Dalian Winter School on Computational Topology
Date: December 520, 2016
Place: Dalian University of Technology (DUT), Dalian, China
Host: School of Mathematical Sciences, Dalian University of Technology
CoHost: School of Mathematics, Liaoning Normal University
Purpose: The school program will provide with some courses on basic aspects of the computational and applied topology, and some frontier talks on modern results and applications of the theory, to the participants who are interested in the areas of topology and its applications.
Invited Lecturers and Courses:
(1) Oleg Musin (University of Texas Rio Grande Valley, USA)
http://www.utb.edu/vpaa/csmt/math/Pages/Musin.aspx
Course: Introduction to computations in discrete geometry (16 hours)
(2) Frank Lutz (Technical University of Berlin, Germany)
http://page.math.tuberlin.de/~lutz/
Course: Algorithmic problems and triangulations of 3manifolds (10 hours)
(3) Miro Kramar (AIMR, Tohoku University, Japan)
http://www.wpiaimr.tohoku.ac.jp/hiraoka_labo/miroslav/
Course: Introduction to topological data analysis (16 hours)
(4) Anton Nikitenko (Institute of Science and Technology, Austria)
https://ist.ac.at/research/researchgroups/edelsbrunnergroup/
Course: Introduction to computational topology (10 hours)
(5) Alexander Tselikov (Senior data scientist, VimpelCom Ltd., Russia)
Course: Big data: from theory to practice (6 hours)
(6) Matthias Dehmer (UMIT, Austria)
http://www.dehmer.org
Course: Big data and data science (4 hours)
Program and Organizing Committee:
Fengchun Lei, Dalian University of Technology, China; fclei@dlut.edu.cn
Oleg Musin, University of Texas Rio Grande Valley, USA; oleg.musin@utb.edu
Andrey Vesnin, Sobolev Institute of Mathematics, Russia; vesnin@math.nsc.ru
Jie Wu, National University of Singapore, Singapore; matwuj@mus.sdu.sg
Homepage: http://math.dlut.edu.cn/info/1019/5614.htm
Local Organizers:
Fengling Li, email: dutlfl@163.com
Huadong Yu, email: yuhuadong@dlut.edu.cn
Youfa Han, email: hanyoufa@sina.com
Sponsors: The school will be supported in part by Dalian University of Technology and some grants from NSFC.
Contact to: Ms. Fengling Li, email: dutlfl@163.com. Please send the preregistration form (或参会回执) before November 10, 2016. Limited accommodation support is applicable before the deadline to submit the preregistration form.
Program Timetable


MON 
TUE 
WED 
THU 
FRI 
Week 1: December 5 – 9, 2016 
1 
8:009:40 
Miro Kramar (L1, M216) 
Miro Kramar (L2, M209) 
Miro Kramar (L3, M212) 
Miro Kramar (L4, M212) 
Miro Kramar (L5, M209) 
2 
10:0011:40 
Anton Nikitenko (L1, M216) 
Anton Nikitenko (L2, M209) 
Anton Nikitenko (L3, M212) 
Anton Nikitenko (L4, M212) 
Oleg Musin (L1, M312) 
3 
13:3015:10 

Andrey Vesnin (T1, M312) 
Matthias Dehmer (L1,L2, M212) 
Matthias Dehmer (L3,L4, M212) 
Anton Nikitenko (T1, M216) 
4 
15:3017:10 

Jie Wu (T1, M312) 

Shiquan Ren (T1, M213) 
Discussion (M209) 
Week 2: December 12 – 16 
1 
8:009:40 
Miro Kramar (L6, , M216) 
Oleg Musin (L3, M209) 
Oleg Musin (L5, M212) 
Frank Lutz (L2, M212) 
Frank Lutz (L3, M209) 
2 
10:0011:40 
Oleg Musin (L2, M216) 
Miro Kramar (L7, M209) 
Frank Lutz (L1, M212) 
Oleg Musin (L7, M212) 
Oleg Musin (L9, M312) 
3 
13:3015:10 
Anton Nikitenko (L5, M212) 
Andrey Vesnin (T2, M312) 
Oleg Musin (L6, M212) 
Miro Kramar (L8, M212) 
Alexander Tselikov (L1, M216) 
4 
15:3017:10 
Miro Kramar (T1, M212) 
Oleg Musin (L4, M312) 
Discussion (M212) 
Oleg Musin (L8, M213) 
Discussion ( M209) 
Week 3: December 19 – 20 
1 
8:009:40 
Frank Lutz (L4, M216) 
Frank Lutz (L5, M209) 



2 
10:0011:40 
Alexander Tselikov (L2, M216) 
Alexander Tselikov (L3, M209) 



3 
13:3015:10 
Frank Lutz (T1, M212) 




4 
15:3017:10 
Alexander Tselikov (T1, M216) 




