Survey on stability of algebraic varieties and Kahler geometry.
problem Stability of algebraic varieties and Kahler geometry.
method Survey and lecture notes.
result Discussion of recent developments and open problems.
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48 results for “AMS Summer Research Institute”
These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is to sketch a proof of Giroux correspondence between open book decompositions of t…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
Authors discuss complex and non-Archimedean geometry, proving a conjecture.
problem Proving a version of the Yau--Tian--Donaldson conjecture for Kähler metrics.
method Relation between complex, analytic, and non-Archimedean geometry.
result Sketch of proof for Yau--Tian--Donaldson conjecture.
Geometric Inequalities on Riemannian and sub-Riemannian manifolds by heat semigroups techniquesmath.DG
Heat semigroups used to solve geometric inequalities on manifolds.
problem Finding geometric inequalities on Riemannian and sub-Riemannian manifolds.
method Heat semigroups techniques applied to Riemannian and sub-Riemannian geometry.
result Applications of heat semigroups in geometric inequalities.
Lectures on using randomness in numerical linear algebra.
problem Efficiency and accuracy in solving large linear algebra problems.
method Randomized algorithms for numerical linear algebra.
result Improved efficiency and accuracy in solving large linear algebra problems.
These notes are based on a lecture series given at the Park City Math Institute in the summer of 2013. The notes are intended as a leisurely introduction to the Kähler-Ricci flow on compact Kähler manifolds, aimed at graduate students with some background in differential geometry.
Introduces data ethics for mathematicians, covering background, open data, and privacy.
problem Ensuring ethical use of data in mathematical research and education.
method Overview of data ethics concepts, societal context, and resources.
result Highlights the importance of ethical considerations in data use.
These notes are adapted from two talks given at the 2004 Clay Institute Summer School on Floer homology, gauge theory, and low dimensional topology at the Alfred Renyi Institute. We will quickly review what we do and do not know about the existence and uniqueness of smooth and symplectic structures on closed, simply-co…
The materials accompany a lecture short course presented at the 2011 Park City Mathematics Institute, Graduate Summer School on Moduli Spaces of Riemann Surfaces. The lectures were part of/coordinated with an overall program, including lectures by Ursula Hamenstadt on Teichmueller Theory, Andy Putman on Mapping Class a…
Shai-am simplifies ML for finance, solving code structure and scalability issues.
problem Challenges in integrating ML for investment strategies, including code structure and scalability.
method Integrates a Python framework with modern open-source technologies to manage containerized pipelines and unified interfaces.
result Facilitates collaborative work in quantitative finance by enhancing reusability and readability.
Explains Higgs bundles and their applications in gauge theory.
problem Understanding Higgs bundles and their mathematical properties.
method Introduction to Higgs bundles, Hitchin fibration, and study of subspaces of moduli spaces.
result Different subspaces of Higgs bundles correspond to flat connections and representations.
Paper discusses how financial institutions' model risk management can benefit academic research.
problem Improving academic research process and mitigating limitations.
method Adopting financial institutions' model risk management practices.
result Lessons from financial institutions can enhance academic research reliability.
These are notes from lectures given at the Clay Institute Summer School on "Floer homology, gauge theory and low-dimensional topology" (Budapest, 2004). The first part describes as background some of the geometry of symplectic fibre bundles and their monodromy. The second part, overviewing joint work with Paul Seidel, …
AI+MPS workshop aims to strengthen AI's role in science.
problem AI's potential to enhance scientific discovery and education.
method Proposes activities and strategic priorities to strengthen AI-MPS link.
result AI and science are becoming increasingly intertwined.
The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four lectures deal with conformal geometry and the conformal tractor calculus, taking as p…
Interbank Credit and the Money Manufacturing Process. A Systemic Perspective on Financial Stabilityq-fin.GN
Interbank credit can create money, leading to financial instability.
problem Systemic instability caused by coordination failures in interbank credit.
method Developed a model of interbank credit coordination under minimal institutions, analyzed through simulation.
result Interbank credit can lead to unbound monetary systems and financial instability.
New AM regularization improves both accuracy and robustness.
problem Lack of robustness in deep neural networks.
method Average margin (AM) regularization for margin classifiers or deep neural networks.
result AM regularization can improve both accuracy and robustness to adversarial attacks.
Real-time machine learning predicts AM process temperatures accurately.
problem Accurate prediction of temperature profiles in AM processes for cost-effective design.
method Ensemble of bagged decision trees (extremely randomized trees) for iterative temperature prediction.
result Mean absolute percentage errors below 1% for temperature profile predictions.
On July 26, 1995, at the University of California, Santa Cruz, a young Dutch mathematician by the name Aise Johan de Jong made a revolution in the study of the arithmetic, geometry and cohomology theory of varieties in positive or mixed characteristic. The talk he delivered, first in a series of three entitled "Dominat…
in [2] is zeromath.DG
Corrects a mathematical lemma to show can be zero.
problem A mathematical lemma's constant was incorrectly assumed to be non-zero.
method Demonstrates can be zero by correcting the original lemma.
result The constant in the lemma can be zero, resolving the issue.
Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth manifolds up to diffeomorphism. In these notes, adapted from six lectures given at the …
AM converges super-linearly for solving mixed linear regression problems.
problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.
Expanded tribute to Bernard Maskit in Notices of the AMS.
problem None specified in the abstract
method None specified in the abstract
result None specified in the abstract
The spaces of Riemannian metrics on a closed manifold are studied. On the space of all Riemannian metrics on the various weak Riemannian structures are defined and the corresponding connections are studied. The space of associated metrics on a symplectic manifold is consider…
Model predicts customer churn in financial institutions using neural networks.
problem Manual feature engineering in customer churn prediction.
method Developed a Multi-layer Perceptron model using Artificial Neural Network architecture.
result Artificial Neural Network model achieved comparable performance to Neuro Solution Infinity software.
