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

By Faltings's Theorem, formerly known as the Mordell Conjecture, a smooth projective curve of genus at least 2 that is defined over a number field K has at most finitely many K-rational points. Votja later gave a second proof. Many authors, including de Diego, Parshin, Rémond, Vojta, proved upper bounds for the number of K-rational points. In this talk I will discuss joint work with Vesselin Dimitrov and Ziyang Gao. We show that the number of points on the curve is bounded as a function of K, the genus, and the rank of the Mordell-Weil group of the curve's Jacobian. We follow Vojta's approach and complement it by bounding the number of "small points" using a new lower bound for the Néron-Tate height.

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

(Joint work with Bertrand Deroin).

Abstract:

A countable group is said to be  left-orderable if it preserves a total order invariant by left multiplication or equivalently if it embeds in the group of homeomorphisms of the line. I'll explain the basics of left orderability, a new perspective in the study of left orderable groups and what is known about left orderability of lattices in Lie groups.

Our main result is that a lattice in a real semi-simple Lie group G of higher rank is left orderable if and only if G is a product of two Lie groups and one factor is the universal covering of SL_2(R). In particular, every lattice in SL_n(R) (if n > 2) is not left orderable. This solves conjectures of Witte-Morris and Ghys.

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.

Abstract:

An isoperimetric profile of a Riemannian manifold is a function that for each positive number $V$ associates the optimal perimeter needed bound a volume equal to $V$. On this talk we'll see how for quasi-Fuchsian 3-manifolds this relates to Renormalized Volume (a studied functional on the deformation space). We will use this relation together with some tools from General relativity (namely the Hawking mass) to prove that, in the appropriate setup, the isoperimetric profile of an almost-Fuchsian 3-manifold stays below the profile of any Fuchsian 3-manifold, and equality occurs if and only if the manifold was Fuchsian to begin with. This is joint work with Celso Viana.

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

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

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