Duality Between the Pseudoeffective and the Movable Cone on a Projective Manifold
Explore duality between pseudoeffective and movable cones on projective manifolds, including recent developments and connections to non-Archimedean Calabi-Yau theorem.
Interlacing Families and Ramanujan Graphs - #ICBS2024
Explore Ramanujan Graphs, interlacing families, and their connections to various mathematical fields. Gain insights into recent developments and open problems in graph theory.
On the p-adic Local Langlands Correspondence
Explore the $p$-adic local Langlands correspondence for ${\mathrm GL}_2({\mathbb Q}_p)$, focusing on geometric constructions from joint works with Dospinescu and Niziol.
L^2-Invariants and Dynamical Invariants in Algebraic Actions
Explore connections between $L^2$-invariants in operator algebra and entropy/mean dimension in topological dynamical systems, focusing on algebraic actions of discrete groups.
Functoriality and Sheaf Property for Wrapped Fukaya Categories
Explore functorial and sheaf-theoretic properties of wrapped Fukaya categories, surveying key results and insights in this advanced mathematical topic.
Function Spaces on Quantum Tori and Their Applications
Explore Sobolev, Besov, and Triebel-Lizorkin spaces on quantum tori, examining their properties and applications in pseudo-differential theory and noncommutative geometry.
Elliptic Cohomology and Enumerative Geometry
Explore the intersection of elliptic cohomology and enumerative geometry, focusing on stable envelopes and their role in understanding q-difference equations.
Dynamical Degrees - #ICBS2024
Explore dynamical degrees, comparing them to other dynamics concepts and delving into key findings using ideas from dynamics, Hodge theory, and geometries.
Measure Rigidity Beyond Homogeneous Dynamics
Explore measure and topological rigidity in dynamical systems beyond homogeneous spaces, examining conditions for rigidity properties on manifolds.
Causal Inference with Mendelian Randomization in Biomedical Studies
Explore Mendelian Randomization for causal inference in biomedical research. Learn innovative methods, overcome challenges, and gain insights into complex disease relationships through simulation and case studies.
The Langlands Project - Connecting Automorphic Forms and Number Theory
Explore the Langlands project's deep connection between automorphic forms and arithmetic, tracing its roots and current challenges in mathematics.
The Chromatic Number of Random Graphs
Explore the chromatic number of random graphs, focusing on lower bounds for G(n,1/2) and its limiting distribution. Discover recent advancements in graph theory and probabilistic methods.
Recent Progress in Random Matrix Theory
Explore recent advancements in random matrix theory, focusing on spectral statistics of normalized adjacency matrices in random d-regular graphs and their eigenvalue rigidity.
Kahler-Einstein Metrics on Fano Manifolds - ICBS 2024
Explore Kahler-Einstein metrics on Fano manifolds, bridging differential and algebraic geometry through singularity formations and recent advancements in the field.
The David-Semmes Problem, Rectifiability, and Harmonic Measure - ICBS 2024
Explore the David-Semmes problem, its solution in codimension one, and its impact on harmonic measure problems. Gain insights into Riesz transforms and n-rectifiability.
Curvature Positivity and $\bar\partial$ Equation with Optimal $L^2$ Estimate - ICBS 2024
Explore recent advancements in multiplier ideal sheaves, multiplier submodule sheaves, and converse L^2 theory. Gain insights into Nakano semipositivity criteria and solutions to Lempert's problem.
Low Moments of Character Sums - ICBS 2024
Explore low moments of character sums, comparing Dirichlet characters to random multiplicative functions and discussing potential applications to non-vanishing.
Open Problems in Diophantine Approximation and Geometry of Numbers
Explore open problems in Diophantine Approximation and Geometry of Numbers, focusing on approximation of subspaces in R^d by rational subspaces and related mathematical concepts.
Geometry and Integers - Connections Between Number Theory and Geometric Structures
Explore connections between non-negative integer sets and diverse geometries, examining functions associated with primitive integer vectors and their relation to convex, toric, and birational geometries.
Magnitude and Path Homology
Explore magnitude and path homology concepts with mathematician Sergei Ivanov, delving into homological algebra, algebraic topology, and simplicial homotopy theory.
Hamiltonicity of Expanders: Optimal Bounds and Applications
Explore optimal bounds and applications of Hamiltonicity in expanders with Nemanja Draganić, delving into extremal and probabilistic combinatorics, Ramsey theory, and theoretical computer science.