He has won both his games to start the tournament and has a half point lead.

It is still early, but Pavel Eljanov is the sole leader of the Gashimov Memorial in Shamkir, Azerbaijan. Eljanov has won both his games and is the only player with a perfect score. Saturday, in Round 2, he beat Pentala Harikrishna of India.

Eljanov was not the only player with a decisive result. Veselin Topalov of Bulagiar, the former World Champion, seems to have overcome his recent slump and is playing well again. In Round 2, he beat Radoslaw Wojtaszek of Poland with some brilliant fireworks. Topalov is now tied for second with Shakhriyar Mamedyarov of the host country, who won in Round 1. Each player has 1.5 points.

All the other games in Round 2 were drawn, but Vladimir Kramnik of Russia came close to winning as he showed some very instructive technique against Teimour Radjabov, the other representative of the host country in the tournament. 

Topalov used a subtle idea in the opening to get Wojtaszek away from his preparation. Wojtaszek was still doing fine until he missed some concrete tactics:

Radoslaw Wojtaszek vs. Veselin Topalov
Gashimov Memorial | Shamkir AZE | Round 2 | 22 Apr 2017 | ECO: D12 | 0-1
1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. e3 Bf5 5. Nc3 e6 6. Nh4 Bg6 7. Nxg6 hxg6 8. Bd3 c5 This kind of plan has been seen before, but it is still unexpected to see Black move the c-pawn again. Clearly, Wojtaszek was not prepared for it.
9. Qb3 Qd7 10. cxd5 exd5 11. dxc5 Nc6 12. Bd2 Bxc5 One benefit of Black's setup is that the open h-file makes it difficult for White to castle kingside. But what else is he supposed to do?
13. Rc1
13. O-O Ng4!? Among other possible moves.
14. h3 Qd6 Is a bit dangerous for White.  )
13... Rd8 14. Na4 Bd6 15. Nc5 Bxc5 16. Rxc5 d4!? White is still okay at this point, but he needed to play very precisely and he did not manage to do that.
17. Bb5?!
17. e4! Wojtaskzek was probably afraid of:
17... Qe7 It looks as if White will lose the e-pawn, but he has the counterattack:
18. Rb5! And Black is forced to defend the pawn on b7, after which White can castle kingside and his e-pawn will be safe.
18... b6 19. O-O  )
17... O-O 18. Bxc6 bxc6 19. f3 An ugly move, but it isn't obvious if Black can exploit it.
19. O-O Ne4! Would lose material.  )
19... Qe7 20. Rc2 Nd5 21. Kf2

In a pleasant position, Topalov came up with a beautiful queen sacrifice that was reminiscent of attacking games from previous eras:

Wojtaszek, Radoslaw vs. Topalov, Veselin
Vugar Gashimov Mem 2017 | Shamkir AZE | Round 2.2 | 22 Apr 2017 | ECO: D12 | 0-1
21. Kf2 Black seems to have many pleasant ways to continue, but Topalov comes up with an ingenious and aesthetically brilliant idea:
21... Rb8 22. Qa3 Rxb2!! 23. Qxb2 The key line is:
23. Qxe7 Rxc2! 24. Qe4 Rxd2+ 25. Kg3 Nxe3 And Black's initiative is just too strong:
26. Qxc6 Rxg2+ 27. Kh3 Rd8 Black will be able to push the d-pawn and also can threaten to play Rd5, etc.
28. Re1 Rxa2 29. Rb1 d3  )
23... dxe3+ 24. Bxe3 Qxe3+ 25. Kg3? Wojtaszek either overlooked Black's 26th move, or perhaps he just wasn't able to calculate it till the end to realize how dangerous it was for him.
25. Kf1! Nf4 26. Qc1 Qe5 White's rook on h1 won't enter the game for a while, and Blacks initiative looks intimidating, but White would be able to hang on.  )
25... Qf4+ 26. Kf2 Rb8! Now White's position collapses, though Black still needs to play precisely.
27. Qc1 Qd4+ 28. Kg3 Ne3 The threat of Nf5, mate, is decisive.
29. Rc5 Rb2 30. Rg1 Rxa2 Black has just too great an initiative.
31. h3 Qd6+ 32. f4 Qd3 33. Kh2 Qe4 34. Rg5 Rc2

Eljanov’s win was very different. Harikrishna was probably better prepared in the opening, and got an early initiative after the players castled on opposite sides. But Harikrishna opted to trade queens, dissipating his initiative:

