Embedded Files
The Research Seminar meets Wednesdays at 2.30pm (unless otherwise stated) in the HIM lecture hall (Poppelsdorfer Allee 45, Bonn). The seminar is organized by Philipp Hieronymi, Jennifer Park, and Florian Pop.
Recordings of past seminars are at the bottom of this page.
Speaker: Sylvy Anscombe (U Paris-Cité)
Date: October 8th
Title: TBA
Abstract: TBA
Speaker: Guang Hu (Dresden)
Date: October 15th
Title: TBA
Abstract: TBA
Date: October 22nd
No seminar, due to the workshop
Speaker: Pantelis Eleftheriou (Leeds)
Date: October 29th
Title: TBA
Abstract: TBA
Speaker: John Alexander Cruz Morales (Universidad Nacional de Colombia)
Date: November 5th
Title: TBA
Abstract: TBA
Speaker: Pierre Touchard (Dresden)
Date: September 3rd
Title: On Groups Recognizing Coordinates
Abstract: The classical result of Feferman-Vaught describes a language in which a product of ℒ-structures ∏ᵢMᵢ eliminates quantifiers. It is, however not always clear whether this language is interpretable in the original language ℒ. To investigate this question, one can first ask whether ∏ᵢMᵢ, or any so-called reduced product, recognizes coordinates (namely, whether the product structure “knows” that it is a product). After providing all the necessary definitions, we will discuss this question in the context of various first order structures and for particular classes of groups. This is joint work with Ilijas Farah and Kyle Gannon.
Speaker: Douglas Cenzer (Florida)
Date: September 10rd
HomogeneousTalkRevised.pdfTitle: Homogeneity and Categoricity of Linear Orderings
Abstract: We introduce the notion of sp-homogeneous and weakly sp-homogeneous linear orderings --- linear orderings which become homogeneous or weakly homogeneous when expanded by partial functions for successor and predecessor.
We demonstrate that these orderings are always relatively $\Delta_4$ categorical and determine exactly which ones are (uniformly) relatively $\Delta_3$ categorical.
We also provide a classification for sp-homogeneity and weak sp-homogeneity. This classification is optimal in that the set of sp-homogeneous linear orderings is $\Pi_5^0$-complete and that the set of weakly sp-homogeneous linear orderings is $\Sigma_6^0$-complete. This result is obtained in the setting of computability theory and also in the setting of descriptive set theory.
This work is joint with Wesley Calvert, David Gonzalez, Valentina Harizanov, Keng Meng Ng.
Date: September 17th
No seminar, due to the introductory school
Speaker: Adele Padgett (Wien)
Date: September 24th
Title: A partial Ax-Lindemann-Weierstrass theorem for the Gamma function
Abstract: It is natural to study the algebraic properties of interesting transcendental holomorphic functions. For example, the complex exponential function is a group homomorphism. Moreover, one can characterize precisely which algebraic varieties are mapped coordinatewise by exp to other algebraic varieties. Analogous characterizations are known for other functions that, like exp, satisfy differential equations. These results are proved using techniques that exploit the differential equations and do not adapt cleanly to differentially transcendental functions. The Gamma function, which extends the factorial function to complex numbers, is an important differentially transcendental function. I will characterize the algebraic varieties mapped by Gamma to other algebraic varieties of the same dimension. This is joint work with Sebastian Eterović and Roy Zhao.
Speaker: Toghrul Karimov (MPI-SWS)
Date: October 1st 11am
Title: Arithmetic Predicates and Decidability of Logical Theories
Abstract: I will discuss some recent results as well as ongoing work, including the following results.
--The first-order theory of <Z; <, n -> tau(n)> is undecidable, where tau is the Ramanujan tau function.
--The existential fragment of the first-order theory of <N; +, {a_1^n: n >=0}, {a_2^n: n >= 0}> is decidable, where a_1,a_2 are positive integers.
--The monadic second-order theory of <N; <, {a_1^n}, ..., {a_k^n}> is decidable, where a_1,...,a_k are positive integers.
Page updated
Google Sites
Report abuse