Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry
Explore p-adic geometry through Riemann-Hilbert correspondence, covering local systems, Galois representations, Hodge theory, and cohomology in this advanced mathematics lecture.
Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 2
Explore p-adic geometry through a Riemann-Hilbert correspondence, examining algebraic differential equations, perverse sheaves, and prismatic cohomology in nonarchimedean fields.
Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 1
Explores the Riemann-Hilbert correspondence in complex and p-adic geometry, discussing its historical context, mathematical foundations, and recent developments in prismatic cohomology.
The Convex Geometry of Blind Deconvolution and Matrix Completion Revisited
Explores convex geometry in blind deconvolution and matrix completion, analyzing dimensional factors in noise bounds and proposing alternative error scaling approaches for low-rank matrix recovery problems.
Optimal Learning from Data
Explore optimal learning from data, including error recovery, discrete optimization, and handling noisy measurements. Insights on deep learning and stochastic settings provided.
Machine Learned Regularisation for Solving Inverse Problems
Machine learned regularization techniques for solving inverse problems, focusing on image reconstruction from tomographic and blurred measurements. Explores data-driven approaches and discusses open mathematical challenges.
Alexander Volberg: The Probability of Buffon Needle to Land Near Cantor Set
Explore the probability of Buffon's needle landing near Cantor sets, delving into unexpected connections with various mathematical fields and theories.
Joshua Zahl- Lens Counting and Restricted Projections
Explore planar incidence geometry and lens counting theory to understand projection theorems, with applications in curve arrangements and intersection patterns.
Carlos Pérez- Fractional Poincaré Inequalities for Doubling and Non-Doubling Weights
Explore fractional Poincaré-Sobolev inequalities using Harmonic Analysis, unifying and improving known results for doubling and non-doubling weights in mathematical analysis.
Harmonic Analysis Techniques for -Almost- Minimizers
Explore harmonic analysis techniques for (almost-)minimizers, focusing on free boundary theory and calculus of variations. Learn about applications to geometric measure theory and domain geometry.
Caleson Estimates on Solutions in Domains with Uniformly Rectifiable Boundaries
Explores elliptic operators and measures on domains with uniformly rectifiable boundaries, presenting estimates for elliptic measure and Green function associated with Dahlber-Kenig-Pipher operators.
Landscape Function and Its Relations With Eigenvectors of a Schrödinger Operator
Explore landscape functions and their connections to Schrodinger operator eigenvectors, covering effective potentials, energy computations, and exponential decay in various contexts.
Fast FPT-Approximation of Branchwidth
Explore efficient graph decomposition techniques and FPT algorithms for approximating branchwidth, with applications in structural graph theory and dynamic programming.
Daniel Dadush- Integer Programming and the Kannan-Lovasz Conjecture
Explore advanced integer programming techniques, lattice theory, and the Kannan-Lovasz conjecture in this high-level overview of solving n-variable integer programs efficiently, with insights into recent progress and key concepts.
Francisco Criado - The Dual 1-Fair Packing Problem and Applications to Linear Programming
Explore proportional fairness in resource allocation, its dual problem, and applications to linear programming algorithms, focusing on geometric relationships and potential improvements.
Cynthia Vinzant - Log Concave Polynomials and Matroids
Explore strong log concavity in polynomials, its applications to matroids, and connections to combinatorics and geometry. Learn about recent developments and their implications.
Sparse Integer Programming Is FPT
Explore sparse integer programming's fixed-parameter tractability, its implications for parameterized complexity, and related concepts in variable dimension optimization.
Face Structures of Tropical Polyhedra
Explore tropical polyhedra's face structures, focusing on monomial tropical polyhedra to overcome issues in classical definitions and investigate combinatorial properties.
Probabilistic Analysis of the Simpler Method and Polytope Diameter
Probabilistic analysis of simplex method and polytope diameter, exploring smoothed, well-conditioned, and random polytopes. Discusses improvements in complexity analysis and diameter bounds using shadow paths.
Tropical Solutions to Hard Problems in Auction Theory
Explore tropical mathematics' applications in auction theory, neural networks, and statistics through polytopes, algorithms, and semigroup matrices, unveiling powerful problem-solving techniques.
Sums in Progressions to Squarefree Moduli Among Polynomials Over a Finite Field
Explore polynomial sums in progressions to squarefree moduli over finite fields, covering Fourier analysis, polynomial anatomy, and arithmetic functions.