Konferenzen  >  Mathematik  >  Algebra

The Fields Institute for Research in Mathematical Sciences

Homotopy theory is in the midst of a renaissance as its usefulness in other areas of mathematics is becoming increasingly recognised. From polyhedral products in geometric group theory, to combinatorial methods in group theory, to topological properties of manifolds and spaces of embeddings, to Morava K-theory in symplectic geometry, to simplicial methods in topological data analysis, to a host of applications in mathematical physics - and these name only a few areas of interaction - homotopy theory over the past ten to fifteen years has significantly extended its reach. This program will assemble a wide range of leading experts to discuss the state of the art in current research, both in terms of core fundamental problems and crossover to other areas, and explore exciting new directions.

Banach Center

TU Graz

Algebraic, number theoretic and topological aspects of rings, algebras and polynomials

Zahlentheorie, Arithmetik,    Geometrie und Topologie

University of Southern California, Los Angeles

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

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

We will gather to celebrate and showcase the spectacular advances in algebraic number theory and arithmetic geometry inspired by the vast research program of Henri Darmon.

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to studying a nascent bridge between commutative algebra and symplectic geometry, with an emphasis on developing Macaulay2 software for homological computations at the interface of these two fields. Recent breakthrough work of Hanlon-Hicks-Lazarev and Favero-Huang employs symplectic techniques to build line bundle resolutions over toric varieties, resolving several conjectures in toric geometry and multigraded commutative algebra. These results have illuminated a striking new connection between commutative algebra and symplectic geometry: this workshop will bring together experts in these fields with the goal of increasing our computational power to study the interplay between them.

For many (affine) algebraic varieties appearing in geometric representation theory and algebraic combinatorics, their coordinate algebra admits the structure of a cluster algebra. These algebraic varieties include (in order of increasing generality) the basic affine space, (double) Bruhat cells, positroid varieties, Richardson varieties, and braid varieties. Roughly speaking, this means that the corresponding algebraic variety comes with a collection of coordinate toric charts, with explicit coordinates and transformation rules between the charts that can be codified via quiver combinatorics. Conversely, the quiver and the coordinates can be read from combinatorial and geometric properties of the variety itself, though this is more of an art than a science. The goal of this workshop will be to understand the combinatorics and geometry underlying these cluster structures in the case of braid varieties, which include all of the cases described above and was established quite recently. The combinatorics can be encoded in two very different objects: weaves and 3D plabic graphs. Both appear in a variety of mathematical settings, including Soergel calculus and connections to high-energy physics. These rich combinatorial objects and their ties to other areas of mathematics inspire many questions about braid varieties, their cluster structures, and beyond.

The Institute for Mathematical and Statistical Innovation (IMSI)

This week-long conference is in celebration of the 10-year anniversary of AATRN, the Applied Algebraic Topology Research Network. It will be the first time that AATRN meets in person, bringing together researchers from different backgrounds—mathematics, statistics, computer science, physics, biology, etc. In other words, AATRN will be “geometrically realized” at the Institute for Mathematical and Statistical Innovation in Chicago, USA!

Geometrie und Topologie,    Verbandstreffen für Mathematiker

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

Linear Algebra over finite fields is a building block for several applications including data storage, error detection and correction, and public-key cryptography. These applications enable the security and possibility of our daily digital lives. This workshop aims to expose and engage junior researchers in the foundations and applications of linear algebra over finite fields.

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

The goal of this workshop is to bring together both senior and junior specialists in the fields of almost complex and non-Kähler geometry to present their latest achievements in research. Key topics will include cohomological properties of complex and symplectic manifolds, analytical techniques in non-Kähler geometry, special structures on complex manifolds, deformations of complex objects, topological aspects of complex and symplectic manifolds, and Hodge theory on almost Hermitian manifolds.

Fakultät für Mathematik, Universität Regensburg

The conference is concerned with the theory of computability and complexity over real-valued data. Computability and complexity theory are two central areas of research in mathematical logic and theoretical computer science. Computability theory is the study of the limitations and abilities of computers in principle. Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The classical approach in these areas is to consider algorithms as operating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot represent general real or complex numbers, unless they are rounded. Most mathematical models in physics and engineering, however, are based on the real number concept. Thus, a computability theory and a complexity theory over the real numbers and over more general continuous data structures is needed. Despite remarkable progress in recent years many important fundamental problems have not yet been studied, and presumably numerous unexpected and surprising results are waiting to be detected. Scientists working in the area of computation on real-valued data come from different fields, such as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics and all branches of analysis. The conference provides a unique opportunity for people from such diverse areas to meet, present work in progress and exchange ideas and knowledge.

