To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Berkovich space has been an important object in the study of non-Archimedean geometry. More recently, Hrushovski and Loeser have introduced a model-theoretic analogue of this object $\hat{V}$ via model theory of algebraically closed valued fields.  They used it to study the homotopy type of Berkovich spaces. In this talk, we will give an introduction to this object and describe some of my works around it. 

Tea for members and participants of the Decidability, definability and computability in number theory virtual program.

To participate, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

The PA seminar is a learning seminar for early career mathematicians (graduate student and postdocs).  Please only join the seminar if you are an early career mathematician.

Abstract: As we saw in the Minicourse, Property (T) or a-T-menability of a group implies lots of interesting consequences. In this talk, we will recall some properties of Property (T) and a-T-menability. After that, we see what rank 1 Lie group, such as SL2,R and Sp(n,1), has Property (T) or a-T-menability.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

We will discuss the following results, from joint work with R. Miller and C. Hall.

Let p,l,q be rational prime numbers, c a positive integer. Let F_l(t) be a rational function field over a finite field of characteristic l>0. Let v be a discrete valuation on F_l(t), and let U be the completion of F_l(t) under v. Let L be an algebraic extension of Q_p or U such that for any finite subfield K of L containing Q_p (resp. U) we have that ord_q([K:Q_p])<c (resp. ord_q([K:U])<c). Then we will call L a q-bounded extension of a local field.  

Now let F be a function field over a field H of constants embeddable into a q-bounded extension of a local field, where in the case of positive characteristic we assume that H contains F_l(t).  Let m be any function field valuation on F (i.e. m is trivial on H).  Let w in F\H.  Let Q^{alg} be the algebraic closure of Q or F_l(t) in H, and let F^{alg}_w be the algebraic closure of Q^{alg}(w) in F.

1.  If H is henselian or is algebraic over a global field, then the valuation ring of m is existentially definable over F.

2.  For any H as above and any m non-trivial on F^{alg}_w, there exists a subset V_m of F, Diophantine over F and  such that the following conditions are satisfied:

--- If x in V_m, then ord_{m}(x) >= 0.
--- If x in F^{alg}_w, and ord_m(x) >= 0, then x is in V_m.
 
3.  For any H as above, H10 is undecidable over F.

Tea for members and participants of the Decidability, definability and computability in number theory virtual program.

To participate, please register here: https://www.msri.org/seminars/25206

Tea for members and participants of the Random and Arithmetic Structures in Topology program.

To participate, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

There are several ways to code the information of one structure into another. Friedman and Stanley introduced Borel embeddings as a way of comparing classification problems for different classes of structures. A Borel embedding of a class K in a class K’ represents a uniform procedure for coding structures from K in structures from K’. Many Borel embeddings are actually Turing computable. When a structure A is coded in a structure B, effective decoding is represented by a Medvedev reduction of A to B. Harrison-Trainor, Melnikov, Miller, and Montalba’n defined a notion of an effective interpretation of A in B and proved that this is equivalent with the existence of a computable functor, i.e., a pair of Turing operators, one taking copies of B to copies of A, and the other taking isomorphisms between copies of B to isomorphisms between the corresponding copies of A. The first operator gives a Medvedev reduction.

The class of undirected graphs and the class of linear orderings both lie “on top” under Turing computable embeddings. The standard Turing computable embeddings of directed graphs (or structures for an arbitrary computable relational language) in undirected graphs come with uniform effective interpretations. We give examples of graphs that are not Medvedev reducible to any linear ordering, or to the jump of any linear ordering. Any graph can be interpreted in a linear ordering using computable Sigma_3 formulas. Friedman and Stanley gave a Turing computable embedding L of directed graphs in linear orderings. We show that there do not exist L_(omega_1,omega) formulas that uniformly interpret the input graph G in the output linear ordering L(G). This is joint work with J. Knight and S. Vatev.

To attend this seminar, please register here: https://www.msri.org/seminars/25205

Anosov representations are discrete, (almost) faithful representations of word-hyperbolic groups into semisimple Lie groups which generalize the notion of convex cocompactness in rank one. They give discrete subgroups of these Lie groups with good geometric and dynamical properties. One feature they do not allow, which we may want in some applications, is the presence of parabolic elements. Relatively Anosov representations are a further generalization which allow for (certain) parabolic elements. We will introduce the notion, and give examples.

Tea for members and participants of the Decidability, definability and computability in number theory virtual program.

To participate, please register here: https://www.msri.org/seminars/25206

Tea for members and participants of the Random and Arithmetic Structures in Topology program.

To participate, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

I will talk about a new approach to support theory for noncommutative (Hopf) algebras which mirrors Avramov and Buchweitz’ support theory for commutative local complete intersections.  I will explain what this support theory entails for ``noncommutative complete intersections", and relevant examples coming from quantum linear spaces, functions on finite group schemes, and quantum groups.  I will also explain how this support theory is used to classify thick ideals in the associated stable representation categories.  No familiarity with these topics is assumed, and everything in the talk should be explained in relatively basic terms.  This is joint work with Julia Pevtsova.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Following Karl Rubin’s lecture last week we will consider the “relative Diophantine notion”: a field extension L/K is Diophantine Stable for a variety V defined over K if V acquires no new rational points passing from K to L. I will discuss results, heuristics, conjectures related to Diophantine Stability, and especially: applications to Hilbert’s Tenth Problem. This consists of both joint work with Karl Rubin; and also a DDC workshop project with Karl Rubin and Sasha Shlapentokh.

Tea for members and participants of the Decidability, definability and computability in number theory virtual program.

To participate, please register here: https://www.msri.org/seminars/25206

Tea for members and participants of the Random and Arithmetic Structures in Topology program.

To participate, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate, please email Tommaso Cremaschi or James Farre.

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

To attend this seminar, please register here: https://www.msri.org/seminars/25205

To participate in this seminar, please register here: https://www.msri.org/seminars/25206