<div dir="ltr">PROXIMO ENCUENTRO: Miércoles 5 de Junio, 12:00hs.<div><span style="font-family:arial,sans-serif;font-size:13px"><br></span></div><div><span style="font-family:arial,sans-serif;font-size:13px">EXPOSITOR: Joseph Miller</span></div>
<div><br></div><div><span style="font-family:arial,sans-serif;font-size:13px">TITULO: </span><span style="font-family:arial,sans-serif;font-size:13px"> </span><span style="font-family:arial,sans-serif;font-size:13px">An introduction to algorithmic randomness</span></div>
<div><span style="font-size:13px;font-family:arial,sans-serif"><br></span></div><div><span style="font-size:13px;font-family:arial,sans-serif">LUGAR: Departamento de Matemática, Aula de</span><span style="font-size:13px;font-family:arial,sans-serif"> seminarios</span><span style="font-size:13px;font-family:arial,sans-serif">, 2do piso, Pabellón 1.</span></div>
<div><br></div><div><span style="font-family:arial,sans-serif;font-size:13px">RESUMEN:</span></div><div><span style="font-family:arial,sans-serif;font-size:13px">Various attempts have been made to give meaning to the idea that an</span><br>
</div><div><div class="gmail_extra"><span style="font-family:arial,sans-serif;font-size:13px">individual binary sequence is random, starting with Von Mises in 1919.</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">He gave the first published axiomatization of probability theory,</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">basing it on a distinguished family of random sequences. The modern</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">approach to defining randomness for individual sequences is rooted</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">Kolmogorov's definition of the complexity of a finite binary string.</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">Kolmogorov complexity is closely related to the most robust notion of</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">randomness for infinite binary sequences, given by Martin-Löf. I will</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">introduce these notions and talk about how they interact with</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">computability theory (my field of study), analysis, and our intuitions</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">about randomness.</span><br></div></div></div>