9:00 - 9:45: Ye, Jinhe: Curve-excluding fields
Given \(C\) a curve over \(\mathbb{Q}\) with genus at least 2 and \(C(\mathbb{Q})\) is empty, the class of fields \(K\) of characteristic 0 such that \(C(K)=\emptyset\) has a model companion, which we call CXF. Models of CXF have interesting combinations of properties. For example, they provide an example of a model-complete field with unbounded Galois group, answering a question of Macintyre. One can also construct a model of it with a decidable first-order theory that is not "large'' in the sense of Pop. Algebraically, it provides a field that is algebraically bounded but not ``very slim'' in the sense of Junker and Koenigsmann. Model theoretically, we find a pure field that is \(TP_2\) and strictly \(NSOP_4\) . Joint work with Will Johnson.

10:00 - 10:45: Gannon, Kyle: Packing numbers and tame measures
We prove that if a local measure admits a suitably tame global extension, then it has finite packing numbers with respect to any definable family. We also characterize NIP formulas via the existence of tame extensions for local measures. This is joint work with Gabriel Conant and James Hanson. 

11:00 - 11:45: Li, Wei: Elimination and Consistency Checking for Algebraic Differential-Difference Equations
Algebraic differential-difference equations, or what are called algebraic delay differential equations, are ubiquitous in applications. Elimination of unknowns is a fundamental tool for studying solutions of equations (linear, polynomial, differential, etc.). The consistency-checking problem for delay differential equations seeks for a general method or algorithm to determine whether an arbitrarily given system of delay differential equations has a sequence solution. We solve this problem positively by proving the effective differential-difference Hilbert Nullstellensatz theorem, in which we derive an explicit upper bound for the number of iterated applications of the distinguished difference and derivation operators, for a reduction of this consistency-checking problem to a well-studied consistency-checking problem for polynomial equations. In this talk, we will first give a brief introduction to the effective Hilbert Nullstellensatz, and then discuss our results on consistency-checking problems for delay differential equations and also for delay PDEs. This is joint work with A. Ovchinnikov, G. Pogudin and T. Scanlon.

14:00 - 14:45: Dobrowolski, Jan: Fields with commuting operators
Motivated by examples such as commuting, or, more generally, Lie-commuting derivations, iterative Hasse-Schmidt derivations, and arbitrary commuting operators associated to local algebras, we propose a model-theoretic framework for studying operators satisfying a "commutativity rule" corresponding to commutativity of certain diagrams of morphisms of algebras. This is a joint work in progress with Omar Leon Sanchez.

15:00 - 15:45: Conversano, Annalisa: Definable rank, o-minimal groups, and Wiegold's problem (online)
A considerable volume of work shows that definable groups in o-minimal structures are strongly related to algebraic groups. In this talk another similarity yet again is presented: every definable group G has finite definable rank. That is, G contains a finite subset that is not included in any proper definable subgroup.  This provides another proof of algebraic groups containing a Zariski dense finitely generated subgroup. If we restrict ourselves to normal definable subgroups, a much stronger result holds: every perfect definable group is normally generated by a single element. The proof is constructive and a normal generator is found explicitly. This provides a positive answer to Wiegold's problem in the o-minimal setting.

16:00 - 16:45: Hong, Jizhan: Towards an immediate expansion
The general idea of a proof of the following result will be presented: on an omega-free pseudo-algebraically closed valued field with a finite exponent of imperfectness, identifying a first-order structure with the collection of all of its definable sets, there is no proper intermediate first-order structure between its first-order structure as a valued field and its first-order structure as a field.

9:00 - 10:00: Pillay, Anand: Open subgroups of p-adic algebraic groups (online)
(Joint with Ningyuan Yao.) We revisit an old question as to whether open subgroups of p-adic algebraic groups G  are p-adic semialgebraic.  We give a positive answer when G is commutative, which together with old results of Prasad yield a positive answer for reductive G.

10:15 - 11:00: Yao, Bokai: Reflection with Absolute Generality (online)
Traditionally, reflection principles in set theory claim that the set-theoretic universe is indescribable. It is natural to consider reflection principles with absolute generality, which asserts that the universe containing everything, including sets and urelements, is indescribable. In the first part of this talk, I will consider the first-order reflection principle in urelement set theory. With the Axiom of Choice, first-order reflection holds just in case the urelements are arranged in a certain way, and this equivalence breaks down without AC. In the second part of this talk, I will present my joint work with Joel Hamkins on second-order reflection principles with urelements. A standard version of second-order reflection, due to Paul Bernays, is often viewed as a weak large cardinal axiom in set theory. With abundant urelements, however, Bernays’ second-order reflection principle interprets a supercompact cardinal.

