Notice

GAIA Workshop on Space Tesselation and Packing

posted Sep 14, 2017, 5:25 PM by Eunyoung Choi   [ updated Sep 14, 2017, 5:29 PM ]

GAIA Workshop on Space Tesselation and Packing
 
  •   Period : Sep. 14 ~ 17, 2017       
  •   Venue : KAIST
 

  Objective :
A Voronoi diagram is a tessellation of space into regions based on the distance to a specific subset of the space. Voronoi diagrams arise in nature and have practical and theoretical applications in many fields of science, including biology, polymer physics and informatics. They have been extensively studied in computational geometry for point sites and the Euclidean metric in two dimensions. Voronoi diagrams can be defined for sites other than points, metrics other than Euclidean, and dimensions higher than 2-dimension. For instance, the retraction method used in robot motion planning uses convex distance functions and the autonomous robot navigations find clear routes in the Voronoi diagrams of walls (or obstacles) of the room. POI sites in a city are amidst obstacles (buildings, rivers, etc) and transportation networks (roads, railways). It is not clear how to generalize known results to more general sites under general metrics in 2-or higher dimensions. More research is needed to handle more general Voronoi diagrams.

Packing is a classical geomeric optimization problem in which the shape of a container is predefined (such as a disk, a square, or a rectangle) and we aim to find a smallest container for input objects while the input objects remain disjoint in their interiors. Packing problems have been studied for a long time. It dates back to 1611 when Kepler studied sphere packing in three-dimensional Euclidean space. There has been recent algorithmic progress on packing problem - packing a set of disks into a smallest disk and packing a set of convex polygons into a given axis-parallel rectangle under translations and rigid motions in the plane. There still are, however, many packing problems for more general objects under various transformations in higher dimensions.

There are many other optimization problems in space tessellation and packing. This meeting serves to trigger extensive collaboration on advanced research in this area.

 
 
- Organizers: Otfried Cheong(KAIST), Hee-Kap Ahn(POSTECH),  Christian Knauer(University of Bayreuth)
- Participants

: Till Miltzow(Université Libre de Bruxelles), Herman Haverkort(TU Eindhoven),

Antoine Vigneron(UNIST), Fabian Stehn(University of Bayreuth), Siu-Wing Cheng(HKUST),

Xavier Goaoc(University of Marne-la-Vallée), Hyung-Chan An(Yonsei University),

Eunjung Kim(LAMSADE, CNRS), Raimund Seidel(Saarland University),

Yoshio Okamoto(University of Electro-Communications), Zuzana Patáková(Charles University),

Sangduk Yoon(POSTECH), Eunjin Oh(POSTECH), Édouard Bonnet(Middlesex University),

Taegyoung Lee(KAIST), Yoonsung Choi(KAIST)

Fall workshop on Surface Matching and Space Tessellations

posted Oct 5, 2014, 6:47 PM by dongwoo park   [ updated Nov 30, 2014, 6:04 PM by GAIA _admin ]

Fall workshop on Surface Matching and Space Tessellations


10/31
12:00 - 14:00 Lunch
14:00 - 15:00 Invited Talk 1 - Andreas Holmsen
15:00 - 15:20 Coffee break
15:20 - 16:40 Session 2
16:40 - 17:00 Coffee break
17:00 - 18:00 Invited Talk 2 - Sang Won Bae
18:00 - 20:00 Dinner

11/1
09:00 - 10:00 Invited Talk 2 - Michael Dobbins
10:00 - 10:20 Coffee break
10:20 - 12:00 Session 3 
12:00 - 13:30 Lunch


1)  The intersection of a matroid and an oriented matroid -  Andreas Holmsen

Abstract: 
I will present a combinatorial result about the intersection of a matroid and an oriented matroid which implies, among other things, Barany's colorful Caratheodory theorem. All the necessary notions will be introduced during the talk.  



2) A point in a $nd$-polytope is the barycenter of $n$ points in its $d$-faces. - Michael Dobbins

Abstract:
In this talk I show that for any positive integers $n,d$ and any target point in a $(nd)$-dimensional convex polytope $P$, it is always possible to find $n$ points in the $d$-dimensional faces of $P$ such that the center of mass of these points is the given target point. Equivalently, the $n$-fold Minkowski sum of the $d$-skeleton of $P$ is a copy of $P$ scaled by $n$. This verifies a conjecture by Takeshi Tokuyama, and may be viewed as loosely analogous to Carathéodory's Theorem. The proof uses equivariant topology.

