Integer-Valued Gromov-Witten Type Invariants - Guangbo Xu
Explore integer-valued Gromov-Witten type invariants in symplectic geometry, focusing on genus zero cases for symplectic manifolds. Learn about recent developments and their applications in mathematical research.
Introduction to Interpretable Machine Learning - Cynthia Rudin
Explore interpretable machine learning with Cynthia Rudin, covering classification, natural language processing, and decision trees. Gain insights into model complexity and information theory applications.
Singularity Formation for Reduced Models of Fluid Equations - Mimi Dai
Explore singularity formation in reduced fluid equation models, focusing on electron magnetohydrodynamics and its connection to Euler equations. Gain insights into nonlinear dynamics and finite-time singularities.
Combinatorial Invariance: A Case Study of Pure Math / Machine Learning Interaction - Geordie Williamson
Explore the intersection of pure mathematics and machine learning through the lens of combinatorial invariance, featuring insights on neural networks and their application to mathematical conjectures.
Localization Schemes - A Framework for Proving Mixing Bounds for Markov Chains
Explore a unified framework for proving mixing bounds in Markov chains, connecting Spectral Independence and Stochastic Localization techniques through the concept of localization schemes.
A Gentle Approach to Crystalline Cohomology - Jacob Lurie
Explore crystalline cohomology and the de Rham-Witt complex in algebraic geometry, with insights on alternative constructions and applications in positive characteristic fields.
Geometry and Topology of Hamiltonian Floer Complexes in Low-Dimension - Dustin Connery-Grigg
Explore Hamiltonian Floer complexes on surfaces, connecting dynamics to Floer chain structure. Discover a new symplectic norm and geometric interpretations of chain complexes using transverse foliations.
3D Magnetic Field Observations Associated With Filamentary Molecular Clouds - Mehrnoosh Tahani
Exploration of 3D magnetic field observations in filamentary molecular clouds, discussing techniques, results, and implications for understanding cloud morphologies and magnetic field structures.
Non-Uniqueness of Leray Solutions of the Forced Navier-Stokes Equations - Dallas Albritton
Explore non-uniqueness in Navier-Stokes equations, focusing on Leray solutions, unstable manifolds, and vortex dynamics in fluid mechanics.
An Introduction to Lifted Expander Graphs - Fernando Granha Jeronimo
Explore lifted expander graphs, their construction, and applications in theoretical computer science. Learn about symmetry structures, coding theory implications, and recent advancements in this field.
Fluid Equations - Regularity and Kolmogorov’s Turbulence Theory
Explore fluid dynamics, Navier-Stokes equations, and Kolmogorov's turbulence theory. Gain insights into regularity results and mathematical confirmations of phenomenological theories.
The Unbounded Denominators Conjecture - Yunqing Tang
Explore the unbounded denominators conjecture in modular forms, its implications, and a new proof approach using arithmetic algebraization theorem.
Dynamics on Character Varieties - William Goldman
Exploration of dynamical systems arising from locally homogeneous geometric structures and flat connections on manifolds, with focus on character varieties and their complex topology.
Spacetime and Quantum Mechanics; Particles and Strings; Polytopes, Binary Geometries and Quiver Categories - Nima Arkani-Hamed
Explore connections between particle physics and mathematics, revealing how spacetime and quantum mechanics emerge from fundamental mathematical structures in combinatorics, algebra, and geometry.
Locally Testable Codes with Constant Rate, Distance, and Locality, Part I - Irit Dinur
Explore locally testable codes with constant rate, distance, and locality. Learn about a new construction based on left-right Cayley complexes, addressing an open question in coding theory.
An Introduction to Determinantal Point Processes - John C Urschel
Explore determinantal point processes: definition, examples, and applications in random matrix theory, combinatorics, and machine learning. Survey key results and open questions.
Gauge Theory and the Analytic Approach to Geometric Langlands - Edward Witten
Explore gauge theory's role in geometric Langlands correspondence, comparing categorical and analytic approaches through quantum states, operators, and gauge theory interpretations.
An Unexpected Small Divisors Instability in General Relativity - Christoph Kehle
Explore an unexpected instability in general relativity, focusing on small divisors and their impact on predictability and uniqueness in gravitational systems.
Linear Spaces of Matrices - Avi Wigderson
Explore linear spaces of matrices with Avi Wigderson, covering motivations, structural results, algorithms, and open problems in mathematics and computer science.
On the Spatial Restricted Three-Body Problem - Agustin Moreno
Explore the spatial restricted three-body problem, global hypersurfaces, and Hamiltonian return maps. Learn about a higher-dimensional Poincaré-Birkhoff theorem and its applications to orbital dynamics.
Local Dissipation of Energy for Continuous Incompressible Euler Flows - Phillip Isett
Explore continuous solutions to incompressible Euler equations exhibiting local energy dissipation, addressing Onsager's conjecture and its implications for hydrodynamic turbulence.