She studied at the University of Vienna beginning in 1993, earning a master's degree (mag.
[1] Her doctoral dissertation, Enumeration of perfect matchings: Rhombus tilings and Pfaffian graphs, was jointly supervised by Christian Krattenthaler and Franz Rendl,[1][3] and her habilitation thesis was A polynomial method for the enumeration of plane partitions and alternating sign matrices.
[1] She worked as an assistant at Alpen-Adria-Universität Klagenfurt from 1999 to 2004,[1][4] with a year of postdoctoral research at the Massachusetts Institute of Technology in 2001.
[1] Fischer won the 2006 Dr. Maria Schaumayer Prize, and the 2009 Start-Preis of the Austrian Science Fund.
[4] With Roger Behrend and Matjaž Konvalinka, Fischer is a winner of the 2019 David P. Robbins Prize of the American Mathematical Society and Mathematical Association of America, for their joint research on alternating sign matrices.