|Speaker :||1.Prof. Chun-Yen Shen (National Taiwan University) 2.Prof. Jun-Yi Guo (National Taiwan Normal University) 3. Dr. Zhibin Du (Academia Sinica)|
|Title :||1.Erdos distinct distances problem in Euclidean spaces and finite fields 2.On the Complexity of Jelly-no-Puzzle 3.Introduction to properties of some graph invariants|
|Time :||2018-09-14 (Fri) 10:30 - 15:00|
|Place :||Seminar Room 617, Institute of Mathematics (NTU Campus)|
1.Erdos distinct distances problem might be the most famous open problem in the area of discrete geometry. Over the years, many different approaches including combinatorics, harmonic analysis, number theory and algebraic geometry have been found useful to attack this problem. In this talk, we will introduce the history of this famous problem and briefly discuss its recent progress. Moreover, a continuous version of Erdos distances problem, the so-called Falconer distances problem will also be introduced in the setting of Euclidean spaces and finite fields. In particular, we will discuss how the problems are related to Fourier analysis in finite fields.
2.This talk will introduce some kinds of slide puzzles whose movable pieces have different colors with normal gravity. Then we will give a proof that Jelly-no-Puzzle is NP-hard and provide some open problems.
3.A graph invariant is used to analyze the quantitative properties of graphs, it keeps unchanged under any isomorphism of a graph. Most of topics in graph theory are actually the researches on graph invariants. In this talk, we will introduce some interesting properties of several graph invariants.