Conferences  >  Mathematics  >  Number Theory, Arithmetic

The Research Institute for Mathematical Sciences (RIMS)

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

Motives were originally introduced by Grothendieck in the sixties to provide a universal source to various cohomology theories of algebraic, geometric and arithmetic nature. The works of Hanamura, Levine and Voevodsky in the nineties, followed by many others, have shed a new light on the subject by introducing triangulated categories of motives and relating them to a newly defined homotopy category of schemes. More recent avatars of motives include the motives with modulus of Kahn, Miyazaki, Saito and Yamazaki or the log-motives of Binda, Park and Østvær, both purposely avoiding A1-invariance.

The Research Institute for Mathematical Sciences (RIMS)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Casa Matemática Oaxaca (CMO)

The Research Institute for Mathematical Sciences (RIMS)

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.

Phone: [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

Algebra,    Geometry and Topology

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

One focus of modern number theory is to study symmetries of numbers that are roots of polynomial equations. Collections of such symmetries are called Galois groups, and they often encode interesting arithmetical information. The theory of Galois representations provides a way to understand these Galois groups and in particular, how they interact with other areas of mathematics. This workshop will investigate how these Galois representations can be put together into families, and search for new arithmetic applications of these families.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

CIRM – Centre International de Rencontres Mathématiques

The purpose of this school is to familiarise advanced Master’s students, Ph.D. students and early career researchers with the central themes of research in arithmetic geometry,and teach them both classical and state-of-the-art tools in the field. The research school is an introduction to the conference SAGA, “Symposium on Arithmetic Geometry and its Applications” and it consists of four 3-day mini-courses, taught by teams of internationally renowned researchers, who are known to be excellent teachers.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

CIRM – Centre International de Rencontres Mathématiques

The conference will focus on the recent developments in arithmetic geometry, its applications and explicit and computational methods in approaching the relevant problems. There will be four main axes around which all talks will be organised: Automorphic forms and moduli spaces; Galois representations: geometric and constructive, modularity; Rational points and obstructions; Effective methods in arithmetic geometry. Leading experts in the field have accepted to contribute to the conference, making it a particularly interesting event.

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,    Geometry and Topology

The conference will report on various aspects of the rapid developments in Number Theory and Arithmetic in the past years. This concerns in particular smooth representation theory, Iwasawa theory, p-adic geometry and p-adic Hodge theory.

CIRM - Jean-Morlet Chair

The theme of the conference will be explicit and computational methods in number theory and arithmetic geometry in a broad sense. The format will include scientific talks as well as time for informal collaboration and for coding projects related to (for example) PARI/GP, SageMath, Magma, OSCAR or the L-Functions and Modular Forms Database.

ICMS - International Centre for Mathematical Sciences

There is a history of fruitful links between low-dimensional topology and number theory, going back at least to Mazur's observation that primes in number rings can be viewed as analogues of knots in a 3-manifold. More recently, the introduction of arithmetic gauge theory by M. Kim and collaborators paves the way to further bring ideas from theoretical physics to bear on fundamental problems in number theory and arithmetic geometry. This conference aims to explore this exciting new direction, and the links between number theory, topology and physics in general, with a particular focus on the role played by gauge fields as a unifying framework.

Geometry and Topology,    Mathematical Physics

CIRM - Jean-Morlet Chair

ln this workshop, we will consider variants of Artin's primitive root conjecture leading to the study of the Galois groups of various radical extensions. Beyond the case of the multiplicative group studied by Lenstra and others, there are now also interesting results for elliptic radicals, and for division points in more general abelian varieties. ln this context, the elliptic analogue of Artin's conjecture is the Lang-Trotter conjecture, which is still open after more than 40 years.

ICMS, The Bayes Centre, Edinburgh

This workshop will bring together leading, as well as early career, researchers on arithmetic statistics and on algorithmic aspects of algebra and number theory, with the aim of fostering collaborations within and between these communities, and to offer early career researchers the opportunity to get a broad overview of the most recent achievements and of the most pressing problems in these fields. The workshop will also celebrate the mathematics of Hendrik W Lenstra Jr.

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.

