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into the following sections: A - Algebra, Number Theory and Logic B - Analysis and Differential Equations C - Discrete Mathematics D - Geometry and Topology E - Numerical Mathematics and Scientific Computing F
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. The specific research areas we will explore are + Adaptive scientific deep learning methods for mathematical physics problems governed by partial differential equations (domain decomposition, adaptive quadrature
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aspects include rough paths and subsequent developments for nonlinear stochastic partial differential equations. The theory of signatures and rough volatility also provides important connections to algebra
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