 And the purpose of this talk will be to give an introduction to my area of research, and to talk a little bit about the simple problems of this. So the purpose of this area is to determine properties of objects through non-invasive methods. So you're familiar with X-rays or MRIs, these are the kind of things that I would like to talk about. So let me introduce first what is not an inverse problem. Take someone you like, that's my brother. He's not the problem. And since you are supposed to know him well, then he should be familiar with his personality and the problem would be, given the personality, to determine the reactions to stimuli. So he would be annoyed to that pair of brothers in there, comparison recreation. I would expect him to laugh at said Robin movies or to be annoyed or confused by Trump's tweets like that, or his presentation yesterday. So this would be what is not an inverse problem. Now an inverse problem would be the opposite, would be to determine their personality based on their reactions to a list of things. So this puts us in a position to make some questions that could be of interest also to the mathematical case. So the first question that we could possibly ask is the question of uniqueness. So can we have a list of reactions to stimuli that can correspond to do different people? So this is the same as saying if every list corresponds to exactly one possible person. If we get to know this, then we have some hope to ask for the reconstruction problem, which is can we cook up a recipe to produce the personality based on the list of the reactions? OK, so other kind of questions that we can ask about this is which list of these makes sense? I mean, can we find out if a list is what's made by a troll or is it like a valid list or also, I mean, if we know that two lists are similar, for example, they differ only on how people react to Shrek. Then can we say something about their personalities? Do they correspond to similar personalities? And also, for example, we can ask also what can we say when we only have access to some partial information, so to partial data? So suppose we only know the reactions to movies or to books or stuff like that, and this puts us. So all of this was to mention that this is related to the calderon problem. So this question dates back when calderon has an engineer in back in Argentina. And the question is following. So when we have a potato, we have a happy potato. We put some boat touch on the boundary. And then this boat touch induces a boat touch in the inside. And that makes a current flow to the outside of the potato. And so we are only measuring things on the boundary of the potato. And the question is, can we determine the conductivity to the inside? And this has applications to American imaging or geophysics that have been quite successful. Calderon has interested in oil perception when he was an engineer. Other kind of inverse problems are X-rays or MRIs. And I'm going to explain a little bit more about X-rays in a second. So for X-rays, what we have is an object. And we throw some rays and try to capture the information over these lines. And then the deputation, we move the inclinations. And when people like to ask, can we say something about this shape? And this is like the problem that dates back to the 1920s, I think. And this turned out to be very useful in the past century. And if this doesn't make too much sense, for example, think of having a beautiful cake and you're able to slide this cake with a knife. And then after you slide it, you get to know how much piece of it is in your knife. And then the question will be, are you determining the shape of your cake? Thank you very much. That's a great topic.