A heat kernel is a special kind of math formula that helps scientists and mathematicians study the flow of heat in different objects or systems. Imagine you have a hot pie that you just took out of the oven. If you cut a slice of that pie and put it on a plate, over time the heat from the pie will start to spread out through the slice, making it cooler.
A heat kernel is like a special tool that can help you study how that heat is going to flow through the pie slice over time. It basically takes into account all the different variables that affect the flow of heat, like the temperature of different parts of the pie slice, its size, how thick it is, and so on.
Scientists and mathematicians use heat kernels in a lot of different fields, like physics, engineering, and computer science. They can be used to study things like how heat moves through a building, how heat spreads through a material being used in manufacturing, or even how heat affects the performance of a computer chip.
So, in simple terms, a heat kernel is a tool that helps us understand and predict the flow of heat in different objects or systems, and it can be used in lots of different fields of science and engineering.