Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications
Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.
Quantitative Cobordism - Exploring Topology and Geometry
Explore quantitative cobordism in topology, focusing on non-constructive existence proofs and connections to geometry. Delve into Manin's principle, Cheeger-Gromov heuristic, and manifold constructions.
Mock Modularity of Calabi-Yau Threefolds - ICBS 2024
Explore modular properties of generating functions for Donaldson-Thomas invariants in Calabi-Yau threefolds, their physical origins, and applications in string theory compactifications.
Homotopy Groups of Spheres - Computation Methods and Recent Progress
Explore homotopy groups of spheres, their computational methods, and recent advancements in topology using motivic homotopy theory and related techniques.
Linear Stability of Ricci Solitons - ICBS2024
Explore linear stability of compact shrinking Ricci solitons, including positive Einstein manifolds. Examine critical aspects, open problems, and recent research findings in Ricci flow and geometric analysis.
Rationality Problems in Algebraic Geometry - ICBS 2024
Explore geometric ideas and constructions in the study of rationality of higher-dimensional algebraic varieties, focusing on recent developments and challenges.
Stability of Sobolev Inequalities - ICBS 2024
Explore quantitative stability of Sobolev inequalities, focusing on Struwe's decomposition and recent advancements in dimensional-dependent estimates for multiple bubbles in various dimensions.
Entropy Analysis and Singularities of Solutions for Nonlinear Hyperbolic Conservation Laws
Explore entropy analysis and singularities in nonlinear hyperbolic conservation laws. Gain insights into open problems, minimal entropy conditions, and phenomena like cavitation and concentration.
Recent Progress on Minimal and Constant Mean Curvature Surfaces
Explore recent advancements in the existence theory of minimal and constant mean curvature surfaces, surveying cutting-edge developments in this mathematical field.
Sheaves on Calabi-Yau 4-folds and Virtual Invariants - An Overview
Explore developments in enumerative geometry on Calabi-Yau 4-folds, including point counting, curve counting, and surface counting, with connections to string theory and physics.
Structure of Equivariant Derived Categories - ICBS 2024
Explore equivariant derived categories, their structure theorems, and applications to GIT quotients and hidden symmetries in algebraic geometry.
Modularity of Donaldson-Thomas Invariants on Compact Calabi-Yau Threefolds
Explore Donaldson-Thomas invariants, their connection to BPS indices, and modular behavior in string theory. Gain insights into computational methods and applications to Gopakumar-Vafa invariants and topological string amplitudes.
Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods
Explore the connection between hybrid high-order and hybridizable discontinuous Galerkin methods for diffusion problems, unveiling new efficient approaches and optimal convergence.
Homological Aspects of Branching Laws in p-adic Groups
Explore homological aspects of branching laws for p-adic group representations, focusing on restriction to subgroups and projective representations in Bernstein blocks.
The KPZ Fixed Point - Understanding Random Growing Interfaces
Explore the KPZ universality class, its fixed point, and connections to random matrix theory and integrable systems in growing interfaces and exclusion processes.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
Growth in Tensor Powers
Explore tensor power decomposition in group representations, focusing on asymptotic behavior and non-negligible summands using symmetric tensor category theory.
Nonlocal Diffusion Model with Dirichlet Boundary Condition - ICBS 2024
Explore nonlocal diffusion models for Poisson equation, focusing on approaches to approximate Dirichlet boundary conditions and analyzing wellposedness and convergence.
The Local Langlands Program and Characteristic p
Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.
Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves
Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
Integrable Billiards and Rigidity - Lecture 1
Explore integrable billiards and the Birkhoff-Poritsky conjecture, focusing on Hopf-type rigidity and its extension to Twist symplectic maps and billiards.