Topology Seminars -
Miami University

Spring 2012

Speaker:

Title:

Abstract: This is a joint work with R. Wilson. We will prove that an arbitrary box product of monotonically normal spaces is discretely generated. In particular, any finite product of monotonically normal spaces is discretely generated. Therefore there exist countable spaces not embeddable into a box product of real lines.

Topology Seminars -
Miami University

Spring 2012

Thursday, January 26, 2012 3:15 pm - Rm 118 BAC

Thursday, January 19, 2012 3:15 pm - Rm 118 BAC

Speaker:

Title:

Abstract: We will give a cycle of talks on topological properties determined to some extent by discrete subspaces of a given space. The first property we are going to talk about is discrete generability which is a convergence property with a flavor of a global one. A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$ there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that discretely generated spaces form a class that contains both Frechet-Urysohn spaces and scattered spaces so discrete generability is a local property with components of a global one. We will present a survey of both recent and old results on discrete generability; the material of the respective lectures is supposed to be sufficient to give a reasonably complete view of the area.

Topology Seminars -
Miami University

Fall 2011

Thursday, November 17, 2011 3:15 pm - Rm 118 BAC

Thursday, November 3, 2011 3:15 pm - Rm 118 BAC

Thursday, October 27, 2011 3:15 pm - Rm 118 BAC

Thursday, October 6, 2011 3:10 pm - Rm 118 BAC

Thursday, September 8, 2011 3:10 pm - Rm 118 BAC

Thursday, September 1, 2011 3:10 pm - Rm 118 BAC

Friday, August 26, 2011 3:10 pm - Rm 118 BAC

Speaker:

Title:

Abstract: We will give a cycle of talks on topological properties determined to some extent by discrete subspaces of a given space. The first property we are going to talk about is discrete generability which is a convergence property with a flavor of a global one. A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$ there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that discretely generated spaces form a class that contains both Frechet-Urysohn spaces and scattered spaces so discrete generability is a local property with components of a global one. We will present a survey of both recent and old results on discrete generability; the material of the respective lectures is supposed to be sufficient to give a reasonably complete view of the area.

Thursday, October 20, 2011 3:15 pm - Rm 118 BAC

Thursday, October 13, 2011 3:15 pm - Rm 118 BAC

Tuesday, September 27, 2011 3:15 pm - Rm 118 BAC

Thursday, September 22, 2011 3:15 pm - Rm 118 BAC

Speaker:

Title:

Abstract: A topological space has ``{\sl countable Noetherian type}'' if it has a base where no element is contained in infinitely many elements of that base. Study of this property goes back to the Russian School of General Topology of the 70-80s (Malykhin, Peregudov and Shapirovskii ${\ldots}$) and was taken up independently by the American School in the 90s. Some fundamental questions about it remain open. For example, if $X^2$ has countable Noetherian type, does $X$ need to have countable Noetherian type too? We will offer some partial answers to this question of Balogh, Bennett, Burke, Gruenhage, Lutzer and Mashburn, both in the positive and in the negative. This definition suggests introducing a cardinal function. Time permitting we will show how this function is related to the Suslin Number (of homogeneous compacta) and present an independence result regarding the value of this function on certain countably supported box products.

This is joint work with Dave Milovich and Menachem Kojman.

Wednesday, October 12, 2011 3:15 pm - Rm 118 BAC

Friday, October 7, 2011 3:15 pm - Rm 118 BAC

Wednesday, September 28, 2011 3:15 pm - Rm 118 BAC

Friday, September 16, 2011 3:15 pm - Rm 118 BAC

Speaker:

Title:

Abstract: In a 1968 paper, John Milnor defined the growth function of a finitely generated group, and asked whether every group has polynomial or exponential growth. Grigorchuk produced the first examples of groups with intermediate growth; that is, he found groups whose growth functions were neither bounded above by polynomials, nor bounded below by exponential functions. Grigorchuk's examples were subgroups of the automorphism group of the infinite rooted binary tree. In Nekrashevych's 2005 monograph, Self-similar groups, he defined the {\sl iterated monodromy group} (IMG) of a post-critically finite complex polynomial. (A polynomial $f$ is {\sl post-critically finite} if the set of forward iterates $f(f(f(f...(f(c))))$ is finite, for each critical point $c$.) The iterated monodromy group of a quadratic post-critically finite polynomial acts on the infinite rooted binary tree, like Grigorchuk's groups. Bux and Perez showed that the iterated monodromy group of $z^{2} + i$ has intermediate growth. This gave the first positive evidence for a conjecture which Bux and Perez attribute to Nekrashevych: If $p(z) = z^{2} + c$ is a post-critically finite quadratic polynomial and $0$ is not a post-critical point of $p$, then IMG$(p)$ has intermediate growth. In this talk (or series of talks), I will confirm this conjecture for two more post-critically finite polynomials. I will make the talks as self-contained as possible. The results come from undergraduate research in SUMSRI that I supervised during the summer.

Thursday, October 6, 2011 3:10 pm - Rm 118 BAC

Thursday, September 8, 2011 3:10 pm - Rm 118 BAC

Thursday, September 1, 2011 3:10 pm - Rm 118 BAC

Friday, August 26, 2011 3:10 pm - Rm 118 BAC

Speaker:

Title:

Abstract: We will give a cycle of talks on topological properties determined to some extent by discrete subspaces of a given space. The first property we are going to talk about is discrete generability which is a convergence property with a flavor of a global one. A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$ there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that discretely generated spaces form a class that contains both Frechet-Urysohn spaces and scattered spaces so discrete generability is a local property with components of a global one. We will present a survey of both recent and old results on discrete generability; the material of the respective lectures is supposed to be sufficient to give a reasonably complete view of the area.

Thursday, September 8, 2011 3:10 pm - Rm 118 BAC

Thursday, September 1, 2011 3:10 pm - Rm 118 BAC

Friday, August 26, 2011 3:10 pm - Rm 118 BAC

Speaker:

Title: