# Persistent Homology

Extra Form
강연자 Gunnar E. Carlsson
소속 Stanford University
date 2014-03-25

Homology is a method for assigning signatures to geometric objects which reects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology devised over the last 10-15 years which extend the methods of homology to samples from geometric objects, or point clouds. We will discuss homology in its idealized form, as well as persistent homology, with examples.

 제목+내용제목내용댓글이름닉네임태그
1. ### Combinatorics and Hodge theory

I will tell two interrelated stories illustrating fruitful interactions between combinatorics and Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter Brändén. They link continuous convex...
Category특별강연 소속미국 프린스턴대 교수, 한국 고등과학원 석학교수 강연자허준이
2. ### 허준이 교수 호암상 수상 기념 강연 (Lorentzian Polynomials)

본격적인 강연은 1:56 부터 시작됩니다. 강연파일은 아래 첨부를 참고하시기 바랍니다. Lorentzian polynomials.pdf
Category특별강연 소속Professor, Stanford University 강연자허준이 교수
3. ### Algebraic surfaces with minimal topological invariants

상산수리과학관 20주년 기념강연
Category특별강연 소속고등과학원 강연자금종해
4. ### A wrapped Fukaya category of knot complement and hyperbolic knot

상산수리과학관 20주년 기념강연
Category특별강연 소속포항공대 강연자오용근
5. ### Regularity of solutions of Hamilton-Jacobi equation on a domain

150902_HYKE.pdf
Category특별강연 소속ENS-Lyon 강연자Albert Fathi
6. ### What is Weak KAM Theory?

The goal of this lecture is to explain and motivate the connection between AubryMather theory (Dynamical Systems), and viscosity solutions of the Hamilton-Jacobi equation (PDE). This connection is the content of weak KAM Theory. The talk sho...
Category특별강연 소속ENS-Lyon 강연자Albert Fathi
7. ### Topological Mapping of Point Cloud Data

One of the important problems in understanding large and complex data sets is how to provide useful representations of a data set. We will discuss some existing methods, as well as topological mapping methods which use simplicial complexes ...
Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
8. ### Structures on Persistence Barcodes and Generalized Persistence

Persistent homology produces invariants which take the form of barcodes, or nite collections of intervals. There are various structures one can imposed on them to yield a useful organization of the space of all barcodes. In addition, there...
Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
9. ### Persistent Homology

Homology is a method for assigning signatures to geometric objects which reects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology...
Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
10. ### Irreducible Plane Curve Singularities

It is very interesting to study what problems can be computed in irreducible plane curve singularities in algebraicgeometry? Then, the aim of this talk is to compute the explicit algorithm for finding the correspondence between the family of...
Category특별강연 소속서울대학교 강연자강정혁
11. ### 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds

Despite of the fact that 4-dimensional manifolds together with 3-dimensional manifolds are the most fundamental and important objects in geometry and topology and topologists had great achievements in 1960's, there has been little known on 4...
Category특별강연 소속서울대학교 강연자박종일
12. ### Queer Lie Superalgebras

The Lie superalgebra q(n) is the second super-analogue of the general Lie algebra gl(n). Due to its complicated structure, q(n) is usually called “the queer superalgebra”. In this talk we will discuss certain old and new results related to t...
Category특별강연 소속Univ. of Texas, Arlington 강연자Dimitar Grantcharov
13. ### Regularization by noise in nonlinear evolution equations

There are some phenomena called "regularization by noise" in nonlinear evolution equations. This means that if you add a noise to the system, the system would have a better property than without noise. As one of examples, I will explain this...
Category특별강연 소속Dep. Math., Kyoto Univ. 강연자Yoshio Tsutsumi
14. ### A New Approach to Discrete Logarithm with Auxiliary Inputs

Let be a cyclic group with generator . The discrete logarithm problem with auxiliary inputs (DLPwAI) is asked to find with auxiliary inputs , ,…, . In Eurocrypt 2006, an algorithm is proposed to solve DLPwAI in when . In this paper, we reduc...
Category특별강연 소속서울대학교 강연자천정희
15. ### Contact topology and the three-body problem

In this talk, we discuss recent work with Albers, Cieliebak, Fish, Frauenfelder, Hofer and Paternain on several aspects of the three body problem. The ultimate goal of this project is to use modern, holomorphic curve techniques to investigat...
Category특별강연 소속서울대학교 강연자Otto van Koert