Conferences  >  Mathematics  >  Graph Theory and Combinatorics

IAS/Park City Mathematics Institute

Extremal graph theory and Ramsey theory are two of the central branches of modern extremal combinatorics, which seeks to understand the size and structure of discrete objects under certain natural constraints. In this course we will explore these topics, seeing both some of the beautiful techniques developed to study such problems, as well as many innocent-looking problems that seem completely out of reach of the currently-known techniques. We will also see some of the many connections these questions have to other areas of mathematics, including geometry, number theory, probability, and theoretical computer science.

Research Theme: Extremal and Probabilistic Combinatorics

hosted in Haifa, Israel

Enumerative combinatorics is a dynamic subfield of the mathematical sciences with many challenging research problems, ingenious and sophisticated techniques, and important applications in various scientific fields. Questions from a broad range of areas, including algebra, topology, probability, computer science, physical, chemical and biological sciences, have some surprising hidden combinatorial structures that require enumerative methods for their solution.

Alfréd Rényi Institute of Mathematics

Eurocomb, the European Conference on Combinatorics, Graph Theory and Applications, is an academic conference in the mathematical field of combinatorics. Topics include algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, graph theory, ordered sets, random methods, and topological combinatorics.

University of Liverpool

This two day Colloquium aims to bring together researchers in discrete mathematics, from areas such as structural and algorithmic graph theory, extremal combinatorics, logic and foundations of Computer Science. There is a four-hour tutorial on Constraint Satisfaction Problems given by Andrei Krokhin (Durham), nine invited talks, and a session with contributed one slide pitches by junior researchers.

Constraint Satisfaction Problems, Extremal Combinatorics, Structural Graph Theory, Algorithmic Meta Theorems.

Mathematical Logic and Foundations,    Optimization Theory, Operational Research

Organized by: UP FAMNIT - University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies; UP IAM - University of Primorska, Andrej Marušič Institute; SDAMS - Slovenian Discrete and Applied Mathematics Society; IMFM - Institute of Mathematics Physics and Mechanics

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

Probability and Statistics, Game Theory,    Information Theory, Foundations of Computer Science

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

Can machines prove theorems? Can they have mathematical ideas? On one hand, category theory offers a formalism for axiomatising ideas from machine learning. On the other hand, mathematicians are excited about the prospect of utilising machine learning techniques to spot new patterns in vast swathes of combinatorial data and hence formulate new conjectures. The purpose of this workshop is to bring together experts from across algebraic combinatorics, category theory, and machine learning in order to make headway on topics at the intersection of these fields.

AGH University of Krakow, Poland

This will be a subsequent event in the series of conferences organized by the Faculty of Applied Mathematics of AGH University of Krakow.

Email: graphs@agh.edu.pl

Algebraic Graph Theory, Algorithmic Graph Theory, Design Theory, Domination Graph Theory, Extremal Graph Theory, Graphs Colouring, Graph Product, Labelings of Graphs, Probabilistic Methods and Random Graphs.

Sun Yat-sen University, Zhuhai Guangdong, China

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.

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.

Algebra,    Number Theory, Arithmetic

The Latin American Algorithms, Graphs, and Optimization Symposium (LAGOS) is a biennial event that brings together researchers and practitioners from around the world. Since 2001, LAGOS has served as a key forum for the exchange of ideas and collaboration. It is the merger of two Latin American conferences: the Brazilian Symposium on Graphs, Algorithms, and Combinatorics (GRACO) and the Latin American Conference on Combinatorics, Graphs, and Applications (LACGA).

Algorithms and Data Structures,    Optimization Theory, Operational Research

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

This workshop encompasses three major aspects of computation within Representation Theory and Algebraic Combinatorics. One concerns the development of efficient algorithms to compute important quantities in order to understand and classify them better. Such problems include structure constants and representation theoretic multiplicities, mutation invariants in cluster algebras, computing dimensions of coinvariant rings, characters of finite-dimensional representations, coefficients of Kazhdan-Lusztig polynomials, web bases etc. This is closely related to understanding what optimality we could expect and in particular the computational complexity aspects of those problems. Their computational complexity class can also be used to understand the existence of combinatorial interpretations, in particular for major structure constants lacking positive formulas like Kronecker and plethysm coefficients. On the other hand, representation theory has seen important applications within computational complexity theory, in the context of Geometric Complexity Theory and Quantum Information Theory.

