, the DOJ will argue against bail for immigrants once again.

Alejandro Jennings, the lead plaintiff in the ACLU case, was a legal resident who was convicted of joyriding when he was 19 and drug possession when he was 24. He spent three years in detention awaiting a decision about his deportation. According to the ACLU, the average detention time today is 404 days,still more than a year. There are 33,854 people in ICE detention facilities on any given day.

Oral argument for this case is not scheduled yet, and a 4-4 tie would affirm the lower court's ruling in favor of the ACLU.

The constitutionality of the death penalty itself is not on the table, but two related questions are: whether racially biased testimony constitutes inadequate defense and merits an appeal, and to what degree lower courts can decide how to determine mental capacity. Both cases come out of Texas, the state with the most executions.

The first case is Buck v. Stephens. Duane Buck, a black man, was convicted of murdering his ex-girlfriend and her friend in 1995. During his sentencing hearing, the prosecutor asked the defense's expert witness, Walter Quijano, whether black people are more dangerous to society. Quijano replied, "Yes."

This testimony is particularly important in Texas, where in order to secure the death penalty a prosecutor must prove to a jury that the defendant is a danger to society, explained Jim Marcus, a clinical professor at the University of Texas Capital Punishment Clinic.

In the early 2000s, Texas Attorney General John Cornyn declared he would allow six cases, including Buck's, to be resentenced because of Quijano's testimony, saying the state had erred in allowing racist testimony to be used at death penalty trials. But by the time Buck's case made it to the federal court system, Cornyn was no longer in office, and the new attorney general, Greg Abbott, opposed granting Buck a hearing. Buck's is the only case of the six that has not been allowed an appeal.

"The bottom line is that Mr. Buck has never had his day in court on this issue," Marcus said. "[The habeas corpus process is] chock-full of procedural technicalities and traps. People lose on technicalities all the time."

The justices will decide whether Quijano's racial bias means Buck's trial lawyers were ineffective — remember, he was called as a witness for the defense — and whether the 5th Circuit should allow Buck an appeal. Texas argues that it denied Buck an appeal because he failed to prove that the outcome of this trial would have been different if it weren't for Quijano's testimony.

Wermiel, the American University professor, said it's hard to know exactly what the impact of the ruling will be. "The facts matter a lot and the facts are egregious, but the Supreme Court is not writing an op-ed piece condemning racism in the death penalty. It's deciding a fairly technical issue," he said.

Oral argument is scheduled for Oct. 5. A 4-4 tie would affirm the Texas court ruling that Buck is not entitled to an appeal.

The second case is Moore v. Texas. Bobby Moore has been on death row for 36 years for murdering a 70-year-old store clerk during a robbery. In 2014, a Texas trial court said Moore was mentally disabled and could not be executed, but an appeals court reversed the decision, saying the court was allowed to rely on a medical standard from 1992 to determine a person's mental status until the Texas Legislature decides otherwise.

The Supreme Court decided that people with mental disabilities could not be executed back in 2002 in a case called Atkins v. Virginia, but it left that medical determination up to the states.

In 2014, in Hall v. Florida, the court ruled that states must rely on modern diagnostic standards and not just IQ scores. In Moore's case, the court will further define and clarify the way states can determine mental incapacity.

Moore's lawyers wanted the court to also look at whether spending 36 years on death row, 15 of those in solitary confinement, is cruel and unusual punishment, but the court decided to hear only the first issue. Oral argument has not been scheduled yet, and a 4-4 tie ruling would affirm the Texas court's decision that Moore can be executed.

involves an Asian-American rock band's battle to get its name trademarked, but the case is perhaps best known for its possible implications for the Washington Redskins' logo.

How the court rules on the band's case will have an impact on the pro football team's fight to get its trademark back after a finding last year that the brand was disparaging to Native Americans. That case is pending before a lower court. In an unconventional move, the team asked the Supreme Court to also rule on its case because of its similarities to Lee v. Tam, but so far the court has decided to hear only Lee v. Tam.

In 2011, Simon Tam, the lead singer of a band called The Slants, tried to trademark the band's name. The U.S. Patent and Trademark Office denied Tam's request, saying it was derogatory to Asians and therefore violated the Lanham Act, which doesn't allow trademarks that "may disparage ... persons, living or dead."

An appeals court disagreed, siding with Tam, and ruling that the Lanham Act violates free speech guaranteed by the First Amendment. "Even when speech 'inflict[s] great pain,' our Constitution protects it 'to ensure that we do not stifle public debate,'" the majority opinion reads.

The U.S. government argues that The Slants can still use their band name without a registered trademark and that the Lanham Act is an important law that protects states from having to approve disparaging terms.

Tam argues that by registering the band's name, he is re-appropriating a once-offensive term. "We should not be afraid of using the expression of who we are to catalyze change," Tam wrote last year in Oregon Humanities magazine. "I named the band The Slants because it represented our perspective — or slant — on life as people of color."

A 4-4 decision would affirm the appeals court's ruling that denying The Slants' trademark by way of the Lanham Act violates the First Amendment.

Last year, the court got into the nitty-gritty of redistricting when it decided by a 5-4 vote that Alabama's new district map was a racial gerrymander. This term, two similar cases are on the docket: one in North Carolina and one in Virginia.

Both cases could be polarizing, as the Alabama case was, and they address an issue the court has grappled with for decades: To what degree should states use race as a factor when redistricting?

Richard Pildes, a law professor at NYU, successfully argued on behalf of the Alabama Democratic Conference and won last year's case. Pildes said that the redistricting cases before the court now will further define the line states have to walk between considering race to guarantee minorities an equal vote (a requirement of the Voting Rights Act) and using race excessively to weaken the minority vote (a violation of the Constitution).

While state legislators are allowed to redraw district lines for political gain, they are not allowed to use race in a way that goes beyond what the Voting Rights Act requires.

"The Court has been reluctant to police the redistricting process for partisan reasons, but they have been very active in policing the process for racial reasons," Pildes said.

In February, a three-judge panel in North Carolina ruled 2-1 that the Legislature unconstitutionally packed African-American voters into two congressional districts, calling this a "textbook" case of racial gerrymandering. The Supreme Court will decide whether to uphold that ruling, based on the previous Alabama decision. A 4-4 tie would affirm the lower court's ruling.

In Virginia, the Legislature's map included 12 state districts that were majority-minority. A three-judge panel split in favor of the Legislature, saying that the maps were constitutionally drawn. The Supreme Court will decide to what degree Virginia used race when redistricting. A 4-4 tie would affirm the lower court's ruling that the map did not constitute racial gerrymandering.