Venue 
Material Pavilion (材料馆), Main campus of DUT. M216 means Classroom 216 in Material Pavilion, etc. 
Course introduction:
(1) Introduction to computations in discrete geometry (18 hours, given by Oleg Musin):
1) Lecture 1: The kissing number problem and Delsarte's method. Friday, Dec 9, 10:00  11:40.
2) Lecture 2: Introduction to Computational Geometry. The point location problem. Monday, Dec 12, 10:00  11:40.
3) Lecture 3: Voronoi diagrams, Delaunay triangulations and their applications. Tuesday, Dec 13, 8:00  9:40.
4) Lecture 4: Optimal properties of the Delaunay triangulation. Tuesday, Dec 13, 15:30  17:10.
5) Lecture 5: Sperner's lemma and envyfree fair divisions. Wednesday, Dec 14, 8:00  9:40.
6) Lecture 6: Extensions of the Sperner  KKM lemma and their applications. Wednesday, Dec 14, 15:30  17:10.
7) Lecture 7: Sphere packings and Tammes' problem. Thursday, Dec 15, 10:00  11:40.
8) Lecture 8: Two  distance sets. Thursday, Dec 15, 15:30  17:10.
9) Lecture 9: Geometrical and topological methods in Image Processing. Discrete analog of the Maxwell  Morse theory. Friday, Dec 16, 10:00  11:40.
(2) Algorithmic problems and triangulations of 3manifolds (10 hours, given by Frank Lutz):
Computational problems in topology typically do not behave as we would expect them to do. For example, standard packages for homology or persistent homology computations extensively use (NPhard) discrete Morse theory as a (fast) preprocessing step to avoid (slow, polynomial time) Smith Normal Form computations. Even worse, the recognition problem for manifolds becomes unsolvable beyond dimension three  yet, in practice, it is rare to ever come across a nonrecognizable manifold.
In this course, we will put the spotlight on
1) fast heuristic procedures to solve NPhard or unsolvable problems in topology;
2) random discrete Morse theory to analyze simplicial complexes;
3) 3manifold and other examples from the library of complicated triangulations.
We will further see that we may encounter an event horizon for standard topological computations. Simple spaces like higherdimensional simplices or higher barycentric subdivisions of spaces suddenly turn into intractable spaces. This puts a limit to topological data analysis.
(3) Introduction to topological data analysis (16 hours, given by Miro Kramar):
Nonlinear dynamical systems play an important role in modeling of various processes in fields ranging from physics, chemistry and biology to many other natural and social sciences. Despite the important role of the nonlinear models and intense efforts of many researchers, the global dynamics of a large number of these models is still far form being properly understood. Our understanding of the dynamics becomes even more tentative if the governing equations are not known and the study of the system is based on the data collected by the experimentalists.
In the first part of this course we will start by introducing problems that can be tackled by using topological data analysis. Then we will explain traditional tools of topological data analysis. We will start by introducing different types of complexes (Czech, Rips, etc.) used for data representation. We will show that under certain conditions, a sampled manifold can be properly reconstructed using the Czech complex. Then we move to the concept of persistent homology. It will allow us to analyze the shape of the data represented by a complex. We will also use persistent homology to quantitatively describe patterns generated by scalar functions. Moreover, we will define a notion of distance between persistence diagrams which quantitatively encodes the differences between the patterns. This will be crucial for our analysis of the dynamics of pattern evolution.
In the second part of this course we will introduce topological methods for analyzing the global attractors of the nonlinear dynamical systems. We will explain how to use Morse decompositions to partition the dynamics into recurrent and gradient like parts. To properly understand the structure of the invariant sets contained inside of the recurrent part we will employ the Conley index theory. We will start by presenting this theory for the dynamical systems given by differential equations. We will focus on the applications and the computational aspects of the theory. Then we will consider its extension to the analysis of the dynamics for the systems observed by experimentalists. This will be demonstrated on the particular problems that were studied by the lecturer over the last years. At the end, we will present some open problems in the field.
(4) Introduction to computational topology (10 hours, given by Anton Nikitenko):
The course is aimed at acquainting the listeners with some of the basic problems and objects of computational topology. We will start with simpler lowdimensional questions concerning graphs, point configurations in the plane and twodimensional manifolds, introducing Voronoi and Delaunay tesselations. We proceed further to shape reconstruction problems in higher dimensions and start by getting to know the important structures used for these purposes: Čech, VietorisRips and Delaunay (also known as Alpha) complexes. We discuss the relevant generalizations of the classical Morse theory to simplicial complexes, due to R. Forman (1998) and U. Bauer and H. Edelsbrunner (2015) and apply them to study the aforemnetioned complexes. Finally we proceed to computational algebraic topology and study homology of simplicial complexes, coming ultimately to the concept of persistent homology, which shows the evolution of the homology of topological space, and its releavce for identifying features of a geometric shape. A part of the course will be devoted to algorithms.
Reference book: H Edelsbrunner,J Harer, "Computational Topology: An Introduction"
(5) Big data: from theory to practice (6 hours, given by Alexander Tselikov):
