Konferenzen zum Thema Zahlentheorie, Arithmetik in den Vereinigten Staaten (USA)

This conference is in the primary algebraic research areas of Michael J. Larsen: Algebraic Number Theory, Arithmetic Geometry and Group Theory. The talks will be aimed at a broad swath of algebraists at all levels. It is our hope to foster interactions across these areas in the spirit of Michael’s own body of work. There will be a contributed talks session (20-30 minutes) for young mathematicians and a professional development workshop.

Algebra,    Geometrie und Topologie

A conference on the interactions between geometry, arithmetic, and groups will be held at the University of Texas, Austin, June 20-24, 2022, celebrating the accomplishments and influences of Alan W. Reid.

Gruppentheorie,    Geometrie und Topologie

Oklahoma State University

The conference is devoted to equidistribution results for algebraic numbers, and more generally, points of small height in various number theoretic settings, with emphasis on applications to arithmetic dynamics.

On April 6, 1972 a young graduate student named Hugh Montgomery and the world-renowned mathematical physicist Freeman Dyson had a conversation in the tearoom at the Institute for Advanced Study which led to a fusion of two disparate fields and an intellectual revolution that is stronger than ever today. Montgomery and Dyson discovered that the zeros of the Riemann zeta-function, important for understanding prime numbers, seem to obey the same distribution patterns as the eigenvalues of large random unitary (or hermitian) matrices, which had been extensively studied by physicists, especially to model the interactions within large atomic nuclei. This stunning connection has held up to extensive numerical and theoretical tests over the intervening years and has been extended to give random matrix models for the low lying zeros of families of L-functions and for the moments and distribution of values of the L-functions in these families and to analogous families over function fields. This conference will bring together 130 mathematical scientists to a meeting that will highlight the progress and the state of the art of results at the nexus of these two fields and will underline the questions most pertinent for further research.

The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.

Kurse und Veranstaltungen für Studenten der Mathematik,    Numerische Analysis

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.

Algebra,    Geometrie und 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.

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. We plan to publish a proceedings volume that will include all of the accepted papers.