Organizer: Chris Laskowski
When: Tuesdays @ 3:30pm
Where: Math 1311

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017

  • Organizational Meeting

    Speaker: Organizational Meeting () -

    When: Tue, August 29, 2017 - 3:30pm
    Where: Kirwan Hall 1311
  • Borel complexity and the Schroder-Bernstein property

    Speaker: Douglas Ulrich (UMD) -

    When: Tue, September 5, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: We show that if a first order theory T has the Schroder-Bernstein property then it is not Borel complete, assuming some mild large cardinals.
  • Countable models of Baldwin-Shi hypergraphs

    Speaker: Danul Gunatilleka (University of Maryland, College Park) -

    When: Tue, September 12, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: We isolate a special case of the ab initio constructions that we propose to call Baldwin-Shi hypergraphs. The theories in question are known to be either strictly stable or omega-stable and are known to have the dimensional order property. It is also known that the in case the theory is strictly stable it is not small. So we count the number of non-ismorphic countable models in the case the theory is omega-stable. We will also take a look at the regular types that arise in this case.
  • Finite-rank ordered Abelian groups

    Speaker: John Goodrick (Los Andes University) - https://matematicas.uniandes.edu.co/~goodrick/

    When: Tue, September 19, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: Recently there have been several advances in the study of ordered Abelian groups (OAGs) whose theories have finite dp-rank. Recall that every complete theory of OAGs has NIP (Gurevich), so it it is interesting to ask which ones are *strongly* dependent in the pure language {+, <} of ordered groups, and which ones have finite dp-rank. We will sketch a new proof of a characterization of such theories, which was discovered independently by several people in the past year.

    Next, we will consider finite dp-rank theories of ordered Abelian groups in languages expanding {+,<}. Here there is much less known, though discrete definable can be analyzed (as in work by myself and Dolich): if there is an Archimedean model, then any discrete definable set must be a finite union of arithmetic sequences. Some preliminary attempts to analyze definable sets and functions will be discussed.

    All the results presented in this talk are joint work with Alfred Dolich.
  • Coarse embeddings into superstable spaces

    Speaker: Bruno de Mendonça Braga (York University) - https://sites.google.com/site/demendoncabraga/home

    When: Tue, September 26, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: In 1981, J. Krivine and B. Maurey introduced the definition of stable Banach spaces, and, in 1983, Y. Raynaud introduced the notion of superstability and studied uniform embeddings of Banach spaces into superstable Banach spaces. In this talk, we will talk about coarse embeddings into superstable spaces. This is a joint work with Andrew Swift.
  • A stable arithmetic regularity lemma in finite-dimensional vector spaces over fields of prime order

    Speaker: Caroline Terry (University of Maryland, College Park) -

    When: Tue, October 10, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: In this talk we present a stable version of the arithmetic regularity lemma for vector spaces over fields of prime order. The arithmetic regularity lemma for $\mathbb{F}_p^n$ (first proved by Green in 2005) states that given $A\subseteq \F_p^n$, there exists $H\leq \F_p^n$ of bounded index such that $A$ is Fourier-uniform with respect to almost all cosets of $H$. In general, the growth of the index of $H$ is required to be of tower type depending on the degree of uniformity, and must also allow for a small number of non-uniform elements. Our main result is that, under a natural stability theoretic assumption, the bad bounds and non-uniform elements are not necessary. Specifically, we present an arithmetic regularity lemma for $k$-stable sets $A\subseteq \mathbb{F}_p^n$, where the bound on the index of the subspace is only polynomial in the degree of uniformity, and where there are no non-uniform elements. This result is a natural extension to the arithmetic setting of the work on stable graph regularity lemmas initiated by Malliaris and Shelah. This is joint work with Julia Wolf.
  • On stable expansions of the integers by multiplicative semigroups

    Speaker: Gabriel Conant (Notre Dame) - https://www3.nd.edu/~gconant/

    When: Tue, October 17, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: We prove that if G is a finitely generated multiplicative semigroup of positive integers, and A is any infinite subset of G, then the expansion (Z,+,A) of (Z,+) by a unary predicate for A is superstable of U-rank omega. The key tool for this result is a theorem of Evertse, Schlickewei, and Schmidt on solutions to linear equations in finite rank multiplicative subgroups of algebraically closed fields. We use this theorem, along with general results of Casanovas and Ziegler, to show that stability of the expansion (Z,+,A) reduces to stability of the induced structure on A, and then to show that this induced structure is monadically stable of U-rank 1.
  • Twists and Twistability

    Speaker: Rebecca Coulson (Rutgers University) - http://sites.math.rutgers.edu/~rlg131/

    When: Tue, October 24, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: We introduce the concept of a twist, which is an isomorphism up to a permutation of the structure's language. We developed this concept in the course of proving results about metrically homogeneous graphs. This concept proved useful for partial classification results as well as finiteness results. The concept of a twist surprisingly is present in other work by Cameron and Tarzi, as well as by Bannai and Ito. We will discuss our results and their connections to other work.
  • NIP theories and machine learning

    Speaker: Vincent Guingoa (Towson University ) - https://tigerweb.towson.edu/vguingona/

    When: Tue, November 7, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: We discuss the basics of machine learning theory, including concept classes, VC-dimension, VC-density, PAC-learning, and sequence compressions. We then explore the relationship between these concepts and model theory.
  • Relativized Lascar groups.

    Speaker: Alexei Kolesnikov (Towson University) - https://tigerweb.towson.edu/akolesni/

    When: Tue, November 14, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: Lascar group is a topological group defined for a first order theory. It is known that any compact group is a Lascar group for a suitable theory. In this talk, I will describe a Lascar group defined for a type in a theory and its connection to the first model-theoretic homology group.
  • Distal and non-distal ordered abelian groups.

    Speaker: Allen Gehret (UCLA) -

    When: Tue, November 21, 2017 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: I will discuss various things we know about distal and non-distal ordered abelian groups. This is joint work with Matthias Aschenbrenner and Artem Chernikov.