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Institute for Pure and Applied Mathematics (IPAM)

We have seen how probability motivates new research directions in algebraic combinatorics and how algebraic combinatorics leads to new discoveries in probability. The aim of the workshop is to further stimulate the cross-infiltration of the ideas between two fields.

Part of the Long Program Geometry, Statistical Mechanics, and Integrability

Simons Laufer Mathematical Sciences Institute (SLMath)

This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

Lie algebras, Representation theory, combinatorics

Mathematical Sciences Research Institute (MSRI)

This workshop will have a view to the future of a broad spectrum of topics including structure and classification of finite dimensional Lie algebras and superalgebras in characteristic p structure of infinite dimensional Lie algebras and their representations deformation theory of algebras, double constructions and elemental Lie algebras diagram algebras and combinatorial representation theory algebraic combinatorics of groups of Lie type:characters, Schur-Weyl duality, Bratteli diagrams, and McKay correspondences quantum groups and crystal bases, particularly for superalgebras and affine algebras examples of fusion categories arising from representations of Drinfeld doubles and other algebras cohomology for finite tensor categories with applications to its underlying geometry

This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

Institute for Pure and Applied Mathematics (IPAM)

While classical “integrable” statistical mechanics has been restricted to one and two dimensions, recent ideas have extended our understanding to (some) higher dimensional situations, or to models on non-planar graphs. These include graph limits, posets, multinomial models, random complexes and random groups, and more. While these topics are quite diverse, they nonetheless have common tools, notably the use of random walks, the graph laplacian, homology theory, and determinants. Topics will include: Benjamini-Schramm limits of graphs, unimodular measures, spanning trees and spanning complexes, chip firing/sandpile models, matroids, higher determinantal processes, random complexes, multinomial models, random groups, rigidity, and statistical physics in more than two dimensions.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to the study of high-dimensional phenomena in discrete analysis and will touch upon themes in additive combinatorics, discrete geometry and extremal combinatorics. Each of these areas, which share many common techniques and ideas, have experienced enormous growth and seen the solution to longstanding problems in recent years. The goal of this workshop is to bring together a range of researchers with expertise in each of these areas to find common ground, start new collaborations and make progress on some of the fundamental questions in these areas.

The main topics for the workshop are: Quantitative estimates on multidimensional Szemerédi-type theorems, Incidence results in higher dimensions, Extremal problems for hypergraphs.

Analysis,    Numerische Analysis

The Graduate Research Workshop in Combinatorics (GRWC) is an annual two-week collaborative research workshop for advanced graduate students and postdocs from all areas of combinatorics. Participants work in small collaborative groups with faculty and postdocs on research problems from across the discipline. The workshops also host a variety of professional development workshops to prepare students and postdocs for industrial and academic careers. Participants have come from institutions around the world.

Email: Combinatorics.Workshop@gmail.com

graph theory, algebraic combinatorics, extremal combinatorics, combinatorial matrix theory, combinatorial games

AMS, American Mathematical Society

Transfer systems are a new combinatorial object that exhibit surprising connections between abstract homotopy theory, equivariant topology, and combinatorics. About ten years ago, Blumberg and Hill defined the related "indexing systems'' as the central algebraic object controlling twisted multiplications that naturally arise in the study of equivariant cohomology theories. Rubin and Balchin--Barnes--Roitzheim independently recast this notion in a much simpler framework, characterizing indexing systems in terms of transfer systems, as a particular kind of weak subposet of the lattice of subgroups of a finite group G , ordered by inclusion. Work of Ormsby--Osorno and teams of collaborators has shown how the natural generalization of this notion to an arbitrary poset has fascinating combinatorial properties, and Balchin--MacBrough--Ormsby have further connected this to abstract homotopy theories on posets. Each of these connections provides exciting results which can be transferred and reinterpreted in the other fields, yielding unexpected new structure and theorems. This MRC will introduce participants to this burgeoning new area, bringing together researchers with interests in combinatorics, algebraic topology, and abstract homotopy theory. The field is rife with open problems, including basic questions about the structure of transfer systems, combinatorics problems associated to counting transfer systems for natural families of posets, identifying connections with other combinatorial structures, and applying the language of model categories to recast and reform these questions.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to current problems relating structural properties of graphs and their connections to modern applications. Specifically, we will focus on graph labelings, invariants, and the characterization of graphs with specific or extremal parameters. We will also study structural properties of families of graphs using methods such as lifts of graphs, both random and algebraic. One goal of the workshop is to unite researchers from various backgrounds in graph theory so that theoretical advancements with a potential to make an impact in applications will result. As an AWM Women in Graph Theory and Applications (WiGA)- affiliated workshop, another goal is to develop and strengthen the support of women in the graph theory community. We welcome all who support this mission.

The main topics for the workshop are: Graph coloring, domination, and labeling and their connections to applications. Characterizing families of graphs with extremal parameters. Generating families of graphs with desired labelings, invariants, or other structural features.

Simons Laufer Mathematical Sciences Institute (SLMath)

This workshop will feature leading experts in several major areas of graph theory, including extremal, probabilistic and structural aspects of the field. Introductory lectures will form an important part of the program, providing background and motivation, and aimed at a general mathematical audience. Complementing these, research talks will share exciting recent developments in graph theory.

extremal graph theory, random graphs, probabilistic methods, structural graph theory, Ramsey theory

Simons Laufer Mathematical Sciences Institute (SLMath)

Many exciting breakthroughs in combinatorics involve innovative applications of techniques from a wide range of areas such as harmonic analysis, polynomial and linear algebraic methods, spectral graph theory, and representation theory. This workshop will present recent developments in this area and facilitate discussions of research problems.

extremal combinatorics, extremal graph theory, probabilistic combinatorics, discrete geometry, additive combinatorics, combinatorial geometry, incidence geometry, arithmetic progressions, Discrete analysis

Algebra,    Analysis

Simons Laufer Mathematical Sciences Institute (SLMath)

In a growing number of applications, one needs to analyze and interpret data coming from massive networks. The statistical problems arising from such applications lead to important mathematical challenges: building novel probabilistic models, understanding the possibilities and limitations for statistical detection and inference, designing efficient algorithms, and understanding the inherent limitations of fast algorithms. The workshop will bring together leading researchers in combinatorial statistics, machine learning, and random graphs in the hope of cross-fertilization of ideas.

combinatorial statistics, random graphs, network inference, network reconstruction, detection, estimation

Komplexe Netzwerke,    Wissenschaftliches Rechnen und Datenwissenschaft