Victoria University of Wellington, School of Mathematics and Statistics

The Australasian Combinatorics Conference (ACC) is the annual conference of the CMSA, and covers all areas of combinatorics in mathematics and computer science. Any researchers in these areas are encouraged to attend and contribute a talk.

Organisers;     Email: 47AustCombCon@gmail.com

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.

Group Theory,    Algebra

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

This workshop will bring together researchers working on two fields seemingly at odds, and incompatible: combinatorial geometry and uncertainty. Combinatorial geometry is a field of counting discrete objects, it is about how things are connected, or in general how discrete objects like points, lines, and circles intersect with each other. On the other hand, modeling uncertainty is about not allowing discrete events to happen precisely, or at least not with confidence. It replaces these notions with probabilistic concepts. How can one count geometric objects and their connectivity properties if there is uncertainty in their very existence?

Geometry and Topology,    Probability and Statistics, Game Theory

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

How hard is it to figure out if there is a way to make a set of logical statements true at the same time by choosing appropriate truth values for their variables? This satisfiability problem is of immense importance both theoretically and practically, and lies right at the heart of mathematics and computer science. On the one hand, today so-called Boolean satisfiability (SAT) solvers are routinely and successfully used to solve large-scale real-world formulas in a wide range of application areas (such as hardware and software verification, electronic design automation, artificial intelligence research, cryptography, bioinformatics, operations research, and sometimes even pure mathematics). On the other hand, this problem is believed to be intractable in general --- though proving that this is so is so is one of the famous million dollar Clay Millennium Problems (the P vs. NP problem) --- and there are tiny formulas for which even the very best SAT solvers today fail miserably.

Boolean satisfiability (SAT)

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.

Algebra,    Geometry and Topology

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

In recent years some of the most exciting breakthroughs in Combinatorics on longstanding conjectures have resulted from innovative applications of established techniques to areas where they have not necessarily been used before. We would like to harness the power of collaboration and bring together open-minded participants with different areas of expertise to produce novel research in a number of globally studied areas including. We aspire to create new productive long-term bonds between members of the global community.

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.

Geometry and Topology,    Algebra

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

The proposed workshop focuses on recent breakthroughs in arithmetic functions, L-functions, and pseudorandomness in Number Theory, as well as new connections to other areas (via both employed methods and applications), such as additive combinatorics, arithmetic statistics, and dynamical systems. Such breakthroughs include the latest advances in the study of various character and exponential sums (e.g., Kloosterman sums), which are powerful and versatile tools for understanding the anatomy of integers; moments, and other averages of L -functions (over number fields and function fields); integers having a prescribed arithmetic structure (e.g., prime, smooth, square-free, sum of two squares), along with their distribution in arithmetic progressions and short intervals, as well as function field analogs of these problems; distribution of elements of multiplicative subgroups; pseudorandomness of arithmetical functions. An essential aspect of these developments is the vast arsenal of tools and techniques that have been conceived, developed, and implemented, ranging from analysis to additive combinatorics, algebraic geometry, and random matrix theory. The proposed workshop will concentrate on the emerging methods that underlie such advances and on possible future directions.

Number Theory, Arithmetic,    Probability and Statistics, Game Theory

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

This workshop concerns cutting edge research in combinatorics and graph theory, an area central to understanding structures which appear in modern technology, such as the internet and communication devices. Problems that were previously intractable can now be approached due to advances in computing. This workshop will feature 4-6 working groups on research on topics including graph matchings and algorithms, combinatorial coding theory, graph invariants, and algebraic graph theory. Research results from the workshop will be incorporated into Sage, a free open-source computer algebra system, and Python.

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.

Courses and Events for Math Students and Early Career Researchers,    Algebra

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

Evolving random structures are discrete mathematical models that evolve randomly `step-by-step’ over time. Such evolving structures are powerful tools, and the topic has been receiving considerable attention from combinatorics, probability, computer science and related communities. For example, in combinatorics some of the best-known extremal constructions arise from natural evolving random hypergraph models, and in probability many interesting dynamic network models arise from carefully crafted evolving random graph models. Interestingly, in combinatorics and probability slightly different sets of ideas have been proposed for analyzing such random evolving structures, which in turn have also found applications in the analysis of randomized algorithms.