The topics of interest include foundational work on various models and approaches for describing computability and complexity over the real numbers. They also include complexity-theoretic investigations, both foundational and with respect to concrete problems, and new implementations of exact real arithmetic, as well as further developments of already existing software packages. We hope to gain new insights into computability-theoretic aspects of various computational questions from physics and from other fields involving computations over the real numbers.

Informationstheorie und Grundlagen der Informatik,    Zahlentheorie, Arithmetik

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

Banach Center

Since its origins in the work of Sophus Lie (now more than a century ago), Lie theory has seen tremendous developments and is now fundamental in many areas of mathematics (like group theory, geometry, symmetric spaces etc) and physics (quantum mechanics, particle physics, theory of gravity). Nowadays there are specialized computer packages such as LiE, the Atlas project, the package Chevie for GAP3, the program ChevLie. Also the more general purpose computer algebra systems GAP4, MAGMA and SageMath have large libraries for dealing with various objects that are central to Lie theory.

The conference aims at bringing the eminent Number Theorists worldwide in the domain of Algebraic Number Theory and young scholars from the country on a common platform to project their work, and foster collaborations to further the development of Mathematical Research.

The areas of particular interest include: Ideal class groups of number fields (algebraic, analytic and computational aspects), Relative class numbers of number fields, Annihilators of class groups, Class field theory, Picard groups, Selmer groups, Diophantine equations, Elliptic curves, Iwasawa Theory, Modular forms and related topics.

Zahlentheorie, Arithmetik,    Gruppentheorie

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to further developing the method of flag algebras and its applications. Flag algebras, developed by Razborov in 2007, allows one to solve problems in combinatorics via streamlined calculations that combine elements from computer engineering and optimization. It led to many recent breakthroughs on long-standing open problems of Erdős, Sós, Turán, Gromov and Zarankiewicz, to name a few. The technique is versatile and can be applied in other settings than graphs and hypergraphs including permutations, oriented graphs, point sets, embedded graphs, and phylogenetic trees.

American Mathematical Society

This 2-day special session will be dedicated to a range of mathematical problems related to motion planning algorithms and their properties. A central role is played by the notion of topological complexity (TC), which is a homotopy invariant depending only on the configuration space of the robot that can be studied using diverse tools from a variety of fields, such as geometry, topology, algebra, combinatorics, etc. This session will include talks on a variety of topics from algebraic topology, geometric topology, and topological robotics, though most will focus on (sequential) topological complexity, Lusternik–Schnirelmann category, robot motion planning problems, and homotopy invariants related to (or analogous to) sectional category. The session aims to bring together scientists from all over the world working on different aspects of motion planning and TC and foster collaboration among them, expose graduate students and junior colleagues to these rich and fascinating areas of research, and identify directions for future work and interaction in these areas.

Event Organizer;     Email: ekanshjauhari@ufl.edu

topological complexity, LS-category, sectional category, motion planning, robotics, applied algebraic topology

Geometrie und Topologie,    Systemtheorie, Regelung und Automatisierung

The quantum interaction models, with the quantum Rabi model as a representative example, have attracted attention as mathematical models describing the fundamental elements of quantum computers. These models are deeply intertwined with various branches of mathematics, including number theory, representation theory, and combinatorics. This conference aims to provide a platform for leading researchers in these mathematical “hot topics” to present their latest findings, while also fostering interdisciplinary discussions among participants. The conference is held in celebration of Professor Masato Wakayama’s 70th birthday and is jointly organized with Crypto-Math CREST.

Zahlentheorie, Arithmetik,    Graphentheorie und Kombinatorik

The International Conference on Ring Theory, Number Theory and Lie Algebra “In Honor of Ali Benhissi's 60th Birthday” aims to provide a comprehensive overview of recent developments in ring theory, number theory and Lie algebra. This conference will cover each of these three topics individually as well as explore their interactions. This event will foster a collaborative and supportive research environment for all researchers, offering them a unique opportunity to exchange ideas and insights. Participants are strongly encouraged to present their work and contribute to discussions within these topics.

This conference will cover a wide range of topics related to algebra, with a particular focus on the following areas: Commutative algebra, Ring Theory, Algebraic and Analytic Number Theory, Algebraic Topology, Lie Algebra

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to studying arithmetic dynamics of multiple maps. In classical arithmetic dynamics, we consider the iteration of a single endomorphism of a variety defined over a field of arithmetic interest — typically a number field or the function field of a curve. An exciting new direction in arithmetic dynamics that holds particular promise for striking new results is what we call "dynamics of multiple maps": dynamical behavior arising from the interaction of two or more endomorphisms on the same space. This includes iteratively applying rational functions on P1 chosen at random from a family according to some probability distribution; a correspondence from a variety X to itself; and forming words from a non-commuting family of involutions on a K3-surface.

