Fall workshop on Surface Matching and Space Tessellations
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
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
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
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
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.
- 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: email@example.com, Tel. 279-2387)
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.
POSTECH, E-mail: firstname.lastname@example.org Tel. 054-279-2326
Complex Geometric Analysis - GAIA @ POSTECH - May 2012
5/7 (Mon) 8-10 p.m.: Kang-Tae Kim (GAIA & Dept of Math, POSTECH),
at the GAIA seminar room), 106 Math Sci bldg.
5/14 (Mon) 8-10 p.m.: Kang-Tae Kim (GAIA & Dept of Math, POSTECH),
at the GAIA seminar room), 106 Math Sci bldg.
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
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.
The advertisement can be found at the homepages of POSTECH and the Korean Mathematical Society also