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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.

Department of Mathematics and Statistics, University of Minnesota Duluth

Four invited lectures and 20-minute contributed talks on topics in combinatorics and graph theory.

Email: mcccc2024@d.umn.edu

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

Institute for Pure & Applied Mathematics (IPAM)

Over the last half a century, Algebra, Combinatorics, and Discrete Geometry have undergone transformations due, in part, to the connections each of these areas have to other fields and the growth of computational approaches used in the study of theoretical mathematics. These areas are closely intertwined, with various algebraic, combinatorial, and geometric objects playing pivotal roles. These objects include monomial ideals, affine semigroup rings, Stanley-Reisner rings, Ehrhart rings, toric rings, Cox Rings, Chow Rings, Gröbner bases on the algebraic side; graphs, matroids, simplicial complexes, polytopes and polyhedral complexes, convex bodies, posets, lattices, arrangements of hyperplanes on the combinatorial and discrete geometry side.

Algebra,    Numerische Analysis

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

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