3) Title: Diameters and Radii of Polygons - Sang Won Bae

Abstract: 
Among parameters describing a planar figure are its diameter and radius.
In the literature, the diameter means the maximum distance between any two points in the figure and the radius the minimum of the maximum distance from a point to its farthest point.
Varying the shape of the figure and the distance function on it, the diameter and radius enjoy a variety of flavor and computational complexity.
In this talk, we restrict the planar figure to be a polygon with or without holes,
and mainly consider the shortest path metric in it as the distance function.
Some basic ideas on the diameter and radius in that sense, recent progress in the computational point of view, and open research problems will be discussed.
 
 
*****Poster is Click here.
 
 

"GAIA Spring School on Differential Geometry" for computer scientists

posted May 28, 2012, 5:54 PM by Jihye Jung

- Title : "GAIA Spring School on Differential Geometry" for computer scientists
- Speaker : Kang-Tae Kim (POSTECH Math Department and The SRC-GAIA)
- Place : Math Science Building room 404
- Lecture 1 (2pm- 3:30pm , May 30): Fundamentals of Plane Cuves

The concept of curvature is the central theme of differential geometry. But why is it so important? How was it developed? What can one do with it? All such questions are natural, important and not-so-easy-to-explain-the-answer-of. I will start with an ancient(?!) explanation based upon the concept of "three consecutive
points" of intersection, which can be understood as the triple-root in modern language. Then the powerful and fundamental Mean-Value-Theorem of Calculus will lead us into the concept of curvature. As soon as we
get this "intuitive" understanding, we shall see the lights shed on the differential equation method differential geometry and its interpretation by dynamics. This will be a "gentle" break-in toward the next lecture.
- Lecture 2 (10am-11:30am, May 31): Principal curvatures and Euler's local theory of surfaces

Once the plane curve theory is "understood", it serves as the key to an understanding of the Euler theory. I will explain Leonard Euler's description of surfaces. Then I will introduce how the theory of curves and surfaces was developed in mathematics. Although more modern developments in mathematics tend to take the path of becoming more abstract and ambitious (to encompass everything in their arms),
we shall stay in the concrete questions such as: What (re)constructs the surfaces (on a "screen")? How does one adapt differential geometric (hence continuous) theories to the discrete situations (such as in a
computer)? Honestly, I do not know the answers that can be acceptable to the computer scientists. But I will give a try and I wish to be able to communicate with the audience in the workshop, based upon these lectures.

Correspondence: 안희갑 교수 ((POSTECH, E-mail: heekap@postech.ac.kr, Tel. 279-2387)
 

GAIA Special Lecture Series - William Haboush (University of Illinois)

posted May 9, 2012, 7:24 PM by Jihye Jung   [ updated May 24, 2012, 10:19 PM ]

GAIA Special Lecture Series

Title: 10 Lectures on Algebraic Groups

Speaker: William Haboush (University of Illinois)

Lectures 1,2,3,5,6,10 will be held at Math. Sci. building Rm 404. Lectures 4,7,8,9 will be held at
 
Math. Sci. building Rm 208.
 

 

Date

Lecture 1

2012 May 21 (Mon) 15:00~16:50

Lecture 2

May 23 (Wed) 15:00~16:50

Lecture 3

May 29 (Tue) 15:30~16:50

Lecture 4

May 30 (Wed) 15:00~16:50

Lecture 5

June 4 (Mon) 15:00~16:50

Lecture 6

June 5 (Tue) 15:30~16:50

Lecture 7

June 8 (Fri) 14:00~15:50

Lecture 8

June 11 (Mon) 15:00~16:50

Lecture 9

June 13 (Wed) 15:00~16:50

Lecture 10

June 15 (Fri) 14:00~15:50

             
             Correspondence: 현동훈  
              POSTECH, E-mail: dhyeon@postech.ac.kr Tel. 054-279-2326                                

   

Seminar on Complex Geometric Analysis - GAIA @ POSTECH - May 2012

posted May 9, 2012, 6:39 PM by Jihye Jung   [ updated May 9, 2012, 6:40 PM ]

Seminar on Complex Geometric Analysis - GAIA @ POSTECH - May 2012

5/2 (Wed) 8:30-9:30 p.m.: Sungmin Yoo (POSTECH graduate student): Berman kernel, metric, cuvature and Bergman-Fuchs formulae, (This presentation is part of QE). 106 Math Sci.

 

5/7 (Mon) 8-10 p.m.: Kang-Tae Kim (GAIA & Dept of Math, POSTECH),
Why
-equation and estimates in complex geometric analysis? (Basics for students)—Lecture I,

at the GAIA seminar room), 106 Math Sci bldg.

