Graduate Workshop in Logic and Combinatorics

ABOUT THE CONFERENCE

DATES & TIMES

 August 10-August 14, 2026.

SCHEDULE

The daily schedule for the workshop can be found here:  Schedule 

SPEAKERS

Tutorials:

• Anton Bernshteyn (UCLA)

Title: Recent trends in descriptive combinatorics

Abstract: Many problems arising across mathematics are inherently combinatorial. For example, as we shall see in this tutorial, the famous Banach--Tarski paradox is really a statement about perfect matchings in certain bipartite graphs. In such examples, the underlying combinatorial structures are often infinite, leading to natural definability concerns. In descriptive combinatorics, these concerns are addressed using tools from topology and measure theory. The subject is growing very rapidly, driven in part by its deep connections to fields such as dynamical systems, probability theory, and computer science. This tutorial will provide a general overview of descriptive combinatorics and introduce some exciting recent developments, including ideas from large-scale geometry and local methods.

• Samuel Braunfeld (Czech Academy of Science)

Title: Model Theory and Structural Combinatorics

Abstract: We will cover some interactions between (generalized) sparsity in structural graph theory and the monadic versions of classical model-theoretic properties. The lecture plan is as follows. 

Lecture 1: Overview, and some model-theoretic preliminaries such as indiscernibility and forking 

Lecture 2: Monadically stable theories of rank 1, and their equivalence with graph classes of structurally bounded degree

Lecture 3: Monadic stability, and the parallels between the model-theoretic and graph-theoretic analysis

• John Griesmer (Colorado School of Mines)

Title: Positive Definite Functions, Additive Combinatorics, and Harmonic Analysis

Abstract: A fundamental problem in additive combinatorics is to identify configurations appearing in "large" subsets of the natural numbers.  For example, the Furstenberg - Sárközy theorem says that if c > 0 and N is sufficiently large, then every subset of  {1, ... , N} having at least cN elements must contain two distinct elements differing by a perfect square.  Roth's theorem on arithmetic progressions says that if c > 0, and N is sufficiently large, then every subset of {1, ... , N} having at least cN elements must contain a three-term arithmetic progression {a, a + d, a + 2d}.

In these lectures we:

• develop the functional analytic approach to these problems, pioneered by Bogolyubov, Følner, Furstenberg, and others, presenting the necessary background in detail, including

  • Invariant means on the integers and other discrete groups

  • Herglotz's theorem characterizing positive definite functions as Fourier transforms of measures

  • Techniques for constructing interesting large subsets of Z

• Prove some of the classic results with these techniques, including the Steinhaus Lemma and the Furstenberg - Sárközy theorem. 

• Survey some recent developments on single recurrence (two-point configurations in large sets), sumsets, and difference sets

REGISTRATION & FUNDING

Please use the following link to register:  Registration/Funding. The deadline to apply for funding has passed but registration to attend is still open. If you still want to apply for funding, please email us at hshea3@uic.edu as there may be some left over. 

SUPPORT

Supported by NSF CAREER Award DMS-2115518