In these lectures we will concentrate on mathematical and algorithmical aspects of data analysis from classical machine learning techniques invented a decades ago to modern approaches which can be applied to solving practical problems. High performance hardware allows us to use vast knowledge base of algorithms not only for task of regression and classification but to task of processing image, video and natural language processing. More than that accumulated data and open source development strategy give researchers opportunities to improve algorithms and create new approaches. We will also cover some aspects of competitive data analysis area which can be used as an intermediate stage between theory and practice to a quick hypothesis testing.
(6) Big data and data science (4 hours, given by Matthias Dehmer)
Lecture 1: Brief overview on computational network analysis and applications
Lecture 2: Aspects of graph entropy measures
Lecture 3: Interconnections between Big data , data science, and network analysis
Lecture 4: Informationtheoretic graph measures
Title and Abstract of Frontier Talks:
Speaker: Miro Kramar (AIMR, Tohoku University, Japan)
Title: Analysis of time scales in data
Abstract: In this talk we will introduce the methods of topological data analysis. Namely, the persistence diagrams which are a relatively new topological tool for describing and quantifying complicated patterns in a simple but meaningful way. We will demonstrate this technique on patterns appearing in dense granular media. This procedure allows us to transform experimental or numerical data, from experiment or simulation, into a point cloud in the space of persistence diagrams. There are a variety of metrics that can be imposed on the space of persistence diagrams. By choosing different metrics one can interrogate the pattern locally or globally, which provides deeper insight into the dynamics of the process of pattern formation. We will use these metrics to identify the important time scales at which behavior of the system changes. We will also discuss a physical interpretation of these time scales.
Speaker: Frank Lutz (Technical University of Berlin, Germany)
Title: Roundness of grains in cellular microstructures
Abstract: Polycrystalline materials, such as metals, are composed of crystal grains of varying size and shape. Typically, the occurring grain cells have the combinatorial types of 3dimensional simple polytopes, and together they tile 3dimensional space.
We will see that some of the occurring grain types are substantially more frequent than others  where the frequent types turn out to be “combinatorially round”. Here, the classification of grain types gives us, as an application of combinatorial lowdimensional topology, a new starting point for a topological microstructure analysis of materials
Speaker: Anton Nikitenko (Institute of Science and Technology, Austria)
Title: Discrete Morse Theory of PoissonDelaunay Mosaics
Abstract: A classical object of interest in stochastic geometry is a PoissonDelaunay mosaic, which is a Delaunay triangulation of a Poisson distributed point cloud. Using generalized discrete Morse theory, we study expected sizes of PoissonDelaunay complexes with radius bound in R^n and obtain precise values for dimensions up to 4. We also find out that there is, perhaps surprisingly, almost no difference if one takes an nsphere instead of R^n.
Speaker: Andrey Vesnin (Sobolev Institute of Mathematics, Russia)
Talk 1
Title: Computation of hyperbolic volumes for polyhedra and 3manifolds.
Abstract: We will survey basic facts on volumes of hyperbolic polyhedra and 3manifolds. We will present volume computations with the Lobachevsky function for some interesting cases. Examples of equal volume compact and noncompact hyperbolic 3manifolds will be discussed.
Talk 2
Title: Computations with hyperbolic structures: rightangled case.
Abstract: We will discuss hyperbolic 3manifolds which can be decomposed into rightangled polyhedra. We will discuss their volumes, arithmeticity and cohomological rigidity.
Speaker: Jie Wu (National University of Singapore, Singapore)
Title: Braids and Robotics.
Abstract: In this introductory talk, we will discuss topological robotics, braid groups, configuration spaces and their connections to homotopy theory.
Speaker: Alexander Tselikov (Senior data scientist, VimpelCom Ltd., Russia)
Title: BigData: Beyond the hype
Abstract: Can value of big data be significant for whole organization? What limitations of production environment cannot be beaten? We will look into practical use cases of applying big data models in big organization with more than 200 mln clients all around the world.
Speaker: Shiquan Ren (National University of Singapore, Singapore)
Title: The Embedded Homology of Hypergraphs and Applications
Abstract: Hypergraphs are mathematical models for many problems in data sciences. In recent decades, the topological properties of hypergraphs have been studied and various kinds of (co)homologies have been constructed. In this paper, generalizing the usual homology of simplicial complexes, we define the embedded homology of hypergraphs as well as the persistent embedded homology of sequences of hypergraphs. As a generalization of the MayerVietoris sequence for the homology of simplicial complexes, we give a MayerVietoris sequence for the embedded homology of hypergraphs. Moreover, as applications of the embedded homology, we study acyclic hypergraphs and construct some indices for the data analysis of hypernetworks.
Hotel:
1. DUT International Conference Center (DUTICC) (neighbor to the South Gate of DUT), http://hotel.dlut.edu.cn/index_ch.asp
2. Yangguangju Hotel (阳光居宾馆) (close to DUTICC)
Transportation: Taking a taxi is the easiest way from Dalian International Airport, or Dalian Train Station, or Dalian North Train Station, to the hotel, and the taxi fare is about 30, 35, or 45 Chinese Yuan, respectively.
School of Mathematical Sciences
Dalian University of Technology
Updated by December 01, 2016