GeoVerse Lab
← Basic Sciences Division

Mathematics Center

Develops mathematical foundations for geophysical modeling, spanning PDEs for wave propagation, inverse theory and regularization, Bayesian inference and uncertainty quantification, and stochastic processes for reservoir modeling.

Mathematics CenterPhysics CenterChemistry CenterBiology CenterAtmospheric Sciences CenterStratigraphy & Sedimentology CenterStructural Geology & Tectonics CenterPetrology & Mineralogy CenterGeochemistry CenterPaleontology & Evolutionary Biology CenterRemote Sensing & Earth Observation CenterHydrogeology & Soil Science CenterPhysical Oceanography CenterMarine Geology & Geophysics CenterChemical Oceanography CenterMarine Biology & Ecology Center
Research Fields 16
Fourier Analysis & Spectral Methods
〰️ Fourier Analysis & Spectral Methods
Fourier analysis is the study of the representation of functions as superpositions of elem…
Regularization Theory & Functional Analysis
📐 Regularization Theory & Functional Analysis
Regularization theory is the branch of functional analysis that makes inverse problems sol…
Bayesian Inference
🎯 Bayesian Inference
Bayesian inference is the theory of learning from data in which uncertainty about unknown …
Stochastic Processes
🎲 Stochastic Processes
A stochastic process is a collection of random variables indexed by time or space, and sto…
Optimization Theory & Linear Programming
📉 Optimization Theory & Linear Programming
Optimization theory is the mathematical study of choosing the best element of a set of adm…
Numerical Methods for PDEs
🧮 Numerical Methods for PDEs
Numerical methods for partial differential equations construct and analyse discrete approx…
Linear Algebra & Matrix Theory
🔢 Linear Algebra & Matrix Theory
Linear algebra and matrix theory is the study of vector spaces and the linear maps between…
Complex Analysis
🌀 Complex Analysis
Complex analysis is the study of complex-differentiable, or holomorphic, functions of one …
Differential Geometry
🌐 Differential Geometry
Differential geometry is the study of shapes using calculus: smooth manifolds, spaces that…
Topology & Dynamical Systems
🧿 Topology & Dynamical Systems
Topology is the study of the properties of space preserved under continuous deformation, c…
Probability Theory & Stochastic Calculus
∫ Probability Theory & Stochastic Calculus
Probability theory is the measure-theoretic study of randomness, built on Kolmogorov's 193…
Wave Equation Mathematics
🌊 Wave Equation Mathematics
Wave equation mathematics is the theory of the partial differential equation u_tt = c² u_x…
Calculus of Variations & Optimal Control
⛰️ Calculus of Variations & Optimal Control
The calculus of variations optimizes over functions: among all curves joining two points, …
Random Matrix Theory
🎼 Random Matrix Theory
Random matrix theory studies matrices whose entries are random variables and, above all, t…
Tensor Analysis
🧊 Tensor Analysis
Tensor analysis is the calculus of tensors, objects with multiple indices whose components…
PDE Theory & Sobolev Spaces
🧩 PDE Theory & Sobolev Spaces
Modern PDE theory is the study of partial differential equations through the function spac…