Operator Algebras, Tensor Categories and Tensor Networks in Topological Order
Explore tensor networks in topological order using operator algebra techniques. Discover quantum symmetries and their mathematical representation through tensor categories.
Curvature-Homogeneous Riemannian 3-Manifolds and Integrable Systems
Explore curvature-homogeneous Riemannian 3-manifolds, surveying known examples and recent discoveries. Delve into connections with integrable systems, particularly Toda lattices, to construct new explicit examples.
Knot Invariants from Finite Dimensional Integration
Explore finite dimensional integration for computing powerful knot invariants, surpassing traditional methods in efficiency and rigor while challenging established notions in knot theory.
Metric SYZ Conjecture for Calabi-Yau Manifolds - ICBS 2024
Explore special Lagrangian torus fibrations on Calabi-Yau manifolds, focusing on recent progress and the Fermat family of hypersurfaces.
A Finite Dimensional Proof of the Verlinde Formula
Explore a purely algebro-geometric proof of the Verlinde formula, examining recurrence relations for curve genus and parabolic points in generalized theta function spaces.
Interface and Its Fluctuation in Interacting Particle Systems - ICBS 2024
Explore particle separation in Glauber-Kawasaki dynamics, interface evolution, and fluctuations. Delve into extended research on anisotropic curvature flow and stochastic partial differential equations.
Hyperbolic and Mixed-Type Problems in Gas Dynamics and Geometry
Explore hyperbolic and mixed-type PDEs in gas dynamics and geometry, focusing on transonic flows and isometric embedding.
Understanding the Relationship Between the Schramm-Loewner Evolution and the Gaussian Free Field
Explore the connection between Schramm-Loewner Evolution, Gaussian Free Field, and Liouville Quantum Gravity through a novel, accessible approach for non-specialists.
Partial Differential Equations and Convexity
Explore elliptic PDEs, convexity preservation, and surprising cases of convexity breaking in evolution equations like porous medium and Stefan problem.
Langlands Duality for the Affine Hecke Category
Explore Langlands duality for affine Hecke category, its applications in representation theory, and potential generalizations to symplectic singularities. Gain insights into geometric local Langlands duality.
Optimal Estimates for Neumann Eigenvalues
Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.
Maxwell Eigensolvers with Overlapping Schwarz Methods - ICBS 2024
Explore advanced overlapping Schwarz methods for Maxwell eigensolvers, including improved condition number bounds and a novel two-level preconditioned Helmholtz subspace iterative method for edge element approximations.
Intersection Theory on Moduli Space of Super Riemann Surfaces
Explore intersection theory on super Riemann surface moduli spaces, including recursion formulas, polynomiality, and applications to JT gravity.
Construction of Solution Landscape for Complex Systems
Explore the novel "Solution Landscape" concept and its applications in complex systems, including nematic liquid crystals, crystalline phases, and Bose-Einstein condensates.
Critical Points of Eisenstein Series and Spectrum of the Lame Operator
Explore critical points of Eisenstein series E2, E4, E6 and their applications to the Lame operator's spectrum in this advanced mathematics lecture.
Particle and Game Theoretic Methods for Multi-scale and High Dimensional Problems
Explore Lagrangian and game theoretic approaches for solving complex PDEs, including front speed computation, high-dimensional entropy production, and turbulent combustion analysis.
Random Walk on Dynamical Percolation: Separating Critical and Supercritical Regimes
Explore random walks on dynamical percolation, examining critical and supercritical regimes in infinite regular trees and lattices. Analyze speed bounds and mean squared displacement.
Gromov-Witten Type Theory and Statistical Physics
Explore connections between Gromov-Witten theory and statistical physics, applying concepts from both fields to gain new insights and tackle complex problems in topological string theory.
Recent Progress on Gamma Conjectures - ICBS 2024
Explore recent advancements in Gamma conjectures, including modifications to Gamma conjecture I and its application over Kähler moduli space.
Hermitian Yang-Mills Connections on Log Terminal Kahler Spaces
Explore Hermitian Yang-Mills theory on mildly singular spaces, focusing on recent results for sheaves and log terminal Kähler spaces.
MAgNet: Mesh Agnostic Neural PDE Solver
Explore innovative neural PDE solver for accurate, scalable climate predictions. Learn about mesh-agnostic architecture combining Implicit Neural Representations and Graph Neural Networks.