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

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

Webs are diagrammatic tools for representing complex calculations graphically. These diagrams first arose from the representation theory of classical groups, and they have since become important in disparate areas of mathematics. In representation theory, they encode morphisms of quantum groups. In topology, webs give rise to powerful link invariants. In algebra and geometry, Kuperberg's \(mathrm{sl}(3)\) web bases have important relationships with the theory of cluster algebras and affine buildings. In combinatorics, they explain certain dynamics on Young tableaux. Recent work by Gaetz--Pechenik--Pfannerer--Striker--Swanson introduced an \(\mathrm{sl}(4)\) web basis that has exploited and extended exciting connections between webs, plabic graphs, and crystals. There are further connections to total positivity, duality conjectures for cluster algebras and mirror symmetry.

Graphentheorie und Kombinatorik,    Gruppentheorie

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

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

Mathematicians have been studying notions of space and geometry for thousands of years. Over time our models for spaces have grown successively more abstract. A major conceptual leap in the 1960's was taken with the theory of algebraic stacks, which are a sort of space with "internal symmetries'' not visible in usual geometric objects. There has been a flurry of recent activity among mathematical researchers in understanding the structure of these spaces. This workshop will bring together researchers developing this state-of-the-art theory with mathematicians at various career stages who are interested in applying this theory in their work. The organizers hope that this week of focused discussion on this topic will help bring these methods to a wider audience and lead to significant new developments both in the foundations of the theory and in applications.

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

A tensor category is a category with a tensor product that satisfies properties similar to the tensor product of vector spaces. A typical example is given by the representation category of a group with the usual tensor product. While the most important examples of tensor categories arise from representation theory, the theory has outgrown its origins and has emerged into a vast and complex theory on its own, providing a unified language for many phenomena in different fields. Tensor categories are now ubiquitous in areas such as representation theory, invariants of links and 3-manifolds, algebraic geometry, higher category theory, quantum computing and mathematical physics. All in all the abstract theory of tensor categories along with its applications has seen a rapid growth over the last 10 - 20 years.

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

Cluster algebras, webs and canonical bases are three different methods that mathematicians have developed in order the understand the symmetries of certain mathematical structures. Each of these three ways arose from, and has applications to, different areas of mathematics. These areas include algebraic geometry, representation theory, topology, and combinatorics, as well as physics. The goal of this workshop is to bring together experts and up-and-coming researchers from each of these areas in order to better understand the still mysterious connections between cluster algebras, webs, and canonical bases. A better understanding of these connections could allow for ideas from one area to be applied to solve problems in other areas.

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

Core objects of study in algebraic geometry and in commutative algebra are called varieties and rings, respectively. Varieties are geometric objects that consist of sets of solutions to polynomial equations. Each variety has a corresponding ring consisting of the polynomial functions that are defined on the variety.

Graphentheorie und Kombinatorik,    Geometrie und Topologie

Our meeting will bring together researchers in various fields of mathematics such as Geometry, Combinatorics and Algebra. Through scientific talks new directions will be given and open problems will be proposed aiming at new collaborations among the participants.

Geometry, Combinatorics, Commutative Algebra.

Graphentheorie und Kombinatorik,    Geometrie und Topologie

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

Free noncommutative (nc) function theory is an analogue of classical function theory where one replaces functions between two complex vector spaces by functions between square matrices of all sizes over these vector spaces that respect matrix size, direct sums, and similarities. It has emerged in the last decade and a half as a vibrant research area with results that are sometimes similar to and sometimes strikingly different from the classical commutative setting, and with interconnections and applications ranging from free rings and free skew fields to free probability and random matrix theory to dimension independent linear matrix inequalities in systems and control. The purpose of this research in teams is to develop new relations between free probability and nc function theory by launching a systematic investigation and usage of asymptotic integration over classical compact matrix groups and their homogeneous spaces. We expect this to open the road for an asymptotic study of Hardy and Bergmann spaces of nc functions and exhibit completely new phenomena regarding Shilov boundaries and uniqueness sets in the nc setting.

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

This workshop aims at bringing together an interdisciplinary scientific community to share some of the state-of-the-art results in the theory of Herglotz-Nevanlinna functions, and to solve common open problems lying at the frontier of pure mathematics, applied mathematics, physics, and engineering. Further development of this theory would lead to significant progress not only in the area of pure mathematics, but also in its applications to antennas, metamaterials, and composite materials.

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

Higher-rank graphs generalize path categories of directed graphs and are intricately connected to various mathematical disciplines. This workshop aims to illuminate the rich interplay between higher-rank graph C*-algebras and fields such as algebra, theoretical physics, and geometry. By examining how these algebras both influence and are influenced by these diverse areas, the event will provide insights into their broader implications and applications. The workshop will bring together experts from different fields and career stages, each offering a unique perspective on higher-rank graphs. and interactions.

Kurse und Veranstaltungen für Studenten der Mathematik,    Graphentheorie und Kombinatorik