Fallon hangs with ‘Jeopardy!’ hero

EVEN Jimmy Fallon wants to party with viral “Jeopardy!” contestant Austin Rogers. Rogers — an NYC bartender who’s accumulated more than $300,000 during a nine-day winning streak on the show — was spotted drinking at the Gaf West on West 48th Street, where he works, when the “Tonight Show” host joined him for a round. We’re told Fallon’s been to the Midtown bar a few times and knew Rogers before he became an overnight game-show sensation. A spy tells us that Rogers was chatting with a group of women about the secrets to his “Jeopardy!” success and how he has to “ride out the fame while he has it.” Rogers, who taped his episodes earlier this year, and Fallon left together to hit another bar, reports The Post’s Lindsey Kupfer. Last week, Fallon wished Rogers luck on the show, tweeting, “Austin, give my best to Trebek. Proud of you! #OG #OriginalGaf ’r” During a “Good Morning America” segment on Thursday, Rogers explained, “I’m not going to say there’s a system or a code, but if you watch enough, you’ll start seeing things repeat . . . If it ever says ‘Romanian poet,’ it’ll be [Eugène] Ionesco. I have no idea who Ionesco is, but I’ve seen that come up three times in episodes across the decades.”