Galyna Livshyts
Georgia Institute of Technology, GA·Mathematics & Statistics
Among all shapes with a given volume, the ball has the smallest surface area. This is why soap bubbles are round, and it is captured by the isoperimetric inequality, one of the oldest results in geometry.
- Fields
Mathematics & Statistics
- Topics
convex geometry
isoperimetric inequality
Brunn-Minkowski inequality
- Grants
- 1 known grant, through Mar 2027
What they work on
- Approach the log-Brunn-Minkowski, (B)-, and Dimensional Brunn-Minkowski conjectures, which predict stronger volume inequalities for symmetric convex bodies, using local versions of isoperimetric-type inequalities.
- Develop a fast algorithm that learns a convex body with respect to a general log-concave measure, a question in asymptotic geometric analysis with potential applications in learning theory.
- Study large random matrices with inhomogeneous profiles using methods based on a new efficient discretization of the unit sphere.
More about the research
This project asks how such shape inequalities become stronger when shapes are convex (having no dents) and symmetric. It also studies a surprising feature of very high-dimensional spaces: as the number of parameters grows, behavior often becomes simpler and more predictable, much as poll results tend to follow a normal distribution.
Why it matters
This is mainly basic mathematics. Settling conjectures about convexity and symmetry would deepen understanding of high-dimensional geometry. The work on learning convex bodies and on inhomogeneous random matrices may eventually inform learning theory, statistics, computer science, and physics, where high-dimensional data and large random matrices often arise.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Artem Zvavitch
Kent State University at Kent, OH·Mathematics & Statistics
Prove Brunn–Minkowski and isoperimetric-type inequalities for principal eigenvalues of real Monge–Ampère operators on convex bodies, using convex geometry and symmetrization.
Melanie Wood
Harvard University, MA·Mathematics & Statistics
Develop a nonabelian analogue of the Cohen-Lenstra heuristics, replacing class groups with Galois groups that encode symmetries of nonabelian extensions of a varying number field.
Cesar Cuenca
Ohio State University, OH·Mathematics & Statistics
Describe the large-scale behavior of continuous and discrete beta-ensembles (Boltzmann distributions generalizing random matrix eigenvalues and random partitions) at different temperature limits, using new versions of free probability.
The school
Georgia Institute of Technology: 50 labs on PI Pages, $1.5B a year on research, 572 research doctorates a year.
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