Cluster Duality and Non-Holomorphic Spectral Curves
Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.
Combinatorics of the Amplituhedron
Explore the amplituhedron's connections to cluster algebras, matroids, and combinatorics in this gentle introduction by Lauren Williams from Harvard University.
Reddening Sequences for Cluster Algebras
Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.
Phase Transitions of Composition Schemes and Their Universal Limit Laws
Explore phase transitions in composition schemes, analyzing critical cases and their impact on asymptotic behavior. Uncover rich limit laws and universal properties in combinatorial structures.
Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
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.
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.
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.
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.
Modelling Phenotypic Delay in the Evolution of Bacterial Antibiotic Resistance
Explore bacterial antibiotic resistance evolution through phenotypic delay modeling, uncovering insights into this critical health challenge.
Infer Global, Predict Local - Bias-Variance Theory for Protein Genotype-to-Phenotype Mapping
Explore bias-variance theory in protein genotype-to-phenotype mapping, focusing on global inference and local prediction techniques.
New Perspectives on Borel Summation - Lecture 4
Explore Airy-Lucas functions through Borel summation, focusing on thimble integrals and hypergeometric Laplace transforms. Gain insights into Stokes phenomenon reflections in the Borel plane.
New Perspectives on Borel Summation - Lecture 1
Explore new perspectives on Borel summation, focusing on linear ODEs and integrals over Lefschetz thimbles, to understand when divergent series solutions produce holomorphic solutions.
Smoothing by Ricci-DeTurck Flow and Applications to Scalar Curvature
Explore Ricci-DeTurck flow's existence theory for non-smooth initial metrics and its applications to scalar curvature rigidity problems in geometry.
DT Invariants and Holomorphic Curves in Complex Integrable Systems
Explore the correspondence between Donaldson-Thomas invariants and holomorphic curves, focusing on mirror symmetry and applications in enumerative geometry.