Leonardo Abbrescia

Leonardo Abbrescia serves as an Assistant Professor in the Department of Mathematics at the Georgia Institute of Technology. His office is located in Skiles 266, and he may be contacted via email at abbrescia@math.gatech.edu or by phone at 404-894-5367.

His research expertise spans:

• Partial Differential Equations
• Geometric Analysis
• Mathematical Physics
• Fluid Dynamics
• Hyperbolic Conservation Laws
• Singularity Theory

Abbrescia's scholarly work centers on the geometric analysis of nonlinear PDEs arising in fluid mechanics and general relativity. He investigates compressible Euler flow, shock wave formation, and quasilinear wave equations through advanced geometric frameworks like the double-null foliation. His methodology integrates differential geometry with functional analysis to derive integral identities and study singularity propagation in multi-dimensional settings.

Analysis of his 13 recent publications (2016-2025) reveals a consistent focus on geometric structures underlying hyperbolic systems. Key trends include the development of novel integral identities for fluid dynamics, stability analysis of wave maps, and applications of vector field methods to nonlinear evolution equations. His work demonstrates particular innovation in connecting geometric foliations to singularity formation in compressible flows.

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Information regarding student advising, research grants, and laboratory teams was not included in the source documentation.