This paper determines the minimal degree sequence for two compact rational knots, namely the trefoil and figure-eight knots. We find explicit projections with the minimal degree sequence of each knot. This is done by modifying a non-compact rational minimal-degree parameterization of the trefoil and figure-eight knots …
COMP-AMS optimizes distributed training with compressed gradients, achieving similar accuracy with less communication.
problem Efficiently training large-scale models in distributed environments with reduced communication costs.
method Distributed optimization framework using gradient averaging and adaptive AMSGrad, with gradient compression and error feedback.
result COMP-AMS achieves the same convergence rate and linear speedup as standard AMSGrad with less communication.
Survey of methods to visualize neural network features.
problem Understanding neural network activation patterns.
method Activation Maximization and Feature Visualization via Optimization.
result Probabilistic interpretation of AM techniques.
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…
This paper improves speech recognition by using raw waveform signals in multi-span CNN acoustic models.
problem Improving speech recognition accuracy using raw waveform signals.
method Proposes a novel multi-span structure for acoustic modelling based on raw waveform signals with multiple CNN input layers.
result Multi-span acoustic models yield a lower word error rate (WER) than traditional FBANK feature-based models.
The study examines dataset usage patterns in machine learning research.
problem Lack of attention to dataset dynamics in machine learning research.
method Analysis of dataset usage patterns across machine learning subcommunities and time periods (2015-2020).
result Increasing concentration on fewer and fewer datasets, significant adoption from other tasks, and concentration across the field on datasets introduced by elite institutions.
This paper surveys a few aspects of the global theory of wave equations. This material is structured around the contents of a minicourse given by the second author during the CMI/ETH Summer School on evolution equations during the Summer of 2008.
Updates and rewrites a 1974 AMS Memoir on Lie groups.
problem Real reductive Lie groups and their representations.
method Rewriting and updating a 1974 AMS Memoir.
result Ties with recent approaches to geometric realization of unitary representations.
The study allocates income based on journal impact and coauthorship contributions.
problem Inequitable income distribution among co-authors of research papers.
method Uses journal impact factor and coauthorship contribution, applying Cantor's theory and Harmonic Credit Index.
result Develops a model for fair income distribution among authors.
Mostow Rigidity Made Easiermath.GT
Simplified proof of a famous geometry result for students.
problem Mostow Rigidity in geometry and topology
method Self-contained, accessible proof for grad students
result Clean and analytically light proof accessible to students
Deep CNN monitors AM quality with high accuracy.
problem Quality control in AM processes.
method Deep Convolutional Neural Network (CNN) model trained and tested online.
result 94% accuracy and 96% specificity in classifying AM quality.
A distributed framework detects genetic risk factors for Alzheimer's disease across multiple institutions.
problem Privacy concerns in collaborative genetic studies.
method Local Query Model (LQM) and Distributed Enhanced Dual Polytope Projection (D-EDPP) screening rule.
result Successfully learned a consistent model across different institutions without compromising privacy.
A new method identifies key dimensions for function analysis.
problem Limitations in Active Subspaces for high-dimensional functions.
method Active Manifolds (AM) method for functions.
result AM reduces approximation error by an order of magnitude compared to AS.
Improved SincNet for better speaker recognition.
problem Speaker recognition challenges and the need for better deep learning models.
method Proposes AM-SincNet, a SincNet-based model with an improved AM-Softmax layer.
result Improved speaker recognition performance, achieving a 40% Frame Error Rate reduction.
Geometrically convex return risk measures on AM-algebras
problem Quantifying risk in time series analysis
method Extending return risk measures to general ordered vector spaces
result Establishing results on finiteness, continuity, separability, and dual and aggregation-based representations
We build an augmentation of the Masur-Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, . Adapting work of Masur-Minsky, we prove that is quasiisometric to Teichmüller space with the Teichmüller metric. A similar …
Speaker-Independent Speech-Driven Visual Speech Synthesis using Domain-Adapted Acoustic Modelseess.AS
Improved visual speech synthesis using adapted ASR acoustic models.
problem Lack of synchronized audio, video, and depth data for speaker-independent speech-driven visual speech synthesis.
method Adapted an ASR acoustic model trained on audio-only data to the visual speech synthesis domain.
result Viewers significantly prefer animations generated from the adapted ASR acoustic model.
A RL approach optimizes metal AM process parameters for consistent melt pool depth.
problem Optimizing process parameters for metal additive manufacturing to ensure repeatability and control microstructure.
method A Reinforcement Learning (RL) framework based on Q-learning is applied to find optimal laser power and scan velocity combinations.
result The RL framework learns optimal process parameters without prior knowledge, providing a model-free approach.
We discuss here researches on econophysics done from India in the last two decades. The term `econophysics' was formally coined in India (Kolkata) in 1995. Since then many research papers, books, reviews, etc. have been written by scientists. Many institutions are now involved in this research field and many conference…
Course on market microstructure models for students.
problem Market microstructure under asymmetric information.
method Introduction to Kyle model and related filtering, enlargement of filtrations, Markov bridges.
result Introduction and brief overview of advanced financial models.
Notes on a theorem with broad applications in dynamical systems.
problem The Oseledets Multiplicative Ergodic Theorem and its applications.
method Introduction and lectures on the theorem and its generalizations.
result Introduction to the theorem and its applications.