Pentala Harikrishna vs. Pavel Eljanov
Gashimov Memorial | Shamkir AZE | Round 2 | 22 Apr 2017 | ECO: E47 | 0-1
1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. e3 O-O 5. Bd3 c5 6. Nf3 b6 7. d5 exd5 8. cxd5 Nxd5!? Isn't the most common move but I think both players had probably looked at it before the game.
9. Bxh7+ Kxh7 10. Qxd5 Bxc3+ 11. bxc3 Qf6 12. Bb2 Nc6 13. O-O-O! A nice and unexpected idea! White is ready to commence operations on the kingside, while it is hard for Black to exploit the weaknesses on White's queenside.
13... Kg8 14. h4 Ba6 15. h5 Qh6 16. Nh4 Qe6 17. Qxe6? An inexplicable decision. White helps Black improve his pawn structure and ruins his initiative. He probably overlooked Eljanov's move after dxe6 and h6, but even then, it is hard to justify going into this endgame.
17. h6! Was perhaps the strongest move. It would lead to a similar continuation as in the game, but White would not have helped Black improve his pawn structure. Black might have then tried to force White to take on e6 by playing:
17... Bc4! But White would not have different possibilities, including the very strong:
18. Qg5! Qxh6 19. Qg3 The open files guarantee White a dangerous initiative on the kingside.  )
17. Qg5!? Was also a perfectly acceptable continuation. White would retain the initiative and Black doesn't yet have threats on the queenside.
17... f6 18. Qg3  )
17... dxe6 18. h6 Bc4! A nice practical move. Black had other options, but, by blocking the a1-h8 diagonal, he insures that White will not be able to retake the initiative. Chances are now about equal, but Eljanov is now dictating the pace.
18... g6 19. c4! Would have been great for White.  )
18... gxh6 19. c4 Would also have given White quite a bit of play on the kingside.  )
19. Nf3 Rad8 [...]

After that, Eljanov took over the initiative and began to press. It seemed that a draw was within reach for Harikrishna, but he made a few more inaccuracies towards the very end:

Harikrishna, Pentala vs. Eljanov, Pavel
Vugar Gashimov Mem 2017 | Shamkir AZE | Round 2.5 | 22 Apr 2017 | ECO: E47 | 0-1
Kg6 45. Bd4? If Harikrishna had calculated that he could force Black to capture on c2 wih the bishop, then he would have done it as it is much easier to block the pawn on b3. But after
45. Rc4! He was obviously afraid that Black would play:
45... Kf5 It does not appear that Rc4 has helped White, but after:
46. Bh8! bxc2 47. Rc5+! Makes a huge Difference. Black is not able to retain his extra pawn:
47... Kg4 48. Re5! Bd5 49. e4 Bc4 50. Rc5 And White should be able to draw.  )
45... bxc2 All wasn't lost even now - Black needs a few moves to move his rook on a2 to the first rank in order to support the pawn on c2. With accurate play, White could have created threats with his own rook on the kingside.
46. Rg8+
46. Rf8 Followed by Rf6+ and Rxe6 would give White counterplay. And if Black tries Bf5 to protect the pawn, White can play e4, forcing an exchange of pawns and reducing the position to a drawn endgame.
46... Kg5 Would be similar to the game. But perhaps White should have played Bf6+ now. The reason will be evident later.  )
46... Kh5 47. Rh8+ Kg4 48. Rg8+?! After this the rook is unable to pose many problems for Black.
48. Bf6! And Rh4 is a very serious threat. It is not easy to keep the bishop on e4 and if the bishop leaves that square, then White can threaten to play e4, cutting the defense of the pawn.
48... Ra4 49. Rh4+ Kg3 50. Rf4 Rb4 51. Bb2! An important defensive idea. But this was line wasn't easy to find and White would still have had to fight for a draw.  )
48... Kf3 49. Rf8+ Bf5 Now the Black rook can maneuver to the first rank and there is little White can do to stop it.
50. Kc1 Ra4 51. Rb8 Ra3 52. Rf8 Ke2 53. Rh8 Rb3 54. Rh2+ Kf1

Mamedyarov made a short draw against Sergey Karjakin of Russia, with the two players following a well-known variation that leads to a perpetual check. (The two are friends and Mamedyarov even helped Karjakin in his preparation for the World Championship last year.)

