Geometry of Fundamental Lemmas
نویسندگان
چکیده
These are notes from the (ongoing) Student Seminar on Geometry of Fundamental Lemmas at Columbia University in Fall 2017, which is organized by Chao Li, Yihang Zhu and myself. A program with more detailed information, written by Chao and Yihang, can be found here.
منابع مشابه
Some Lemmas to Hopefully Enable Search Methods to Find Short and Human Readable Proofs for Incidence Theorems of Projective Geometry
Search methods provide short and human readable proofs, i.e. with few algebra, of most of the theorems of the Euclidean plane. They are less succesful and convincing for incidence theorems of projective geometry, which has received less attention up to now. This is due to the fact that basic notions, like angles and distances, which are relevant for Euclidean geometry, are no more relevant for ...
متن کاملFundamental lemmas for the determination of optimal control strategies for a class of single machine family scheduling problems
Four lemmas, which constitute the theoretical foundation necessary to determine optimal control strategies for a class of single machine family scheduling problems, are presented in this technical report. The scheduling problem is characterized by the presence of sequence-dependent batch setup and controllable processing times; moreover, the generalized due-date model is adopted in the problem....
متن کاملA case study in formalizing projective geometry in Coq: Desargues theorem
Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized in the literature, the non-degeneracy conditions lead to long technical proofs. In addition, when considering higher-dimensions, the amount of incidence relations (e.g. point-line, point-plane, line-plane) induce numerous technical lemmas. In this article, we investigate formalizing projective plane geomet...
متن کاملRelative volume comparison theorems in Finsler geometry and their applications
We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
متن کاملGraph removal lemmas
The graph removal lemma states that any graph on n vertices with o(n) copies of a fixed graphH may be madeH-free by removing o(n) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory and computer science. In this survey we discuss these lemmas, focusing in particular on recent improvements to ...
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 2017