Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
Scalar Curvature Rigidity and Extremality in Dimension 4
Explore scalar curvature rigidity in 4D using Finsler-Thorpe trick and twisted spinor methods. Discover area-extremal properties of 4-manifolds with nonnegative sectional curvature.
Recent Inequalities on the Mass-to-Capacity Ratio
Explore new inequalities for mass-to-capacity ratio on manifolds with nonnegative scalar curvature, revealing proofs of positive mass theorem and applications in geometry.
A Gift for Louis: The New Aperiodic Monotile
Explore the groundbreaking discovery of a new aperiodic monotile, unraveling its mathematical significance and implications for tiling theory.
Understanding Integrability, Chaos and Thermalization from Low Frequency Noise
Explore integrability, chaos, and thermalization through low frequency noise analysis, gaining insights into complex physical systems.
When Your Big Data Seems Too Small: Accurate Inferences Beyond the Empirical Distribution - Part 2
Explore advanced techniques for accurate distribution inferences with limited data. Learn to de-noise empirical distributions, estimate population spectra, and recover low-rank matrix approximations.
Topological Recursion, Painlevé Equation, Exact WKB and Resurgence
Explore topological recursion's connections to WKB, Painlevé equations, and BPS structures. Delve into resurgence properties and non-linear Stokes phenomena in Painlevé transcendents.
Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties
Explore the evolution of topological symplectic structures, wild Riemann surfaces, and character varieties in global Lie theory. Discover connections to quantum groups, hyperkähler geometry, and integrable systems.
Introduction to Resurgence via Wall-crossing Structures - Lecture 2
Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
Introduction to Resurgence via Wall-crossing Structures - Lecture 1
Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.
Positive Mass Theorem for Asymptotically Hyperbolic Manifolds
Explore the positive mass theorem for asymptotically hyperbolic manifolds and its implications in AdS/CFT correspondence and global invariants at conformal infinity.
Intrinsic Flat Stability of the Positive Mass Theorem for Graphical Manifolds
Explore intrinsic flat stability of positive mass theorem for graphical manifolds, focusing on asymptotically flat and hyperbolic cases. Gain insights into rigidity, stability, and ongoing research.
Blow Up for the 1D Cubic NLS and Related Systems
Explore singularity formation in 1D Schrödinger equations with cubic nonlinearity and its connections to Schrödinger map and vortex filament equation.
Continuous Time Bubbling for the Harmonic Map Heat Flow in Two Dimensions
Explore continuous time bubbling in harmonic map heat flow, focusing on finite energy maps from plane to two-sphere without symmetry assumptions.
Stability and Asymptotic Behavior of Fronts in Bidomain Models
Explore stability and asymptotic behavior of fronts in bidomain models with Hiroshi Matano's in-depth analysis and insights.
Solitons and Channels in Nonlinear Wave Equations
Explore non-radiative solutions in nonlinear wave equations and their connection to soliton resolution, using new energy estimate channels for radial solutions.
Area-Minimizing Integral Currents: Singularities and Structure - Lecture
Explore area-minimizing integral currents, their singularities, and structure. Delve into dimension bounds, fractal properties, and recent progress towards proving key conjectures in geometric measure theory.
Number Theory over Function Fields - Lecture 6
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 5
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.
Number Theory over Function Fields - Lecture 4
Explore recent progress in number theory using polynomial analogues over finite fields, connecting geometric perspectives to topology, probability, and automorphic forms.
Number Theory over Function Fields - Lecture 3
Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.