The field of arithmetic statistics is a fast-moving area of number theory, dealing with distributional results for many basic and important objects: ranks of elliptic curves, central values of L-functions, number fields, modular symbols, orbits of discrete groups etc. The techniques involved come from diverse areas of mathematics e.g. automorphic forms, ergodic theory, spectral theory, dynamical systems, probabilistic number theory, representation theory and random matrix theory. This workshop intends to bring together researchers of all career levels to present their work and exchange ideas and techniques on arithmetic statistics. Motivated by the programme of Mazur and Rubin based on their computational study of elliptic curves over abelian extensions of fixed degree, the meeting will focus on modular symbols, Manin's noncommutative modular symbols, equidistribution of lattice points on the sphere, Heegner points, and closed geodesics, including the error term in the Prime Geodesic Theorem.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

This proposal focuses on new problems and new methods at the interface of harmonic analysis (taken in a very broad sense) and ergodic theory, with applications focused in number theory. A special emphasis is on equidistribution problems on arithmetic symmetric spaces, effective methods in homogeneous dynamics, periods of automorphic forms, families of L-functions over number fields and functions fields, and applications of Fourier uniqueness.

Analysis,    Calculus, Differential Equations and Integration

Hausdorff Center for Mathematic

This school provides an introduction to some of the main topics of the trimester program. It is mainly directed at PhD students and junior researchers.

CIRM - Jean-Morlet Chair

The spring school serves an introduction to the conference "Arithmetic Statistics", and aims to provide PhD students and early stage researchers with the necessary background to enable them to fruitfully partake in the conference. lt will also be an occasion for Master students to have an introduction towards research in number theory.

Courses and Events for Math Students and Early Career Researchers,    Probability and Statistics, Game Theory

CIRM - Jean-Morlet Chair

The theme of the conference is a type of number theory that has become very popular over the last decades, and that is influenced by the possibility of « experimentally » studying arithmetic objects with the help of a computer. Thanks to the wide availability of computer algebra systems, essentially any number theorist nowadays has this possibility at his fingertips. There are concrete objects that are not so easily determined « by hand », such as fundamental units in number fields of higher degree, or Mordell-Weil generators of point groups of elliptic curves, and a first impression of « what these typically look like » is often obtained by numerical experimentation.

Lorentz Center

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.

Algebra,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Interest in specialization of polynomials and Galois groups goes back at least to the work of Hilbert on the inverse Galois problem. This theory has found an abundance of applications in Algebra, Number Theory, Group Theory, and Arithmetic Geometry. In recent years, the area is blooming and we see striking results that open completely new horizons: The discovery of Hilbert irreducibility properties of algebraic groups, its connection with expanders and random walks, the interrelation with arithmetic-geometric properties of parametrizing varieties, and the exciting progress on the Cohen-Lenstra heuristics. The conference aims to bring together leading experts and young researchers interested in the area. We plan to leave an abundance of free time, dedicated to informal discussions. We believe that this will encourage the transfer of ideas, techniques, and will foster new collaborations and new research directions.

Algebra,    Group Theory

Random Matrix Theory (RMT) is ubiquitous in the mathematical and physical sciences because of its broad range of applications and its predictive power, which allow accurate calculations and asymptotic analysis that are not accessible through traditional techniques. The interdisciplinary nature of RMT is epitomized by Prof. Jon Keating’s career, which has been characterized by the rare ability of initiating new areas of research by bringing together areas of mathematics that on the surface have little in common. This conference will feature leading mathematicians working at the interface of quantum chaos, analytic number theory, probability and random matrix theory.

The purpose of this workshop is to honour the 70th birthday of Professor Roger Heath-Brown FRS, which takes place on 12th October 2022. Professor Heath-Brown has been a leading figure in analytic number theory for over fifty years. He has more than 180 publications since 1974, and nearly 3000 citations, by over 1000 authors. These are monumental numbers by the standards of pure mathematics. During the course of his career, Professor Heath-Brown has revolutionised many different branches of analytic number theory, inspiring new generations of number theorists to go further than ever before. His research is studded with gems, whose impact is still reverberating in modern day research.

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

Numerical Analysis and Computational Mathematics,    Geometry and Topology

CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

Algebra,    Geometry and Topology