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

Abstract: In joint work with Brian Lawrence, we show that, assuming standard motivic conjectures (Fontaine-Mazur, Grothendieck-Serre, Hodge, Tate), there is a finite-time algorithm that, on input (K,C) with K a number field and C/K a smooth projective hyperbolic (i.e. genus > 1) curve, outputs C(K). The algorithm has the property that, if it terminates, the output is unconditionally correct --- one uses the conjectures to show that it always terminates in finite time.

On the other hand, in certain cases (i.e. after imposing conditions on K and C) there is an unconditional finite-time algorithm to compute (K,C)\mapsto C(K), using potential modularity theorems instead. Example: given K totally real of odd degree and a\in K^\times, one can effectively compute C_a(K) where C_a : x^6 + 4y^3 = a^2.

I will focus on the first of these two results but will try to mention at least the ideas that go into the second if time permits.

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.

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

Abstract:

We outline a method for reducing diophantine problems over certain infinitely ramified extensions of the p-adic numbers to their characteristic p analogues. More generally, this reduction also applies in the context of first order statements.  The proof uses basic machinery from perfectoid geometry together with an unpublished result by van den Dries.

Motivated by the above reduction, we then report on some work in progress on the characteristic p side. More specifically, motivated by the work of Denef-Schoutens, we address the diophantine problem over Fp[[t]]^{perf} assuming resolution of singularities in positive characteristic.  

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

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

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.

To participate, please email Tommaso Cremaschi or James Farre.

Abstract: In this talk I will state the Margulis Superrigidity Theorem and explain how one can obtain the Margulis Arithmeticity Theorem from it. I will then discuss how this method of proof was applied by Bader, Fisher, Miller, and Stover in their recent paper Arithmeticity, Superrigidity and Totally Geodesic Submanifolds to show that arithmeticity follows from their superrigidity result.

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

This mini course is an introduction to the theory, computation, and applications of Picard-Fuchs differential equations.  The main prerequisite is knowledge of basic complex algebraic geometry at the introductory graduate level.  We will develop a thorough understanding, from several different theoretical perspectives, of some of the key examples in the mathematics and physics literature.  This course should be of interest to geometers, model theorists, and physicists alike.

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

Abstract: I will talk about some results obtained by several persons concerning a question of Julia Robinson.

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

After about five years in academia, with NSF grants, a bunch of publications, and a couple of awards for my articles, I realized that the academic life didn’t work for me personally or intellectually. So, I reinvented myself as an industrial mathematician.

I am glad I did I made the transition. I have worked on some very interesting projects in a wide range of fields. I have the enjoyed seeing my work having practical impact. And, I have had great colleagues and get to mentor some very some intelligent and motivated junior staff.

In this discussion, I will share some of my industry experiences, lessons learned about the industrial mindset, and some of the current math problems being tackled today by industry.

To participate in this event, 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

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

Abstract:
I will describe some aspects of joint work with Antoine Ducros (https://arxiv.org/abs/1204.6277) where we define, for the non-archimedean analytic spaces of Berkovich, an analogue of the classical calculus of differential forms and currents on complex analytic manifolds. A first version of the theory appeared on arXiv in 2012, and I will try to emphasize aspects which emerged since we started to revise this still unpublished manuscript. Besides the complex analytic picture which is used as a guide throughout our work, the theory is built on ideas from tropical geometry, a construction of A. Lagerberg on R^n, and on the presence, within non-archimedean spaces, of polyhedral real subspaces (skeleta) on which real calculus can be performed.

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

Abstract: We present new results on the complexity of the classification problem of countable structures and their computational complexity. We show that the elementary bi-embeddability relation on the class of graphs is analytic complete under Borel reducibility by giving a reduction from the bi-embeddability relation on graphs. We then compare the degree spectra with respect to these equivalence relations. The degree spectrum of a countable structure with respect to an equivalence relation E is the set of Turing degrees of structures E-equivalent to it. We show that the degree spectra of structures with respect to bi-embeddability and elementary bi-embeddability are related: Every bi-embeddability spectrum of a graph is the set of jumps of Turing degrees in the elementary bi-embeddability spectrum of a graph.

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

A Deligne Complex for Artin Monoids

(Based on joint work with Rachael Boyd and Ruth Charney)

I will introduce a new geometric construction associated to an Artin monoid. Artin groups are a generalization of braid groups and the Artin monoid is the monoid with the same generators and relations as in the Artin group. In 1995, Charney and Davis introduced the Deligne complex, a CAT(0) cube complex, which they use to prove the K(pi,1) conjecture for FC type Artin groups. In a recent paper, Boyd, Charney and I use Boyd’s construction of a monoid coset for an Artin monoid to create a version of the Deligne complex for an Artin monoid. 

In this talk, I will first discuss Artin monoids, how they differ from Artin groups, and why Artin monoids are interesting objects to study. Then I will outline the construction of the Deligne complex for an Artin monoid. Finally I will discuss some of the geometric properties of this complex that we have derived, including the fact that the Deligne complex of a monoid is always contractible, with a locally isometric embedding into the Deligne complex of the group. 

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

This mini course is an introduction to the theory, computation, and applications of Picard-Fuchs differential equations.  The main prerequisite is knowledge of basic complex algebraic geometry at the introductory graduate level.  We will develop a thorough understanding, from several different theoretical perspectives, of some of the key examples in the mathematics and physics literature.  This course should be of interest to geometers, model theorists, and physicists alike.

To attend this seminar, you must register in advance, by clicking HERE.

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

Abstract: This is work in progress, joint with Nick Ramsey (UCLA).

A conjecture, now disproved by Chernikov, Hrushovski, Kruckman, Krupinski, Pillay and Ramsey, asked whether any group with a simple theory is definably amenable. It is well known that the counting measure on finite fields gives rise to a non-standard counting measure on pseudo-finite fields (the infinite models of the theory of finite fields). It was unknown whether other PAC fields possessed a reasonable measure, and in this talk, we will show that some of them do, although the measure we define does not have all the nice properties of a counting measure when the field is not pseudo-finite.  This result can be used to show that if G is a group definable in an e-free perfect PAC field, then G is definably amenable.

We hope to extend our results to the wider class of bounded perfect PAC fields.

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

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

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

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.

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

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.

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 event, 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