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.
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.
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.
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.
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.
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.
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 $V_\kappa$.
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
First speaker: Daniel kalmanovich, HU
Title: On the face numbers of cubical polytopes
Abstract:
Understanding the possible face numbers of polytopes, and of subfamilies of interest, is a fundamental question.
The celebrated g-theorem, conjectured by McMullen in 1971 and proved by Stanley (necessity) and by Billera and Lee (sufficiency) in 1980-81, characterizes the f-vectors of simplicial polytopes.
Expansivness is a fundamental property of dynamical systems.
It is sometimes viewed as an indication to chaos.
However, expansiveness also sets limitations on the complexity of a system.
Ma\~{n}'{e} proved in the 1970’s that a compact metric space that
admits an expansive homeomorphism is finite dimensional.
In this talk we will discuss a recent extension of Ma\~{n}'{e}’s
theorem for actions generated by multiple homeomorphisms,
based on joint work with Masaki Tsukamoto. This extension relies on a
