Perturbation at Blow Up of Self-Similar Solution for Modified Korteweg-de Vries Equation
Explore stability and perturbation of self-similar solutions' blowup dynamics in the modified Korteweg-de Vries equation, with applications to fluid dynamics and vortex patch formation.
Initial Classification of Global Behavior Around Multi-Solitons for the Nonlinear Klein-Gordon Equation
Explore nonlinear Klein-Gordon equation's global behavior near multi-solitons, focusing on unstable mode tracing and energy transfer mechanisms in three-dimensional space.
Late Time Tail of Waves on Dynamic Asymptotically Flat Spacetimes of Odd Space Dimensions
Explore late time asymptotic behavior of wave equations in odd spatial dimensions, uncovering new insights for dynamic backgrounds and nonlinear cases. Gain understanding of black hole interiors.
Scattering for Wave Equations with Sources and Slowly Decaying Data
Explore scattering solutions for wave equations with polynomially decaying sources, analyzing radiation fields and asymptotic behavior near the lightcone in nonlinear wave contexts.
Extremal Critical Collapse in Gravitational Systems
Explore the formation of extremal black holes in gravitational collapse, challenging the third law of black hole thermodynamics and introducing the concept of extremal critical collapse.
Formation of Quiescent Big Bang Singularities
Explore general relativity's big bang singularities, recent stability results, and a new condition for big bang formation in Einstein-non-linear scalar field settings.
Non-Regular Spacetime Geometry via Metric Measure Geometry
Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.
Stable Blowup for the Higher-Dimensional Skyrme Model
Explore stable blowup mechanisms in higher-dimensional Skyrme models, focusing on finite-time blowup at self-similar rates in 5+1 dimensions compared to 3+1 dimensions.
Haunted Einstein-Yang-Mills Wormholes in Nonlinear Waves and Relativity
Explore infinite sequences of static spherically symmetric wormhole solutions in SU(2) Einstein-Yang-Mills equations, featuring phantom field "hauntings" in traversable tunnels between universes.
Dispersion Estimates for Dirac Equations with Aharonov-Bohm Magnetic Fields
Explore dispersive properties of 2D Dirac operators with Aharonov-Bohm potentials, examining flow components and deducing sharp Strichartz estimates for advanced mathematical analysis.
Weakly Turbulent Solution to the Schrödinger Equation on the 2D Torus with Potential
Explore a smooth solution to the linear Schrödinger equation on a 2D torus, examining logarithmic H^1 Sobolev norm growth and infinite-time blowup using adapted CKSTT techniques.
The Modified Energy Method for a Nonlocal Quasilinear Wave Equation
Explore nonlinear waves and relativity through the modified energy method for a nonlocal quasilinear wave equation in this advanced mathematics lecture.
Waves on Kerr-de Sitter Space
Explore wave propagation on Kerr-de Sitter spaces in the subextremal range, featuring updates on joint research with Peter Hintz and Oliver Petersen.
Scattering Towards the Spacelike Singularity in Kasner Spacetimes
Explore Kasner spacetimes and spacelike singularities in General Relativity through hyperbolic systems, examining blow-up asymptotics and the interplay between Cauchy and asymptotic data.
Festina Lente and Branes in Quantum Gravity
Explore universal bounds on brane tension in de Sitter space using the Festina Lente conjecture, cosmic censorship, and charged black hole evolution in quantum gravity.
Taxonomy of Infinite Distance Limits in Quantum Gravity Moduli Spaces
Explore geometric classification of light towers in quantum gravity moduli spaces, examining constraints, evidence, and applications in infinite-distance limits.
Quintessence: From String Theory to Observations and Back
Explore quintessence in string theory and its observational implications, bridging theoretical concepts with empirical evidence in cosmology.
Primordial Stochastic Gravitational Wave Backgrounds in Multi-field Inflation
Explore stochastic gravitational wave backgrounds in multi-field inflation, examining frequency profiles and potential visibility in LISA, unlocking insights into early universe processes.
Fully Stabilized Minkowski Vacua in the 26 Landau-Ginzburg Model
Explore fully stabilized Minkowski vacua in the 26 Landau-Ginzburg model, examining theoretical implications for string theory and quantum gravity.
Tensionless Strings Limits in 4D Conformal Manifolds
Explore three infinite distance limits in 4D superconformal field theories, their AdS/CFT correspondence, and connections to tensionless strings in AdS. Gain insights into CFT Distance Conjecture and high-energy state density.
What if String Theory Has a de Sitter Excited State?
Explore the concept of de Sitter space as an excited state in string theory, examining its implications and differences from traditional coherent states.