Title: Chang's Conjecture (joint with Monroe Eskew)
Abstract:
I will review some consistency results related to Chang's Conjecture (CC).
First I will discuss some classical results of deriving instances of CC from huge cardinals and the new results for getting instances of CC from supercompact cardinals, and present some open problems.
Then, I will review the consistency proof of some versions of the Global Chang's Conjecture - which is the consistency of the occurrence many instances of CC simultaneously.
Speaker: Ron Adin, Bar-Ilan University
Title: Cyclic permutations, shuffles and quasi-symmetric functions
Abstract:
By a theorem of Stanley, the distribution of descent number over all the shuffles of two permutations depends only on the descent numbers of these permutations. For a quantitative version of this result and its cyclic analogue, we use a new cyclic counterpart of Gessel's ring of quasi-symmetric functions, together with an unusual homomorphism and a mysterious binomial identity.
No previous acquaintance assumed.
the spectrum of the existence of a universal model
תמצית/abstract: קיוּם מוֹדל כולל של תורה בעצמה נתוּנה זו שאלה טבעית בתוֹרת המוֹדלים ובתוֹרת הקבוּצוֹת. נטפל בתנאים מספיקים לאי קיוּם, אין צוֹרך בידיעוֹת מוּקדמוֹת.
The existence of a universal model (of a theory T in a cardinal lambda) is a natural question in model theory and set theory. We shall deal with new sufficient conditions for non-existence. No need of previous knowledge
Generic derivations on o-minimal structures Antongiulio Fornasiero
A derivation on a field K is a map d from K to K such that d(x + y) = d(x) + d(y) and d(x y) = x d(y) + d(x) y.
Given an o-minimal structure M in a language L, we introduce the notion L-derivation, i.e derivation compatible with L. For example, if M is the field of reals with exponentiation, then we further require that the derivation d satisfies d(exp x) = exp(x) d(x).
This talk is a survey on results concerning the Teichmuller space of negatively curved Riemannian metrics on M. It is defined as the quotient space of the space of all negatively curved Riemannian metrics on M modulo the space of all isotopies of M that are homotopic to the identity. This space was shown to have highly non-trivial homotopy when M is real hyperbolic by Tom Farrell and Pedro Ontaneda in 2009.
Title: Chang's Conjecture (joint with Monroe Eskew)
Abstract:
I will review some consistency results related to Chang's Conjecture (CC).
First I will discuss some classical results of deriving instances of CC from huge cardinals and the new results for getting instances of CC from supercompact cardinals, and present some open problems.
Then, I will review the consistency proof of some versions of the Global Chang's Conjecture - which is the consistency of the occurrence many instances of CC simultaneously.
We address the semistable reduction conjecture of Abramovich and Karu: we prove that every surjective morphism of complex projective varieties can be modified to a semistable one. The key ingredient is a combinatorial result on triangulating lattice Cayley polytopes. Joint work with Karim Adiprasito and Michael Temkin.
The lecture consists of two parts: first 30 minutes an algebra-geometric introduction by Michael Temkin, and then a one hour talk by Gaku Liu about the key combinatorial result.
The purpose of this talk is to survey several results from Hjorth's theory of turbulent polish group actions.
We will start by discussing certain classification problems associated with Borel equivalence relations, and present the notions of Borel reductions and smooth relations, and the E_0 dichotomy theorem of Harrington-Kechris-Louveau.
For $\kappa < \lambda$ infinite cardinals let us consider the following generalization of the Lowenheim-Skolem theorem: "For every algebra with countably many operations over $\lambda^+$ there is a sub-algebra with order type exactly $\kappa^+$".
We will discuss the consistency and inconsistency of some global versions of this statement and present some open questions.
Model theory and geometry of fields with automorphism
I will review some of the model-theoretic geometry of difference varieties, and some open problems. A difference variety is defined by polynomial equations with an additional operator $\si$ interpreted as a field automorphism.