 

5/14 (Mon) 8-10 p.m.: Kang-Tae Kim (GAIA & Dept of Math, POSTECH),
Why
-equation and estimates in complex geometric analysis? (Basics for students)—Lecture II

at the GAIA seminar room), 106 Math Sci bldg.

 

End of the CGA seminar of Spring semester 2012.

Seminar on Complex Geometric Analysis - GAIA @ POSTECH - April 2012

posted Apr 3, 2012, 1:21 AM by Jihye Jung   [ updated Apr 17, 2012, 5:53 PM ]

Seminar on Complex Geometric Analysis  - GAIA @ POSTECH - April 2012 

                       

4/2 (Mon) 8-10 p.m.: Kang-Tae Kim (GAIA & Dept of Math, POSTECH),
On the almost complex structures, I ; (Basics for students) at the
GAIA seminar room), 106 Math Sci bldg.


4/4 (Wed) 8-10 p.m.: Hyeseon Kim (GAIA of POSTECH),
On the Wermer sets and beyond, at the GaiA seminar room), 106 Math Sci bldg.


4/9 (Mon) 8-10 p.m.: Kang-Tae Kim (GAIA & Dept of Math, POSTECH),
On the almost complex structures, II ; (Basics for students), at the
GaiA seminar room, 106 Math Sci bldg.


4/11(Wed) 8-10 p.m.: Ninh Van Thu (GAIA & Vietnam National University),
Introduction to the Zalcman manifolds , at the GAIA seminar room, 106
Math Sci bldg.

4/21 (Sat) POSTECH-PNU Workshop, at PNU in Busan, Korea.


4/28 (Sat) The Spring Meeting of The Korean Mathematical Society.


4/30 (Mon) 8-10 p.m.: Heungju Ahn (Dept of Math, POSTECH),
On some ∂ ̅-problems, at the GAIA seminar room, 106 Math Sci bldg.
 
 

Seminar on Complex Geometric Analysis - GAIA @ POSTECH - March 2012

posted Mar 16, 2012, 12:05 AM by Jihye Jung   [ updated Apr 6, 2012, 12:04 AM ]

 
 
 
Seminar on Complex Geometric Analysis

GAIA @ POSTECH

March 2012

 

3/5 (Mon) 8-10 p.m.  Kang-Tae Kim (POSTECH), Introduction to Riemannian Geometry, I (Basics); at Rm 106 (GaiA seminar room), Math Sci bldg.

3/9 (Fri) 5-6 p.m. Kang-Tae Kim (POSTECH),Semicontinuity theorems, Department colloquium, Rm 404, Math Sci bldg.

3/12 (Mon) 8-10 p.m. Kang-Tae Kim (POSTECH), Introduction to Riemannian Geometry, II (Basics); at Rm 106 (GaiA seminar room), Math Sci bldg.

3/15 (Thu) 8:30-10:30 p.m. Nikolay Shcherbina (Wuppertal, Germany), On defining functions of strongly pseudoconvex unbounded domains, at Rm 106 (GaiA seminar room), Math Sci bldg.

3/19 (Mon) 8-10 p.m. Sachiko Hamano (Fukushima U., Japan), A representation of reproducing kernel by using spans, at Rm 106 (GaiA seminar room), Math Sci bldg.

3/21 (Wed) 8-10 p.m. Nikolay Shcherbina (Wuppertal Univ., Germany), More on pluri-subharmonic defining functions of unbounded domains, at Rm 106 (GaiA seminar roon), Math Sci bldg..

3/23 (Fri) 5-6 p.m. Nikolay Shcherbina (Wuppertal Univ., Germany), On defining functions of strongly pseudoconvex domains in complex spaces, Department colloquium, at Room 404.

3/26 (Mon) 8-10 p.m. Kang-Tae Kim, Introduction to Riemannian Geometry, III (basics); at Rm 106 (GaiA seminar room), Math Sci bldg.

3/29 (Thu) 8-10 p.m. Liyou Zhang (Capital Normal Univ., Beijing, China), On some recent results in Bergman geometry ; at Rm 106 (GaiA seminar room), Math Sci bldg.
 
 
 

대수기하학 세미나 일정표

posted Feb 28, 2012, 12:06 AM by dongwoo park   [ updated Mar 16, 2012, 12:10 AM by Jihye Jung ]

대한민국과학기술대연합 대국민 서명운동

posted Jan 30, 2012, 12:15 AM by dongwoo park   [ updated Jan 30, 2012, 12:21 AM ]

Visiting positions are open now!

posted Nov 15, 2011, 5:31 PM by dongwoo park   [ updated Mar 16, 2012, 12:21 AM by Jihye Jung ]

The advertisement can be found at the homepages of POSTECH and the Korean Mathematical Society also

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