Logic Seminar

Fall 2010

Generally meeting (unless otherwise noted):- UCLA, MS 6943, Chairman's Conference Room, (please note change of room from listed schedule) Fridays, 2-3:30pm.

We will start October 1. Clinton Conley will speak on Indecomposably infinite Borel chromatic number

Abstract: The Borel chromatic number of a graph on a Polish space is the least number of colors needed to color its vertices by a Borel function. Kechris-Solecki-Todorcevic (1999) isolate a graph G_0 which is minimal among graphs with uncountable Borel chromatic number, and ask whether there is an analogous minimal object among graphs of infinite Borel chromatic number. We investigate this question and some refinements. This is joint work with B.D. Miller and A.S. Kechris.

October 8: Isaac Goldbring will speak on Ends of groups from a nonstandard perspective.

Abstract: An important geometric invariant of a finitely generated group is its space of ends. The space of ends of an arbitrary topological space may be intuitively described as the set of "path components at infinity." For proper geodesic spaces, I show how to use the language of nonstandard analysis to make the aforementioned heuristic precise. When this nonstandard characterization is applied to the case of a Cayley graph of a finitely generated group, it becomes easier to perform calculations and prove theorems, as will be illustrated through a few examples. I will end the talk with some ideas for future applications.

October 15: Probably no seminar, in view of the logic meeting at Rutgers over the weekend.

Otober 22, 29: Grigor Sargsyan will speak on On the prewellordering given by mice.

November 5: Adrian Ioana will speak on Cocycle superrigidity for profinite actions of property (T) groups.

November 12, 19: Miodrag Sokic will speak on Ramsey property of finite posets with linear orderings.

November 26, break for thanks giving.

December 3, 10: Matt Foreman will speak on Measure Preserving diffeomorphisms of the torus.

Abstract: In 1931, motivated by physical examples, von Neumann proposed classifying the ergodic measure preserving transformations of standard probability spaces. Much recent work has used the tools of descriptive set theory to show that this is impossible for abstract measure preserving transformations. This talk, which discusses joint work with B. Weiss, extends the anticlassification theorems to the space of measure preserving diffeomorphisms of the 2-torus.