Dynamics of BCZ Cocycles and the Riemann Hypothesis
Explore the BCZ map's connection to Farey fractions, horocycle flow, and the Riemann Hypothesis. Gain insights into recent developments in BCZ cocycles and their dynamical implications.
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.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
Locally Symmetric Varieties with Moduli Interpretation
Explore complex algebraic geometry, focusing on realizing moduli spaces as locally symmetric varieties through Hodge theory. Survey existing results and examine Calabi-Yau manifolds with complex hyperbolic ball periods.
Rigidity and Multiplicity of Singularities Associated to Ample Vector Bundles
Explore rigidity and multiplicity of singularities in ample vector bundles, focusing on irreducible desingularization and multiplicity formulas for isolated singularities.
Hypergraph Bipartite Turan Problems
Explore recent findings on hypergraph bipartite Turan problems, including solutions to challenges posed by prominent researchers in the field.
New Geometric Structures in the Langlands Program
Explore new geometric structures in the Langlands program, including the moduli space of G-bundles on the curve, and their role in constructing the semi-simple local Langlands correspondence.
Asymptotic Orthogonality Relation for GL(n,R) - ICBS 2024
Explore generalized Dirichlet character orthogonality for GL(n,R), extending classical number theory to higher dimensions with applications.
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.
Functions on the Commuting Stack via Langlands Duality - ICBS 2024
Explore complex reductive group theory, analyzing cocenters of affine Hecke categories and calculating Whittaker object endomorphisms to derive formulas for commuting stacks.
Recent Progress in Ramsey Theory
Explore recent advancements in Ramsey Theory, focusing on new techniques and proofs related to Ramsey numbers and graph coloring. Gain insights into geometric, algebraic, probabilistic, and combinatorial methods.
Average Heights of Abelian Varieties with Complex Multiplication
Explore the arithmetic properties of abelian varieties with complex multiplication, focusing on Colmez's conjecture and its implications for periods and L-functions.
Heights of Algebraic Cycles and Special Values of L-Series - ICBS 2024
Explore heights of algebraic cycles and their connections to L-series special values, focusing on CM points and Gross-Schoen cycles on elliptic curves.
Finiteness Questions for Étale Coverings with Bounded Wild Ramification at the Boundary
Explore finiteness questions for étale coverings with bounded wild ramification at the boundary in characteristic p>0 algebraic geometry, including recent work and open problems.
Applications of Additive Combinatorics to Problems in Fractal Geometry
Explore applications of additive combinatorics in fractal geometry, focusing on self-similar sets with overlaps and recent advancements in the field.
Computing Differentials in the Adams Spectral Sequence and the Last Kervaire Invariant Problem
Explore advanced methods for computing differentials in the Adams spectral sequence and uncover recent progress on the Last Kervaire Invariant Problem in dimension 126.
Structures Robust Under Randomness - Probabilistic Combinatorics and Thresholds
Explore robustness of discrete system substructures under random subsampling, examining thresholds in random graphs and key conjectures in probabilistic combinatorics.
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.
Homogeneous Dynamics and Probabilistic Diophantine Approximations - Cauchy Limit Laws for Linear Forms
Explore homogeneous dynamics and probabilistic Diophantine approximations, focusing on Cauchy limit laws for linear forms with random coefficients and lattice counting problems.
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.