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American Mathematical Society

Diophantine equations are systems of polynomial equations solved over integers or rational numbers. Diophantine geometry is the study of Diophantine equations using ideas and techniques from algebraic geometry. It is one of the oldest subjects of mathematics and the most popular part of number theory connecting it to algebraic geometry.

The goal of this session is to explore recent developments in the theory of arithmetic geometry and with special focus on curves and Jacobian varieties. We intend to bring together mathematicians, working on this area of research, from the USA and from Europe encouraging further cooperation and discussion. We will especially encourage younger mathematicians and graduate students and newcomers in the area.

The session will focus on the following topics, but we will be open and welcoming to talks which do not fall in the list of topics below.

Tél.: [2477607447];     Email.: shaska@risat.org

algebraic curves, Abelian varieties, isogenies, torsion points, Tate modules, heights, weighted heights, height conjectures, Brauer group, K3 surfaces, Kummer varieties, Néron-Tate heights, Minimal models, minimal height, Néron models, Brauer-Siegel theorem, Mordell-Lang conjecture, Mordell-Weil, Bombieri-Lang conjecture, Vojta’s conjecture

Algèbre,    Géométrie et topologie

Mathematical Sciences Research Institute (MSRI)

This workshop will feature expository lectures about current developments in Diophantine geometry. This includes the uniform Mordell—Lang for rational points on curves, the Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

Algèbre,    Géométrie et topologie

CIRM - Jean-Morlet Chair

In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry). The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

In the early 1920s, Emmy Noether introduced the fundamental concept of a Noetherian ring, a notion that has had a remarkably broad impact on mathematics over the last century. In this conference, we celebrate Noether's legacy with research talks from many areas of algebra, broadly construed, including algebraic geometry, commutative algebra, number theory, and representation theory.

Algèbre,    Géométrie et topologie

ICERM

This will be a one-week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time set aside for research and collaboration. This workshop is an activity of the Simons Collaboration 'Arithmetic Geometry, Number Theory, and Computation' and is supported by the Simons Foundation.

Program Staff;     Tél.: [1-401-863-5030];     Email.: info@icerm.brown.edu

Mathématiques numériques,    Géométrie et topologie