Abstract: For each $f : [0,1] to mathbb{R}^{+}$, consider the relation $E_{f}$
on $[0,1]^{omega}$ defined by
$(x_{n}) E_{f} (y_{n})$ iff $sum_{n < omega} f(|y_{n} - x_{n}|) < infty$.
We study the following problems:
(i) When is $E_{f}$ an equivalence relation?
(ii) Which equivalence relations can be obtained in the form $E_{f}$?
(iii) For what $f,g : [0,1] to [0,1]$ is $E_{f}$ Borel reducible to $E_{g}$?
In our talk, we answer (i), we initiate a study of (ii) and we obtain various
conditions for (iii). In particular, we show that for every
$1 leq p < q < infty$, the partial order $leq_{B}$ of Borel reducibility
on the set of equivalence relations
${ E : E_{Id^{p}} leq_{B} E leq _{B} E_{Id^{q}}}$
is more complicated than expected. For example, it is consistent that every
linear order of cardinality continuum embeds into it.
Monday, November 9th
Paul Ellis (PLEASE NOTE: CHANGE OF ROOM), University of Connecticut
"The classification problem for finite rank dimension groups"
Time: 5:00 PM
Location: Hill 705
Monday, November 2nd
Chloe Perin, Hebrew University
" Induced definable structure on cyclic subgroups of the free group"
Time: 5:00 PM
Location: Hill 525
Abstract: Let C be a cyclic subgroup of a finitely generated free group F.
We show that the intersection of a definable set D in F^n with C^n is in
the Boolean algebra of cosets of subgroups of C^n. In other words, the
definable structure induced by the embedding of C in F is no richer than
the definable structure on C.
We make extensive use of Sela's geometric techniques for studying the
first-order theory of the free group, in particular of his construction
of "formal solutions" to an equation.
Monday, October 26th
Saharon Shelah, Rutgers University/Hebrew University
"Preservation of ultrafilters"
Time: 5:00 PM
Location: Hill 525
Monday, October 19th
Saharon Shelah, Hebrew University/Rutgers University
"Infinitary logics with interpolation III"
Time: 5:00 PM
Location: Hill 525
Monday, October 12th
Saharon Shelah, Rutgers University/Hebrew University
"Infinitary logics with interpolation II"
Time: 5:00 PM
Location: Hill 525
Monday, October 5th
Saharon Shelah, Hebrew University, Rutgers University
"Infinitary logics with interpolation"
Time: 5:00 PM
Location: Hill 525
Monday, September 28th
Scott Schneider, Wesleyan University �
"Borel superrigidity for actions of low rank lattices"
Time: 5:00 PM
Location: Hill 525
Abstract: TBA
Monday, September 21st
Simon Thomas, Rutgers University
"On the number of universal sofic groups II"
Time: 5:00 PM
Location: Hill 525
Abstract: First I will complete the proof that if $CH$ fails, then
there exist $2^{2^{aleph_{0}}}$ universal sofic groups up
to isomorphism. Afterwards I will define the notion of a
sofic group and discuss some of the many open problems in
this area.
Monday, September 14th
Simon Thomas, Rutgers University
" On the number of universal sofic groups"
Time: 5:00 PM
Location: Hill 525
Abstract: If $CH$ fails, then there exist $2^{2^{aleph_{0}}}$
universal sofic groups up to isomorphism. On the other hand,
it is currently not even known whether there exist two
nonisomorphic universal sofic groups if $CH$ holds. (This talk
should be intelligible to anyone who knows the definition of
an ultraproduct. It is not necessary or even helpful to know
the definition of a sofic group.)
This page was last updated on September 16, 2009 at 12:37 pm and is maintained by webmaster@math.rutgers.edu.
