Car shuts off and turns on immediately?

I was driving my 2013 Corolla on the highway going 80mph and the car shut off. I assume it was trying to turn itself back on because it eventually did when I was pulling to the shoulder. I got off on an exit and at the exit it also turned off. But turned itself back on nearly immediately. Pulled into a parking lot and it shut off completely at the entrance. Tried to turn it on and it was just cranking. Tried like two more times and on the third it turned on. Drove it home for about 20 minutes and it did not shut off. Any idea as to where I can get started or things I could check for. Please and thank you. From what I have seen, it may be fuel related. No check engine light. Something that I noted that has never happened was the fuel gauge was off. When it first turned off in the highway it read below the full line which is where I believe it should be (only 60 miles after full tank). Once at the parking lot it marked 3/4. Now that I drove it home it went back to or near the original mark. Car turns on just fine. No stalling immediately. No rough idling. Drives fine. I guess it will shut off at random drive times.