Tagungen und Workshops zum Thema Zahlentheorie, Arithmetik

Centre of Geometry and Topology at the University of Copenhagen

In this Masterclass, we will learn about the high dimensional cohomology of moduli spaces such as the moduli space of curves, graphs, and lattices. These moduli spaces are classifying spaces of groups such as mapping class groups, automorphism groups of free groups, and arithmetic groups. We will learn about duality groups whose high dimensional cohomology of these moduli spaces is related to the low degree homology groups with twisted coefficients. We will also discuss graph homology and tropical curves.

The masterclass is aimed at advanced graduate students and postdocs with an interest in algebraic topology and geometric group theory. Connections with algebraic geometry and number theory will be mentioned but this is not the primary focus.

Email: patzt@math.ku.dk

Group cohomology, moduli spaces, duality groups, geometric group theory, arithmetic groups

Geometrie und Topologie,    Gruppentheorie

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

There is an age-old relationship between arithmetic and geometry, going back at least to Euclid's Elements. Historically, it has usually been geometry that has been used to enrich our understanding of arithmetic, but the purpose of this workshop is to study the flow of information in the other direction. Namely, how can arithmetic enhance our understanding of geometry? This meeting will bring together researchers from both sides of the partnership, to explore ways to bind the two fields ever closer together.

Kurse und Veranstaltungen für Studenten der Mathematik,    Geometrie und Topologie

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

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.

Kurse und Veranstaltungen für Studenten der Mathematik,    Geometrie und Topologie

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

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

One remarkable development in algebraic number theory over the last two decades is the proof of many cases of the main conjecture of Iwasawa theory for elliptic curves over the rational, leading to spectacular advances on the Birch and Swinnerton-Dyer conjecture. Over the past few years, the methods used to prove these results have been refined to remove some of their hypotheses and extended to other settings, but despite these improvements some important cases remain largely open. This workshop aims to foster new developments in these directions by clarifying the state of the art of the aforementioned results, identifying some of the technical limitations of the current methods, and encouraging the exchange of ideas between participants with different areas of expertise, while also bringing new researchers (recent PhDs and post-docs) in the area up to speed on current methods and results.

The GTA 2021 conference will bring together world class researchers in mathematics and computer science. Its main objectives are to discuss recent advances in the fields of algebraic geometry, number theory and their applications, as well as to foster international collaborations on connected topics. While contributions from all related areas of mathematics and computer science are welcome, particular emphasis will be placed on research interests of our late colleague Alexey Zykin, namely: global fields and abelian varieties; zeta-functions and L-functions; algebraic geometry over finite fields; their applications to cryptography, error-correcting codes, sphere packing, etc.

Algebra,    Geometrie und Topologie

Y-RANT is a (relatively) new conference aimed at postgraduate students and early career researchers in algebraic number theory, promoting discussion and sharing of ideas between members of the community. Participants are strongly encouraged to register to give short talks on their research or other topics of interest. We will do our best to accommodate all participant's talks, however this might not be possible due to time constraints. In addition there will be three keynote talks given by senior researchers in the field.

Algebra,    Kurse und Veranstaltungen für Studenten der Mathematik

The conference ELAZ 2021 will be organised jointly by the Banach Center Institute of Mathematics of the Polish Academy of Sciences, the Polish Mathematical Society, and the Faculty of Mathematics and Computer Science of Adam Mickiewicz University.

ELAZ stands for “Elementare und Analytische Zahlentheorie”, i.e. “Elementary and Analytic Number Theory”. It is a conference series held biannually since the year 2000. It is open to both young and experienced mathematicians, and is well known for its high scientific level. (postponed version of ELAZ 2020)

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

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

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

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.

Gruppentheorie,    Geometrie und Topologie

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

The Functoriality conjectures, formulated by Langlands in 1967, have been a driving force behind much of the work in both Number theory and Representation theory in the last 50 years. This workshop will explore a relatively new approach to the conjectures stemming from Langlands' recent proposal called ``Beyond Endoscopy''. This proposal has since blossomed in the work of many mathematicians and has produced very interesting recent results in several areas of mathematics from algebraic geometry through representation theory to analytic number theory.

Kurse und Veranstaltungen für Studenten der Mathematik,    Algebra

CIRM – Centre International de Rencontres Mathématiques

CONFERENCE

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

The Fields Institute

Spec(Q) is the first conference to celebrate and promote research advances of LGBT2Q mathematicians specialising in algebraic geometry, arithmetic geometry, commutative algebra, and number theory. This conference aims to highlight strong mathematical research in a wide array of algebraic geometry, broadly defined. The conference will feature some plenary talks by world-leading researchers from a range of areas of algebraic geometry. To facilitate new connections across the various threads of algebraic geometry, plenary talks at Spec(Q) will be aimed a general algebro-geometric audience.

Algebra,    Geometrie und Topologie

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