Logic seminar, Spring 2013
Tuesday, 1/29: Isomorphism types of $\aleph_2$-dense subsets of $\mathbb{R}$, part I
Justin Moore, Cornell University
Wednesday, 1/30: Introduction to countable Borel equivalence relations, part I
Clinton Conley, Cornell University
Tuesday, 2/5: Isomorphism types of $\aleph_2$-dense subsets of $\mathbb{R}$, part II
Justin Moore, Cornell University
Wednesday, 2/6: Countable Borel equivalence relations, part II
Iian Smythe, Cornell University
Tuesday, 2/12: Epistemic game theory
Adam Bjorndahl, Cornell University
Wednesday,2/13: Countable Borel equivalence relations, part III
Iian Smythe, Cornell University
Tuesday, 2/19: Language-based games
Adam Bjorndahl, Cornell University
Wednesday, 2/20: Countable abelian group actions and hyperfinite equivalence relations, part I
Hossein Lamei Ramandi, Cornell University
Tuesday, 2/26: A norm for Tsirelson space
Diana Ojeda Aristizabal, Cornell University
Wednesday, 2/27: Countable abelian group actions and hyperfinite equivalence relations, part II
Hossein Lamei Ramandi, Cornell University
Tuesday, 3/5: Universal locally countable partial orders from recursion theory, and countable Borel equivalence relations
Andrew Marks, Caltech
Wednesday, 3/6: Countable abelian group actions and hyperfinite equivalence relations, part III
Jeffrey Bergfalk, Cornell University
Tuesday, 3/12: A norm for Tsirelson space, part II
Diana Ojeda Aristizabal, Cornell University
Wednesday, 3/13: Group colorings and Bernoulli subflows
Jeffrey Bergfalk, Cornell University
Tuesday, 3/26: Model theory within a subsystem of second-order arithmetic
David Belanger, Cornell University
Wednesday, 3/27: Introduction to the theory of cost
Diana Ojeda Aristizabal, Cornell University
Tuesday, 4/2: Model theory within a subsystem of second-order arithmetic, part II
David Belanger, Cornell University
Wednesday, 4/3: Cost and treeable equivalence relations
Adam Bjorndahl, Cornell University
Tuesday, 4/9: Countable locally nilpotent group actions and hyperfinite equivalence relations
Brandon Seward, University of Michigan
A Borel equivalence relation is hyperfinite if it is the
increasing union of Borel equivalence relations having finite classes. A
long-standing open problem in descriptive set theory asks if Borel actions
of countable amenable groups always induce (via their orbits) hyperfinite
equivalence relations. In this talk I will discuss joint work with Scott
Schneider which shows that this question has a positive answer for free
Borel actions of countable locally nilpotent groups.
Wednesday, 4/10: Local complexity among treeable equivalence relations
Clinton Conley, Cornell University
Group-theoretic rigidity techniques such as Zimmer and Popa cocycle superrigidity
have been instrumental in works of Adams-Kechris, Thomas, and Hjorth (among others)
in realizing complexity in the partial order of Borel reducibility among countable Borel
equivalence relations. We introduce an elementary notion of rigidity which interacts
better with Borel reducibility, allowing us to localize various complexity results
to just above measure hyperfinite in the class of treeable equivalence relations.
This is joint work with Ben Miller.
Tuesday, 4/16: Complicated residually finite groups
Mark Sapir, Vanderbilt University
We give the first examples of computationally complicated
residually finite finitely presented groups. This is a joint work with
Olga Kharlampovich and Alexei Miasnikov.
Wednesday, 4/17: Cost and treeable equivalence relations, part II
David Belanger, Cornell University
Tuesday, 4/23: Borel Complete Sections on Bernoulli Shifts
Su Gao, University of North Texas
Constructions of layered Borel complete sections with regularity properties are important for hyperfiniteness proofs and general study of countable Borel equivalence relations. A classical theorem of Slaman-Steel gives the existence of vanishing layers of Borel complete sections. In this talk I prove a boundedness property for any layered Borel complete sections for the Bernoulli shift on Z. This implies that layered Borel complete sections with certain desirable properties do not exist. This is joint work with Steve Jackson and Brandon Seward.
Wednesday, 4/24: The Gaboriau-Lyons dynamic version of the von Neumann conjecture
Scott Messick, Cornell University
Tuesday, 4/30: A Computability Theoretic equivalent to Vaught's Conjecture.
Antonio Montalbán, UC Berkeley
We find two computability theoretic properties on the models
of a theory T which hold if and only if T is a counterexample to
Vaught's conjecture.
Wednesday, 5/1: The Gaboriau-Lyons dynamic version of the von Neumann conjecture, part II
Scott Messick, Cornell University
Tuesday, 5/7: Algorithmic Randomness via Random Algorithms
Mia Minnes, UC San Diego
Algorithmic randomness defines what it means for a single mathematical object to be random. This active area of computability theory has been particularly fruitful in the past several decades, both in terms of expanding theory and increasing interaction with other areas of math and computer science. Randomness can be equivalently understood in terms of measure theory, Kolmogorov complexity (incompressibility), and martingales.
In this context, we present a novel definition of betting strategies that uses probabilistic algorithms also studied in complexity theory. This definition leads to new characterizations of several central notions in algorithmic randomness and addresses Schnorr's critique, a longstanding philosophical question in algorithmic randomness. Moreover, these techniques have yielded new proofs of complicated separation theorems and suggest new approaches for tackling one of the biggest open questions in the field (KL = ML?). This is joint work with Sam Buss.