Thursday, July 2, 2015

Re-writing exam essay

Enjoy and life

            Should people sometimes do things that they do not enjoy to doing? To answer this question is important to take in account that living in our society is a complex situation that involves different sort of problems that all people must lead. For instance, all of us have to take medicine to overcome different kind of illness, instead off stay at home and allows that our body fights against with them. On the contrary, people will be fired from their job and their medical insurance is going to be canceled. Indeed, be part of the modern social system imposes to all people a limit to our natural freedom and pushes us to accept some restrictions to our behaviors as a way to be part of it, no matter our level of enjoyment.

             First at all, it is clear that all citizens should work as way to get a minimum level of life quality. If all of us want to eat, rest, have medical assistant, study, or share with someone, we need to do a profitable activity that allows us make money. Economical resources are necessary to do simple things in our life that are impossible to reach without them, as taking a bus to go a restaurant, paying tuition fees to study in a high quality institution, going to the beach, even preparing a lunch or dinner. If you enjoy work you are in a paradise, otherwise you should do it or dead in the way.

            Second, being part of our social system reduces our freedom because of the social and legal rules. All kind of societies needs rules that are necessary to lets us live together. When you are a part of a social structure, you must follow some of norms that come from either the society or legal system. Driving restrictions, taxes, public policies, and other matters are examples about what is the cost of living nowadays. Following rules is vital to do either simple or complex things in our society, that it is an obligation no matter our sense of enjoyment.

            Finally, there is a personal area reserves for our enjoyment that it is not able to be intervened by the society or government. After Declaration of Human Rights and other international instruments, it is admitted for all of us that we can do everything that it is not prohibited by the social system. Kelsen recognizes, in the early 50’s, the existence of a closure rule which allows to all people do as much as they want as long as they fulfill with their social duties. This space is reserved for enjoyment and has fun time.

            To sum up, being part of our reality obligates us to do different activities that are imperative no matter our sense of enjoyment. As we are inside our society, people have to follow some social rules and behaviors that cannot avoid.

Wednesday, July 1, 2015

John's research statement

Research statement

                I am interested in number theory and p-adic analysis. My research focuses on studying the relationships between the pseudo differential equations and the Markov processes. To this end, I have used a lot of techniques from number theory and classical theory of differential equations. Some of the equations that I have studied include the p-adic heat equation and some generalizations of this using homogeneous polynomials instead of the classical laplacian. Furthermore, I have applied the theory of the Igusa’s local zeta function for finding a closed form for the solution of the p-adic heat equation. All these models have attracted people’s attention since the mid 80’s because of their relation with alternative models for quantum mechanics. Also, there is a lot of attention from outside of the mathematics because of the connection with some models in statistical physics. For example, people know that some proteins have very complex hierarchical structures and the setting of p-adic analysis is well suited for this. My long term research agenda is to study a broad class of pseudo differential equations that have a probabilistic interpretation and to use the tools of the side of the equation for obtaining new probabilistic models.