So don't worry about the title because my message here, my main message is that somehow

we need to look for simplicity in mathematical models.

The previous speaker presented some equations where the equations were the motivation for the,

have the equations were the motivation for doing the work. So, and my research area is

mainly applied the differential equations and I really want to collaborate with people from the

experimental area. So that's why I have this this longest title here and some main partners

from Brazil and also Mats-Jurstrand from the Frau Hofer Chalmers. Chalmers is a Chalmers

University in Sweden that I visited last year. And but other than all these I also worked a

little bit with PDEs, worked and still work in hydrodynamics and hydraulics. And in this

paper for example here, I remember that in the first day of this conference someone presented

something about the shallow water equations but I decided to present you some ideas related to

mathematical modeling of cancer. That is the main thing that I would say that I did in the last

15 years and this including this work here that is under review. So I am also a member of the

Brazilian Society of Applied Mathematics and it's very interesting to say that this society is also

enrolled or it will be probably in the next edition of this conference in San Carlos. That

is a very special place for me because I got my PhD over there in numerical analysis. But here

I'm showing you this book that I wrote after just after finishing my master's degree and

this and also my dissertation had some impact in the motivation of some people to work of this

area of cancer modeling and because of that perhaps some in the exam of admission of this

university they also put a question related to my dissertation and it has everything to do with

modeling what I did. Of course we have the purpose of the modeling. If it's possible

experiments and data, useful data for performing the modeling and somehow the modeling requires

some abstraction and maybe this is a very good way of presenting what we think or what we do

when we are doing modeling. We have something, the object of study that has its own complexities

and we try to keep things simple but still useful. So I was trained as a physicist so the

first thing I think when I'm thinking about modeling or a model in physics is the atomic

model but people from biology for example use animals as a model for example studying cancer

as you see here or also some cell culture to study things in a more even more simple setting

and in mathematics for example we can say that we can model some process for example that evolves

in time using this equation here. Okay it's a very simple equation so it really fits what I want to

show you here that is the simplicity so with that in mind we can also think in epidemiology

if we want and since this is the solution of the previous equation and yeah in the beginning of

this epidemic in Brazil I was just teaching a course on fitting, curve fitting for students

and why not to use this and also we can okay here is another thing related to that the SIR model

but there's an X here also that is not let's say involved in this part of the dynamics we have here

this part of the infected individuals that are symptomatic and some term that accounts for

isolation and I did some work on that too but I just to say something more about simplicity we

can think about this equation here very simple as well but it allows us to measure for example

this constant R or the Boltzmann constant just using not even the exponential but this straight

line here that is the approximation to the first order or if we move for the context of

modeling or cancer modeling we can also have some equation that models cell survival when

the radiation is used but it has another term here and this quadratic term and here it's very

interesting because since the 70s this remained as and it still remains at some sense as a very

good way of performing fittings for this kind of data for this phenomena but until 2015 or

something there was no explanation or something from first principles on how to understand that

after this this papers here and to really to model that in a proper way you have to

understand the phenomena how things are going in this in this effect of radiation and basically

it's the these two parameters alpha and beta can be interpreted as a part of their done of the

effect of the radiation that is known recognized and some other part that is recognized but it's

not repaired so this is was a very interesting contribution of mathematics to this phenomena so