2018 Jun 13

# Logic Seminar - Nick Ramsey - "Keisler measures in simple theories"

11:00am to 1:00pm

## Location:

Ross 63
Keisler measures were introduced in the late 80's by Keisler but they became central objects in model theory only recently with the development of NIP theories. This led naturally to the question of whether there might be a parallel theory of measures in other tame classes, especially in the simple theories where pseudofinite counting measures supply natural and interesting examples. We will describe some first steps toward establishing such a theory, based on Keisler randomizations and the theory of independence for NSOP1 theories in continuous logic.
2016 Dec 28

# Logic seminar - Matthew Foreman, "Better lucky than smart: realizing a quasi-generic class of measure preserving transformations as diffeomorphisms"

4:00pm to 6:00pm

## Location:

Ross 70
Better lucky than smart: realizing a quasi-generic class of measure preserving transformations as diffeomorphisms.
Speaker: Matthew Foreman
Abstract: In 1932, von Neumann proposed classifying measure preserving diffeomorphisms up to measure isomorphism. Joint work with B. Weiss
shows this is impossible in the sense that the corresponding equivalence relation is not Borel; hence impossible to capture using countable methods.
2017 Dec 06

# Logic Seminar - Daoud Siniora - "Automorphism groups of homogeneous structures"

11:00am to 1:00pm

## Location:

Math 209

A special class among the countably infinite relational structures is the class of homogeneous structures. These are the structures where every finite partial isomorphism extends to a total automorphism. A countable set, the ordered rationals, and the random graph are all homogeneous.
2018 Jan 10

# Logic Seminar - Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

11:00am to 1:00pm

## Location:

Ross 63

The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics. It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more.
A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.
2017 Apr 24

# Logic seminar

Repeats every week every Monday until Sun May 21 2017 except Mon May 01 2017.
12:00pm to 2:00pm

12:00pm to 2:00pm
12:00pm to 2:00pm

## Location:

Ross 63
We will take a close look at the first few steps of the construction of the Bristol model, which is a model intermediate to L[c], for a Cohen real c, satisfying V
eq L(x) for all x.
2018 May 30

# Logic Seminar - Gianluca Paolini - "On the Admissibility of a Polish Group Topology"

11:00am to 1:00pm

## Location:

Ross 63
In [Sh771] Shelah rediscovered an old result of Dudley on the non-admissibility of a Polish group topology on an uncountable free group. Crucial to his proof is a so-called Compactness Lemma for Polish groups, concerning satisfaction of algebraic equations for certain sequences of group elements converging to 0 (in distance).
2017 Mar 01

# Logic seminar - Yair Hayut, "Weak Prediction Principles"

4:00pm to 6:00pm

## Location:

Ross 70
Weak Prediction Principles
Speaker: Yair Hayut
Abstract: Jensen's diamond is a well studied prediction principle. It holds in L (and other core models), and in many cases it follows from local instances of GCH.
In the talk I will address a weakening of diamond (due to Shaleh and Abraham) and present Abraham's theorem about the equivalence between weak diamond and a weak consequence of GCH. Abraham's argument works for successor cardinals. I will discuss what is known and what is open for inaccessible cardinals.
2017 Nov 22

# Logic Seminar - Yair Hayut - "Chang's Conjecture at many cardinals simultaneously"

11:00am to 1:00pm

## Location:

Math 209

Chang's Conjecture is a strengthening of Lowenheim-Skolem-Tarski theorem. While Lowenheim-Skolem-Tarski theorem is provable in ZFC, any instance of Chang's Conjecture is independent with ZFC and has nontrivial consistency strength. Thus, the question of how many instances of Chang's Conjecture can consistently hold simultaneously is natural.

I will talk about some classical results on the impossibility of some instances of Chang's Conjecture and present some results from a joint work with Monroe Eskew.
2018 Apr 11

# Logic Seminar - Shahar Oriel - "The infinite random simplicial complex"

11:00am to 1:00pm

## Location:

Ross 63
This talk will be a review of a paper by Andrew Brooke-Taylor and Damiano Testa
2016 Dec 27

# Special logic seminar - Itaï BEN YAACOV, "Baby version of the asymptotic volume estimate"

10:00am to 12:00pm

## Location:

Shprinzak 102
I'll show how the Vandermonde determinant identity allows us to
estimate the volume of certain spaces of polynomials in one variable
(or rather, of homogeneous polynomials in two variables), as the degree
goes to infinity.
I'll explain what this is good for in the context of globally valued
fields, and, given time constraints, may give some indications on the
approach for the "real inequality" in higher projective dimension.
2018 May 09

# Logic Seminar - Immanuel Benporat - "Arbault sets"

11:00am to 1:00pm

## Location:

Ross 63
Arbault sets (briefly, A-sets) were first introduced by Jean Arbault in the context of Fourier analysis. One of his major results concerning these sets,asserts that the union of an A-set with a countable set is again an A-set. The next obvious step is to ask what happens if we replace the word "countable" by א_1. Apparently, an א_1 version of Arbault's theorem is independent of ZFC. The aim of this talk would be to give a proof (as detailed as possible) of this independence result. The main ingredients of the proof are infinite combinatorics and some very basic Fourier analysis.
2017 Mar 15

# Logic seminar - Rizos Sklinos, "Non-equational stable groups"

4:00pm to 6:00pm

## Location:

Ross 70
Non-equational stable groups.
Speaker: Rizos Sklinos
Abstract: The notion of equationality has been introduced by Srour and further
developed by Pillay-Srour. It is best understood intuitively as a notion
of Noetherianity on instances of first-order formulas. A first-order
theory is equational when every first-order formula is equivalent to a
boolean combination of equations.
Equationality implies stability and for many years these two notions were
identified, as only an "artificial" example of Hrushovski (a tweaked
2017 Nov 08

# Logic Seminar- Itai Ben Yaacov - "Reconstruction for non-aleph0-categorical theories?"

11:00am to 1:00pm

## Location:

Math 209

It is a familiar fact (sometimes attributed to Ahlbrandt-Ziegler, though it is possibly older) that two aleph0-categorical theories are bi-interpretable if and only if their countable models have isomorphic topological isomorphism groups. Conversely, groups arising in this manner can be given an abstract characterisation, and a countable model of the theory (up to bi-interpretation, of course) can be reconstructed.
2018 May 23

# Logic Seminar - Alejandro Poveda Ruzafa - "A Magidor-like study of $C^{(n)}$-cardinals"

11:00am to 1:00pm

## Location:

Ross 63
The notion of reflection plays a central role in modern Set Theory since the descovering of the well-known Lévy and Montague \textit{Reflection principle}. For any $n\in\omega$, let $C^{(n)}$ denote the class of all ordinals $\kappa$ which correctly interprets the $\Sigma_n$-statements of the universe, with parametes in $V_\kappa$.
2018 Mar 21

# Logic Seminar - Jorge Julián Prieto Jara - "Differentially closed fields and quasiminimality"

11:00am to 1:00pm

## Location:

Ross 63

Zilber introduced quasi-minimal classes to generalize the model theory of pseudo exponential
fields. They are equipped with a pregeometry operator and satisfy interesting properties such
as having only countable or co-countable definable sets. Differentially closed fields of
characteristic 0, rich examples of a \omega-stable structures, are good candidates to be
quasiminimal. The difficulty is that a differential equation may have uncountably many
solutions, and thus violate the countable closure requirement of quasiminimal structures.