About 800 students from across the country will gather at Lexington High School next weekend for an annual debate tournament known officially as the Lexington Winter Invitational. Janet McMahan, a cochairwoman of this year’s edition of the Big Lex, said students from 85 high schools in 18 states will participate in the competition, which starts Friday and wraps up on the Rev. Martin Luther King Jr. holiday next Monday. Topics will include transportation infrastructure policy, how terrorists are tried in the United States, income disparity, and the US Constitution’s Second Amendment. The gathering also serves as a quarterfinals qualifier for the annual Tournament of Champions held in Lexington, Ky. Students in the Lexington High debate program will be volunteering to help run the event instead of competing. Last year, local families hosted about 300 debate participants at their homes during the tournament weekend, McMahan said.