Can you say something about solutions "without" finding them?

- 연사: Prof. Hoon Hong
            (Dept. of Math, North Carolina State University)
- 일시: 2012년 5월 2일 (수) 오후 5시
- 장소: 이화-포스코관 강의실 464호

Abstract:
One of main activities in math is "solving" equations. But why do we solve equations? In most cases, it is because we want to know something (properties) about the solutions.

A typical way is to find the solutions first (which is usually hard) and then inspect them to read off the desired properties (which is usually easy). To think about it, it is sort of "wasteful" since the explicit solutions contain much more additional information.
As an analogy, suppose that you just want to get a memory card. Would you buy an expensive laptop computer first and then take out a memory card from it and throw away the laptop?!

Naturally a question arises: Can we determine desired properties of solutions "without" finding the solutions?

This kind of questions were asked and being asked by great mathematician of the past and the present (and will be asked... by you).
In this talk, we will go over a few beautiful results due to great mathematicians of the past such as Sylvester, Sturm, Hermite, Bezout, Cayley, Macaulay, Hilbert, etc and some recent results, as time allows.