Jing Wang
Purdue University, IN·Mathematics & Statistics
How does the shape of a space affect the way a random process moves through it? A diffusion, like a particle wandering at random, spreads differently on a flat plane than on a curved surface.
- Fields
Mathematics & Statistics
- Topics
stochastic processes
diffusion processes
sub-Riemannian geometry
- Grants
- 1 known grant, through Jun 2027
What they work on
- Study geometrically meaningful stochastic functionals on Grassmannian and flag manifolds, spaces of subspaces, and link them to degenerate diffusions associated with the Berard-Bergery fibration.
- Develop a new analytic characterization of sub-Riemannian model spaces using heat kernels, which describe how heat spreads, as part of rigidity theorems in both compact and non-compact settings.
- Investigate isoperimetric-type problems in metric measure spaces by relating the spectrum of a domain to the exit time of a diffusion process from that domain, using probabilistic and analytic methods.
More about the research
This project studies that link between geometry and randomness, joining probability, analysis and differential geometry. Its main focus is non-smooth settings such as sub-Riemannian geometry, where motion is allowed only along certain directions, like a car that can drive forward and turn but not slide sideways. The grant notes that some of these problems connect to control systems and data science.
Why it matters
This is basic mathematics. It deepens understanding of how the geometry of a space, including restricted-motion sub-Riemannian spaces, shapes the behavior of random processes. The grant notes that some of these questions relate to control systems and data science, areas these results could eventually inform.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jian Song
Rutgers University-New Brunswick, NJ·Mathematics & Statistics
Study the Yau-Tian-Donaldson conjecture for constant scalar curvature Kahler metrics on projective manifolds, testing uniform K-stability for models as a sufficient condition for existence.
Laura Fredrickson
University of Oregon, OR·Mathematics & Statistics
Verify the Gaiotto–Moore–Neitzke conjectural description of the hyperkähler metric on Hitchin moduli spaces, especially near singular fibers, using constructive analytic techniques and geometric microlocal analysis.
Xuwen Zhu
Northeastern University, MA·Mathematics & Statistics
Study how gravitational instantons, four-dimensional spaces that solve Einstein's equations, degenerate and how their moduli spaces are structured, using geometric microlocal analysis and PDE techniques.
The school
Purdue University: 43 labs on PI Pages, $932M a year on research, 833 research doctorates a year.
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