11:15 - 12:00: Bentzen, Bruno: Analytic and synthetic judgments in constructive semantics
Traditionally, we say that a proposition is analytic when true solely by virtue of its meaning and synthetic otherwise. This well-established semantic distinction deserves to be explained not only classically but also from the opposing constructive perspective, where meaning and truth are rooted in provability. In 1994 the Swedish logician Per Martin-Löf undertook such a project in the setting of his constructive type theory. His distinction has been widely accepted by those sympathetic to constructivism without ever being challenged until very recently. In this talk, I raise some objections to Martin-Löf's distinction between analytic and synthetic judgments in constructive type theory and propose a revision of his views.

14:00 - 14:45: Halevi, Yatir: Models of elliptic curves, using model theory
Given an elliptic curve \(E\) over an algebraically closed valued field \(K\) there exists an integral separated smooth group scheme \(\mathcal{E}\) over \(\mathcal{O}_K\) with generic fiber \(E\). The definable group \(\mathcal{E}(\mathcal{O})\) is the maximal generically stable subgroup of \(E\). My plan is to give the basic notions needed to state this theorem and give some outline of the proof. Knowledge in basic algebraic geometry (and algebraic groups) will be assumed but not of general group schemes.

15:00 - 15:45: Kaplan, Itay: Cofinal families of finite sets with finite VC dimension (online)
(Joint work with Omer Ben-Neria and George Peterzil) In a recent work with Bays, Ben-Neria and Simon related to externally definable sets in NIP theories, a set theoretic question related to the VC-dimension of cofinal families of finite sets in sets of uncountable cardinality popped up. I will discuss the motivation for this question and give some answers.

16:00 - 16:45: Hoffmann, Daniel: Oscillations in space of types (online)
We generalize a notion of rank from topological dynamics, which was introduced by Glasner and Megrelishvili, to apply it in non-metrizable dynamical systems, like the space of types. This rank counts oscillations of elements of the Ellis semigroup at a given point and, in some sense, refines the well-known Cantor-Bendixson rank. Then we characterize a couple of the main dividing lines in the stability hierarchy by the values our rank can take, values counted in the dynamical system where Aut(M) acts on S(M). A joint work with Alessandro Codenotti.

9:00 - 10:00: Chong Chi Tat: Bounded set existence axioms in reverse mathematics
The ``big five’' subsystems of second order arithmetic in reverse mathematics are defined in terms of set existence axioms. In this talk we introduce an extension of the notion of set existence and discuss its role in the study of subsystems weaker than arithmetic comprehension, as well as applications in the analysis of combinatorial principles. We also explore a number of related foundational issues.

10:15 - 11:00: Yang, Yue: Ramsey's Theorem, Its Tree Versions and Halpern-Läuchli Theorem in Reverse Mathematics
I will start with some history of the studies of Ramsey's Theorem in reverse mathematics, especially with restricted induction. Then I will move on to the tree version of Ramsey's Theorem. Finally, I will report some working in progress, joint with Chitat Chong and Wei Li from NUS and Lu Liu from Central South University, on Halpern-Läuchli Theorem.

11:15 - 12:00: Wu, Liuzhen: Definability of the nonstationary ideal on \(\omega_1\)
The nonstationary ideals are natural nontrivial ideals defined on all uncountable regular cardinals. In this talk, various aspects of definability of nonstationary ideals on uncountable cardinals are explored. The main focus is the definability of nonstationary ideal on \(\omega_1\) (\(NS_{\omega_1}\) for short) in some canonical models of set theory. In particular, under MM or (*) axiom, \(NS_{\omega_1}\) is not \(\Pi_1\) definable. On the other hand, it is consistent that in some model of \(PFA\) , \(NS_{\omega_1}\) is \(\Pi_1\) definable. This is based on the accumulated work of Aspero, Hoffelner, Larson, Schindler, Sun, Wu.

14:00 - 14:45: Peng, Yinhe: On the topological basis problem
For a class \(\mathcal{K}\) of uncountable regular topological spaces, a subclass \(\mathcal{B}\) is a basis if every space in \(\mathcal{K}\) contains a subspace in \(\mathcal{B}\). An important and interesting problem in set-theoretic topology is the topological basis problem: which class of topological spaces has a finite (or even 3-element) basis? In this talk, I will introduce the answers of the topological basis problem on different classes of spaces.

15:00 - 15:45: Shen, Guozhen: A surjection from square onto power
In this talk, we prove that the existence of an infinite set $A$ such that $A^2$ maps onto $2^A$ is consistent with $\mathsf{ZF}$. This gives a negative solution to a long-standing problem proposed by John Truss. This is joint work with Yinhe Peng and Liuzhen Wu.