Dennis Gaitsgory (born 17 November 1973) is an Israeli-American mathematician. He is a mathematician at Max Planck Institute for Mathematics (MPIM) at Bonn and is known for his research on the geometric Langlands program.

Born in Chișinău (now in Moldova) he grew up in Tajikistan, before studying at Tel Aviv University under Joseph Bernstein (1990–1996). He received his doctorate in 1997 for a thesis entitled "Automorphic Sheaves and Eisenstein Series". He has been awarded a Harvard Junior Fellowship, a Clay Research Fellowship, the prize of the European Mathematical Society, and a Breakthrough Prize in Mathematics for his work.

His work in geometric Langlands resulted in a joint 2002 paper with Edward Frenkel and Kari Vilonen, establishing the conjecture for finite fields, and a separate 2004 paper, generalizing the proof to include the field of complex numbers as well. This was followed by a series of papers in 2024 that claim to prove the (categorical, unramified) geometric Langlands correspondence, by a team of led by Gaitsgory and Sam Raskin; for this, Gaitsgory was awarded the 2025 Breakthrough Prize in Mathematics.

Prior to his current appointment at MPIM Bonn, he was a professor of mathematics at Harvard and an associate professor at the University of Chicago from 2001–2005.

In 2025, he received the Breakthrough Prize in Mathematics.

Gaitsgory's father, Vladimir Gaitsgory, is an applied mathematician at Macquarie University.