The final four

7
On rational connectedness of globally F-regular threefolds (pdf) Gongyo, Yoshinori; Li, Zhiyuan; Patakfalvi, Zsolt; Schwede, Karl; Tanaka, Hiromu; Zong, Runhong Adv. Math. 280 (2015), 47-78 MR3350212   MSC:14E30 (13A35,14D06,14M22)
17
Free energy fluctuations for directed polymers in random media in $1+1$ dimension (pdf) Borodin, Alexei; Corwin, Ivan; Ferrari, Patrik Comm. Pure Appl. Math. 67 (2014), no. 7, 1129-1214 MR3207195   MSC:82D10 (60B20,60H15,60K35,60K37)
18
A case of the dynamical Andre-Oort conjecture (pdf) Ghioca, Dragos; Krieger, Holly; Nguyen, Khoa Int. Math. Res. Not. IMRN 2016, no. 3, 738-758 MR3493432   MSC:37P55 (14H45)
19
Rank-finiteness for modular categories (pdf) Bruillard, Paul; Ng, Siu-Hung; Rowell, Eric C.; Wang, Zhenghan J. Amer. Math. Soc. 29 (2016), no. 3, 857-881 MR3486174   MSC:18D10 (57R56,81R50)