Research Prospectus
نویسنده
چکیده
I work in geometric group theory, which is the study of groups via the metric spaces on which they act. I use combinatorial, geometric, and topological tools to study the coarse geometry of infinite discrete groups. Coarse geometry is the natural setting for studying discrete groups, since their metric geometry is only well-defined up to bounded distortion. Gromov [65] revolutionized the field by proposing to study groups as if they were manifolds. Central to this program are various coarse notions of curvature, especially Gromov hyperbolicity, which is a coarse analogue of negative sectional curvature. Roughly speaking, a group is hyperbolic if its geodesics behave as if they are in hyperbolic space Hn; for instance, hyperbolic groups admit useful boundaries and analogues of geodesic flows, and hyperbolicity puts strong constraints on their subgroups and cohomology (see [26]). However, many interesting groups are not hyperbolic. This leads to the following natural problem, which has been at the center of an active area of research in geometric group theory and geometric topology for decades:
منابع مشابه
The Hong Kong Baptist University Adapting Kernel-based Methods to Semi-supervised Learning: from Multi-class Svm to Spectral Analysis a Research Prospectus Submitted to the Thesis Committee for Pursuing the Degree of Master of Philosophy Department of Computer Science by Wu Zhili
This prospectus proposes a preliminary research topic about fusing the kernel-based SVM method and the similarity-based spectral clustering into a semi-supervised learning algorithm under the scope of learning from both labeled and unlabeled data. For the past nine months before the prospectus comes out, much effort has been put to extend the bloomed SVM to more practicable multi-class learning...
متن کاملalgebra for digital design derivation 1 Research Prospectus Algebra for Digital Design Derivation
متن کامل
algebra for digital design derivation 1 Research Prospectus Algebra for Digital Design Derivation
متن کامل
Suggested Guidelines for the Preprospectus and Prospectus
Department of Ecology and Evolutionary Biology This document describes suggested guidelines for preparation of the preprospectus and prospectus required for advancement to PhD candidacy in EEB. Prior to writing the preprospectus and prospectus, each student is responsible for obtaining approval from her/his advisor and committee that these suggested guidelines are in accordance with the goals s...
متن کاملStudies of drinking in Jewish culture. II. Prospectus for sociological research on Jewish drinking patterns.
متن کامل
Prospectus 3 i LINKAGE OF MULTISCALE MULTISOURCE MULTI-TIER DATA FOR THE PURPOSES OF REGIONAL ASSESSMENTS AND MONITORING A Research and Outreach Prospectus of Advanced Mathematical, Statistical, and Computational Approaches
G. P. Patil, Mathematical and Environmental Geospatial Statistics and Analysis Department of Statistics, The Pennsylvania State University W. L. Myers, Remote Sensing, Natural Resources, and Software School of Forest Resources, The Pennsylvania State University C. Taillie, Computational Statistics and Stochastics Department of Statistics, The Pennsylvania State University Stephen Rathbun, Depar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016