
Learn strategies for solving related rate problems, including soap bubbles, cylindrical tanks, right triangles, conical tanks, and street light scenarios using similar triangles.

Explore statistical inverse problems and PDEs, covering Bayesian approaches, computational challenges, and mathematical guarantees for algorithms in high-dimensional settings.

Exploring efficient computation of homological representations in dynamical systems, with applications to differential equations and parameter space analysis.

Explores semi-Lagrangian discretisation of Monge-Ampère operator on P1 finite element spaces, discussing challenges and solutions for numerical methods in solving Monge-Ampère equations, with applications in inverse reflector problems.

Explore multiscale problem-solving techniques, focusing on Local Orthogonal Decomposition for PDEs. Learn about convergence, high-contrast data, and applications to time-dependent problems.

Explore white noise initial data in solving 4NLS, covering Hamiltonian PDE, globalization arguments, and limit equations. Gain insights into complex mathematical concepts and proofs.

Explore stochastic differential equations with degenerate noise, focusing on controllability and applications to oscillator networks. Gain insights into exponential mixing and solid controllability.

Explore entropy methods for hypocoercive equations, focusing on BGK and Fokker-Planck models. Learn about decay rates, auxiliary functionals, and regularization techniques in non-symmetric systems.

Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.

Overview of uncertainty quantification for kinetic equations, covering Monte Carlo methods, multi-fidelity techniques, and stochastic Galerkin particle methods. Explores computational challenges and recent advancements in the field.

Explores nonlinear degenerate cross-diffusion systems with nonlocal interaction, proving global existence of weak solutions using a semi-implicit JKO scheme for applications in social sciences, finance, and biology.

Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.

Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.

Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Eldan's Stochastic Localization technique and its implications for the slicing problem.

Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.

Explore reduced order models for solving partial differential equations, focusing on complexity reduction and efficient simulations in multiphysics problems.

Explore the interplay between differential equations and mixed Hodge structures, focusing on periods, kappa series, and motific gamma in number theory and algebraic geometry.

Explore the topology of cycles, limit cycles, and related mathematical concepts in this advanced graduate-level lecture on Hilbert's 16th problem and o-minimality.

Explore harmonic maps between surfaces, their applications, and connections to Teichmüller theory in this advanced lecture on geometric analysis and complex geometry.

Explore sums of squares in differential equations, focusing on hypoellipticity. Learn about key theorems, counterexamples, and applications in this advanced mathematics lecture.

Lecture on linearized instability for neutral functional differential equations with state-dependent delays, presenting recent research findings in advanced mathematics.