Career
He competed in the FIDE World Chess Championship 2004, held in Tripoli, Libya, where he was knocked out in the first round by Utut Adianto. By winning the 2007 Aeroflot Open in Moscow, Alekseev qualified for the 2007 Dortmund Sparkassen Chess Meeting, where he shared second place – behind World Champion Vladimir Kramnik – with Viswanathan Anand and Péter Lékó. In 2010 he played board 2 for Russia"s second team at the 40th Chess Olympiad, held in Khanty-Mansiysk, Russia.
His team finished sixth.