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Explore recent developments in thin-film lithium niobate for high-speed, low-power optical modulation and future optical links.
Explore MeshCNN, a neural network designed for triangular meshes, leveraging edge-based operations for efficient 3D shape analysis and task-driven feature extraction.
Explore contact structures, open book decompositions, and tightness characterization in 3-manifolds. Investigate preservation of tightness under Legendrian surgery.
Explore nanohertz gravitational wave detection using pulsar timing arrays, focusing on NANOGrav's 15-year dataset and its implications for astrophysics and theories of gravity.
Explore ZZ instantons in c=1 string theory, examining non-perturbative effects on closed string scattering and identifying a dual state in matrix quantum mechanics.
Explore the resolution of the bounded $L^2$ curvature conjecture in general relativity, examining minimal curvature tensor assumptions for controlling Einstein equation space-times.
Explore complex Brunn-Minkowski theory and its applications in Kähler geometry, focusing on uniqueness theorems and generalizations of Bando-Mabuchi's work on Kähler-Einstein metrics.
Explore instability and non-uniqueness in fluid dynamics, focusing on Leray solutions to Navier-Stokes equations and Vishik's findings on 2D Euler systems.
Explore recent findings connecting D-modules with singularities, focusing on Bernstein-Sato ideals and monodromy in polynomial mappings.
Explore geometric realization of quantum simple Lie super-algebras, S-duality, and connections to geometric Langlands correspondence and relative Langlands duality.
Explore multiscale analysis for decomposing high-dimensional measures, deriving functional inequalities using renormalization group methods in statistical physics.
Explore Weyl-strength subconvexity for Dirichlet L-functions, examining the subconvexity problem and progress on obtaining the Weyl exponent via the method of moments.
Explore quantitative bounds in polynomial Szemerédi theorem and related problems in additive combinatorics, harmonic analysis, and ergodic theory.
Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
Explore Hilbert's Sixth Problem in statistical physics and kinetic theory, examining the derivation of macroscopic laws from microscopic systems in classical and quantum settings.
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