Burján started the World Cup for the first time in February 2011 in Moscow and finished 32nd over 1000 m and 28th place over 1500 m. At the European Short Track Championships 2011 in Sheffield , 29th place over 1000 m and 1500 m was his best placement. In January 2013 he won the bronze medal with the relay at the 2013 European Short Track Championships in Malmö . The following year he won silver with the relay over 3000 m at the Junior World Championships in Erzurum . In the 2014/15 season he achieved his first podium finishes in the World Cup with two second places with the relay. At the 2015 European Short Track Championships in Dordrecht and at the 2015 Short Track World Championships in Moscow, he won the silver medal with the relay. In the 2015/16 season, after finishing third with the relay in Montreal at the beginning of the season, he won his first World Cup victory in Shanghai with the relay. At the 2016 European Short Track Championships in Sochi , he won the silver medal with the relay. In March 2016, he finished fourth with the relay at the Short Track World Championships in Seoul . In the 2016/17 season he won in Calgary and Gangneung with the relay and achieved his first podium finish in the individual World Cup in Dresden with second place over 1500 m. In January 2017 he came in fourth place with the relay at the European Championships in Turin . At the 2017 Short Track World Championships in Rotterdam , he won the bronze medal with the relay. At the 2018 European Championships in Dresden he won the bronze medal with the 5000 m relay and the gold medal with the 5000 m relay at the 2018 Winter Olympics in Pyeongchang . He also achieved 30th place over 1500 m there. In March 2018 he finished 20th in the all- around competition and eighth place in the relay at the World Championships in Montreal.
In the 2018/19 season, Burján won in Calgary and Salt Lake City with the relay and achieved third place with the relay and second place with the mixed relay in Dresden . At the 2019 European Championships in Dordrecht , he won the gold medal with the relay. In March 2019 he won the bronze medal with the relay at the World Championships in Sofia . In the all-around competition he achieved 20th place there.
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Hungary
Shanghai 1
Calgary 1st
Gear inclination 1
Salt Lake City 3