Kramnik’s game against Radjabov was very instructive. I was particularly impressed by his plan to trade his light-squared bishop for a knight, at the cost of a pawn, in order to obtain a position with a “good” knight vs. a “bad” bishop. But Kramnik got a little impatient and let Radjabov off the hook by allowing him some counterplay:

Vladimir Kramnik vs. Teimour Radjabov
Gashimov Memorial | Shamkir AZE | Round 2 | 22 Apr 2017 | ECO: A48 | 1/2-1/2
1. d4 Nf6 2. Nf3 g6 3. Bg5 Bg7 4. c3 O-O 5. Nbd2 d5 6. e3 Nbd7 7. Be2 Re8 8. O-O e5 9. Bh4 c6 10. Bg3 e4 11. Ne5 Nxe5 12. Bxe5 Bf8 13. Bg3 Bd6 14. Bh4 h6 15. c4 Be6 16. Rc1 Kg7 17. cxd5 cxd5 18. Nb1 Qb8 19. Kh1 Nd7 20. Bb5! Kramnik notices that the Black light-squared-bishop will always be quite passive, so he wants to create a position in which he has a good knight vs. that bad bishop.
20... Bxh2 Radjabov takes the free pawn. He might have been worried that Kramnik would now play f4, but Kramnik had something entirely different in mind:
21. g3!? g5 22. Bxd7 Bxd7 23. Kxh2 gxh4 Black has won a pawn, but White has the good knight against Black's passive bishop.
24. Nc3 Qd6 25. Qh5 hxg3+ 26. fxg3 f5 27. Ne2 In the next moves few moves, Kramnik demonstrates exquisite technique. He does not hurry in developing his strategy and slowly builds pressure on Black based on the superiority of his minor piece.
27... Rac8 28. Nf4 b6 29. Rg1 Rf8 30. Kh1 Rc6 31. Qh4 Rxc1 32. Rxc1 Rc8 33. Rf1 Rf8 34. Rf2 White can play on both the sides of the board, while Black must play defensively.
34... Rf7 35. Rc2! Switching back to the queenside as Black cannot challenge the White rook for the c-file.
35... Rf8 36. Qh5! Rf7
36... Rc8 Was no longer possible because of
37. Rxc8 Bxc8 38. Qe8! Bd7 39. Nh5+ Kh7 40. Qf7+ Kh8 41. Nf6  )
37. a3 Re7 38. b4 Rf7 39. Qh4 Rf8 40. Nh5+ Kg6 41. Nf4+ Kg7 42. Qh5 Rf7 43. Kh2 Re7 44. Qe2 Be8 45. Qa6 Black still cannot play Rc7 without losing the d-pawn.
45... Bf7 46. Qc8 Qd7 White could have avoided the exchange of queens, but I don't see how that would have helped him.
47. Qb8 Qb7 48. Qxb7 Rxb7 49. a4 A remarkable position. White is down a pawn, but unquestionably he is the one playing for a win. The Black bishop couldn't be much worse, and White also controls the c-file. The question is: How will he improve his position?
49... Kf6 50. Rc6+ Kg5 51. Kh3 Rd7 52. a5?! Kramnik gets a bit impatient and allows Black some counterplay.
52. Kg2! With the threat of Nh3+ would be quite annoying.
52... h5 53. Kh3! White actually has a plan for improving his position:
53... Re7 54. Rc8 Rd7 55. Rh8 Re7 56. Rh7 Rd7 If White plays Nh5, then after Be8! An exchange of rooks is forced and the pawn on a4 will fall.
57. b5! Black is basically in zugzwang. Either Nxd5 or Nxh5 cannot be stopped.  )
52... bxa5 53. bxa5 Rb7! Finally Black has some activity!
54. a6 Rb3! 55. Rc7
55. Ng2 Be8 56. Rc7 Bb5 57. Rxa7 Bf1!  )
55... Kf6 56. Rxa7 Rxe3 Black is able to save the game thanks to his passed e-passed.
57. Rc7 Ra3 58. a7 Ra2 59. Rb7 e3 60. g4 fxg4+ 61. Kxg4 h5+ 62. Kf3 Ra3 63. Ng2 h4 64. Nxe3 h3 65. Kf4 Be6 66. Nf1 Ra4 67. Kg3 Ra3+ 68. Kf4 Ra4 69. Kf3 Ra3+ 70. Ne3 Kg5 71. Rg7+ Kf6 72. Rc7 Kg5 73. Rg7+ Kf6

I think the endgame would be very instructive to analyze in depth. My analysis is somewhat hasty and it would be easy to improve the play on both sides. But, it is definitely a useful exercise to analyze it deeper without the aid of engines. 

Despite his loss in Round 1 from being overly aggressive, Wesley So of the United State kept to that style in Round 2 against Michael Adams of Britain, but he was not able to make any headway.

The highlight of Round 3 may be Kramnik vs Topalov — two former World Champions who have been playing well in this event and who have a fierce rivalry based on their bitter 2006 World Championship match. Their matches are always exciting. So vs. Wojtaszek and Eljanov vs. Mamedyarov will also probably be very exciting as well.

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Parimarjan Negi is an Indian grandmaster who is the second-youngest ever to earn the title (at 13 years 4 months and 22 days). Ranked No. 80 in the world, he is a junior at Stanford University. He can be found on Twitter at @parimarjan.