This isn't a tournament report per se; rather, it's just that so many events are going on or just finished that it seemed reasonable to give everyone the big picture. So here goes, starting with two big rapid events that are still underway.
1. Carlsen - Predojevic. This is a four-game rapid match between world #1 Magnus Carlsen and his friend and somewhat older rival from their junior days, Borki Predojevic. Friday's two games were both drawn, and the next two days will be Saturday.
2. Geneva Masters. This rapid event is far more interesting, as there are more players, and they are more closely matched. This is a two-stage event, with two four-player sections, each section running a double round-robin. The scoring system is interesting, with players either winning or losing matches with nothing in between. If the rapid games finished in a 1-1 tie, the players would continue with a pair of blitz games, and if that finished 1-1 as well an Armageddon blitz game would settle things once and for all.
In group A, Shakhriyar Mamedyarov won all three of his matches, dispatching Vladimir Kramnik and Yannick Pelletier 1.5-.5 and then Judit Polgar by drawing the Armageddon game with Black. Kramnik beat Polgar 1.5-.5 and edged Pelletier 2.5-1.5, thereby qualifying for the second stage. As for Pelletier-Polgar, the former upset the latter 2-0.
In group B, Hikaru Nakamura also won all three matches, and in dominant style. Romain Edouard drew the regular games with Nakamura, but after that Nakamura won everything: both blitz games against Edouard, and then the four rapid games with Alexandra Kosteniuk and Etienne Bacrot. Bacrot won the other two matches, and after his feisty start Edouard even lost to Kosteniuk 2-0 in the final match.
From here on out it's time for knockout matches, with the winner of one section taking on the runner-up of the other. Thus the pairings are Nakamura-Kramnik and Mamedyarov-Bacrot.
3. Russian Championship Semi-Final. (Officially but misleadingly referred to as the Russian Championship Higher League.) This is a qualifier for the actual championship (the "Super-Final") in October. Winning the tournament would be nice, but what really counts is qualification, which is available to several players. (I'm not sure exactly how many, so readers are strongly invited to fill in this knowledge gap!) With one round to go, Ernesto Inarkiev and Anton Shomoev lead with 6/8, half a point clear of Aleksey Goganov, Alexander Motylev and Ian Nepomniachtchi; eight players are a further half point behind.
4. Ukranian Championship. After winning his first three games coming out of the gate, Ruslan Ponomariov proceeded to draw his next seven. That allowed Yuriy Kryvoruchko to catch him with a win in round 10, and they both won in the final round to tie for first with 7.5 points. Unfortunately for Ponomariov, it was too late, and Kryvoruchko took the title on tiebreak.
5. Women's Grand Prix. The latest FIDE women's grand prix tournament took place in Dilijan, Armenia, and Humpy Koneru won with an undefeated 8/11, a point ahead of Anna Muzychuk and Nana Dzagnidze and a full two and a half points ahead of reigning women's champion Anna Ushenina. Humpy has been knocking at the door of the women's title for several years now, generally thwarted in her ambitions by ex-champ Hou Yifan. Will this be the cycle when she finally breaks through?
6. U.S. Junior Championship. We last mentioned the tournament on the eve of the final round, and an exciting finale it was, too. Pre-tournament favorite Daniel Naroditsky and the young upstart Luke Harmon-Vellotti shared the lead with 5.5/8, half a point ahead of the really young Samuel Sevian. Sevian did his part and won handily, but Naroditsky pulled out a tough win as well. Harmon-Vellotti was involved in a really crazy game with Jeffrey Xiong, and fortunately for Naroditsky Xiong pulled a draw out of the fire. It was an exciting tournament, and as I can't recall a stronger field top to bottom, especially when ages are taken into account, I think the future of U.S. chess is looking good - as long as these players stick with the game! (And don't move abroad, e.g. to Italy....)