Explore new isoperimetric inequalities and their applications in systolic geometry and minimal surfaces in this 52-minute lecture from the Colloque des sciences mathématiques du Québec. Delve into Yevgeny Liokumovich's Aisenstadt Prize-winning research, which introduces two novel isoperimetric inequalities for k-dimensional submanifolds in R^n or Banach spaces. Discover how these inequalities lead to a new systolic inequality, confirming Larry Guth's conjecture, and an asymptotic formula for minimal submanifold volumes, validating Mikhail Gromov's prediction. Gain insights into collaborative work with Boris Lishak, Alexander Nabutovsky, Regina Rotman, Fernando Marques, Andre Neves, and Larry Guth, advancing understanding in mathematical geometry and topology.