Young Towers for Geodesic Flows on Certain Non-Positively Curved Surfaces - ICTP 2021
Explore geodesic flows on non-positively curved surfaces through Young towers, covering history, results, Jacobi fields, and hyperbolic maps with expert Carlos Matheus.
Beyond Lazy Training for Over-parameterized Tensor Decomposition
Explore over-parameterization in tensor decomposition, comparing lazy training and gradient descent approaches. Discover how gradient descent can leverage low-rank data structure beyond lazy training regimes.
An Approach to Assigning Semantics to Persistent Homology Classes
Explore a novel approach to interpreting persistent homology classes in applied settings, overcoming traditional limitations by leveraging comparative measurements against known models.
Hyperbolic Geometry, the Modular Group and Diophantine Approximation - Lecture 1
Explore hyperbolic geometry, modular groups, and Diophantine approximation in this advanced lecture. Delve into fundamental concepts, geodesic flows, and subgroups of SL(2,R), with proofs and examples.
Building Human Intelligence at Scale, to Save the Next Generation from ChatGPT
Innovative approaches to scale human intelligence and education in the era of AI, drawing from game theory and real-world problem-solving experiences across mathematics, pandemic control, and live math education.
Persistence-Based Skeletonization of Images
Explores algorithms for splitting images into convex polygons using topological persistence, including Convex Constrained Mesh and Persistent Resolution-Independent Mesh for edge detection.
Topology of Artificial Neuron Activations in Deep Learning
Explore the topology of artificial neuron activations in deep learning, from image classification to natural language processing, with insights on convolutional neural networks and transformer-based models.
Cell Complex Neural Networks
Exploring neural network computations on cell complexes, generalizing graph neural networks and introducing inter-cellular message passing schemes that consider underlying topology.
RipsNet- Fast and Robust Estimation of Persistent Homology for Point Clouds
Estimating persistence diagrams of point clouds using neural networks for faster, more robust topological analysis. Overcomes computational complexity and sensitivity to outliers in practical applications.
Enabling a Machine to Sense Geometry
Explore how to construct a reach space of kernels on persistent modules, enabling machine intelligence to sense geometry, with applications in synthetic and real scenarios.
Transportation Engineering for Connected and Automated Vehicles
Explore the impact of connected and automated vehicles on transportation engineering, focusing on mathematical challenges and opportunities in this emerging field.
Basic Traffic Models and Traffic Waves
Explore fundamental traffic models and wave phenomena in vehicular flow, examining mathematical concepts crucial for understanding and optimizing autonomous vehicle systems.
Deep Learning of Dynamical Systems for Mechanistic Insight and Prediction in Psychiatry
Explore deep learning techniques for analyzing dynamical systems in psychiatry, uncovering mechanisms, and predicting outcomes using neural and behavioral data from various sources.
Surface Quotient Singularities and Big Cotangent Bundle
Explore hyperbolic properties of surfaces with big cotangent bundle, including the Green-Griffiths-Lang conjecture and a new bigness criterion for orbifold surface resolutions.
Geometry, Topology, Group Actions, and Singularities in the Americas
Explore the intersection of geometry, topology, group actions, and singularity theory in this conference talk, fostering collaboration among experts across the Americas and beyond.
Andras Nemethi- Multivariable Poincaré Series of Complex Singularities
Explore multivariable Poincaré series in complex singularities with Andras Nemethi. Delve into advanced mathematical concepts at the intersection of geometry, topology, and singularity theory.
Semistable Reduction - A Progress Report
Explore recent advancements in resolving singularities of complex varieties, including functorial weak semistable reduction and the proof of the semistable reduction conjecture.
Blow Up Formulae and Invariants II - Dimension Theory
Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.
Integer Optimization for Predictive & Prescriptive Analytics in High Stakes Domains
Explore integer optimization techniques for developing interpretable, robust, and fair decision-tree models to assist high-stakes decision-making in social services and healthcare domains.
Learning for Decision-Making Under Uncertainty - IPAM at UCLA
Explore data-driven methods for uncertainty in decision-making, including mean robust optimization and techniques to reshape uncertainty sets, with applications in portfolio optimization and inventory management.
Bernhard Schölkopf- From Statistical to Causal Learning
Explore the evolution of AI systems, from symbolic to statistical and causal approaches, examining key challenges in machine learning and the role of causality in advancing AI understanding and modeling.