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Galyna V. Livshyts studies convex geometry, analysis and high-dimensional probability theory. Her research page connects these areas through geometric inequalities and properties of convex sets.^[ref]

Her course Topics in Concentration of Measure and Convexity by Galyna V. Livshyts develops concentration of measure, isoperimetric inequalities and Steiner symmetrization. Replacing each parallel fibre of a set by a centred interval of the same length preserves volume while increasing symmetry, making some inequalities easier to prove. The course page credits the written notes to students, with editing by Livshyts.^[ref]