Events

Gian Cordana Sanjaya, University of Waterloo

Multiplicatively dependent integer vectors on a hyperplane

In 2018, Pappalardi, Sha, Shparlinski, and Stewart counted the number of multiplicatively dependent n-tuples of algebraic integers in a fixed number field, ordered by pointwise Weil height. Extending this work, in a joint with with Afifurrahman and Iverson in 2026, we count the number of multiplicatively dependent n-tuples of rational integers lying on a hyperplane, ordered by maximum absolute value. In this talk, we will discuss about the multiplicatively dependent tuples, some motivations behind them, and how to count these tuples, leading to the main results of both papers.

MC 5479

Noah Nazareth, University of Waterloo

The jump of a structure III

We will continue our proof of the Ash-Knight-Manasse-Slaman and Chisholm theorem. We will then define and discuss effective bi-interpretability and start the proof of the first jump inversion theorem for structures.

MC 5403

Fateme Peimany, University of Waterloo

DCCM: the differential expansion of CCM

We introduce the theory of compact complex spaces called CCM and expand it to DCCM, the theory of differentially closed CCM-structures. Finally, we will explain the good model-theoretic properties of DCCM and open problems in this theory.

MC 5403

Boris Li, University of Waterloo

Filtered Deformations of Trivariate Polynomial Rings

Among non-commutative rings, those satisfying a polynomial identity (PI) are especially well-behaved. They share many properties with commutative rings, which we understand well. Etingof asked whether every filtered deformation of a finitely generated commutative domain, over an algebraically closed field of positive characteristic, is PI. In this talk, we will answer this question of Etingof affirmatively for deformations of polynomial rings in three variables. In the pre-seminar, I will define and discuss the properties of filtered deformations

MC 5403