9:00 - 9:50: Theodore A. Slaman: Extending Borel's Conjecture from Measure to Dimension
Borel (1919) defined a set of real numbers $A$ to have strong measure zero if for every sequence of positive numbers $(e_i)$ there is an open cover of $A~$, $(U_i)$, such that for each $i$, the diameter of $U_i$ is less than $e_i$.  Besicovitch (1956) showed that $A$ has strong measure zero if and only if $A$ has strong dimension zero, which means that for every gauge function $f$, $A$ is null for its associated measure $H^f$.  We say that a subset of $A$ of $\mathbb{R}^n$ has strong dimension $f$ if and only if $H^f(A)>0~~$ and for every gauge function $g$ of higher order $H^g(A)=0$.  Here, $g$ has higher order than $f$ when the limit as $t$ goes to $0$ of the ratio $g(t)/f(t)~~$ is equal to $0$.

Borel conjectured that a set of strong measure zero must be countable.  This conjecture naturally extends to the assertion that a set has strong dimension f if and only if it is sigma-finite for $H^f$.  Sierpinski (1928) used the continuum hypothesis to give a counterexample to Borel's conjecture and Besicovitch (1963) did the same for its generalization.  Laver (1976) showed that Borel's conjecture is relatively consistent with ZFC, the conventional axioms of set theory including the axiom of choice.  We will discuss the proof that its generalization to strong dimension is also relatively consistent with ZFC. Slides

10:10 - 11:00: YU, Liang: When $\underline{A+xA=\mathbb{R}}~$?
We investigate which algebra substructures $A$ of reals so that there is a real $x$ for which $A+xA=\mathbb{R}$ . Slides

11:10 - 12:00: Kyle Gannon: Examples of generic sampling
Generic sampling is a method by which one can sample countable sequences of types over a monster model with respect to a "nice" Keisler measure. One can then ask which kinds of events almost surely happen with respect to these random processes. In this talk, we focus on some examples and discuss some recent connections to the theory of graphons. This is joint work with Ackerman, Freer, Hanson, and Patel. Slides

14:00 - 14:50: PENG, Yinhe: Iterated forcing with a minimal damage to a strong coloring
I will introduce an iteration of ccc posets with minimal damage to a strong coloring and its applications. For example, (1) Martin's axiom is strictly stronger than its restriction to forcing notions satisfying countable chain condition in all finite powers. (2) Some strong colorings are consistent with Martin's axiom. In other words, some corresponding properties can be made ccc indestructible via a ccc forcing. Slides

15:00 - 15:50: YU, Jing: Embedding Borel graphs into grids of asymptotically optimal dimension
Let $G$ be a Borel graph all of whose finite subgraphs embed into the $d$-dimensional grid with diagonals. We show that then $G$ itself admits a Borel embedding into the Schreier graph of a free Borel action of $\mathbb Z^{O(d)}$. This is joint work with Anton Bernshteyn. Slides

16:10 - 16:50: WANG, Zongshun: Bilateral Gradual Semantics for Weighted Argumentation
Abstract argumentation is a reasoning model for evaluating arguments based on various semantics. Recently, gradual semantics has received considerable attention in weighted argumentation, which assigns an acceptability degree to each argument as its strength. In this talk, we propose to enhance gradual semantics by non-reciprocally incorporating the notion of rejectability degree. Such a setting offers a bilateral perspective on argument strength, enabling more comprehensive argument evaluations in practical situations. To this end, we first provide a set of principles for our semantics, taking both the acceptability and rejectability degrees into account, and propose three novel semantics conforming to the above principles. These semantics are defined as the limits of iterative sequences that always converge in any given weighted argumentation system, making them preferable for real-world applications. Slides