Wall-crossing
Wall-crossing happens when a character or object switches from one side of a wall or boundary to the other. Imagine you are playing a game of tag outside, and there is a big wall separating you and your friend. If your friend runs around the wall and tags you from the other side, that is an example of wall-crossing.
Now, in math and physics, wall-crossing refers to a concept where certain mathematical objects called "moduli spaces" change in a particular way as you move around a boundary in your space. To put it simply, a moduli space is a set of possible solutions to a problem. When we talk about wall-crossing in this context, we mean that the set of possible solutions changes when we move around in the space. Just like when your friend crossed the wall, things can look different on the other side.
This concept is important in many fields of science, such as string theory and algebraic geometry, where moduli spaces are used to study complex systems. By understanding how solutions change across boundaries in these spaces, researchers can make predictions about how these systems will behave in different scenarios.
Now, in math and physics, wall-crossing refers to a concept where certain mathematical objects called "moduli spaces" change in a particular way as you move around a boundary in your space. To put it simply, a moduli space is a set of possible solutions to a problem. When we talk about wall-crossing in this context, we mean that the set of possible solutions changes when we move around in the space. Just like when your friend crossed the wall, things can look different on the other side.
This concept is important in many fields of science, such as string theory and algebraic geometry, where moduli spaces are used to study complex systems. By understanding how solutions change across boundaries in these spaces, researchers can make predictions about how these systems will behave in different scenarios.