Rachael Alvir, University of Waterloo
Conclusion of the Fundamentals of Computability Theory
We will finish presenting results from Soare's book. We will look at Low n and High n sets.
MC 5403
Brady Ali Medina, University of Waterloo
Co-Higgs Bundles and Poisson Structures.
There is a correspondence between co-Higgs fields and holomorphic Poisson structures on P(V) established by Polishchuk in the rank 2 case and by Matviichuk in the case where the co-Higgs field is diagonalizable. In this thesis, we extend this correspondence by providing necessary and sufficient conditions for when a co-Higgs field induces a Poisson structure on V and P(V), showing that the co-Higgs field must either be a function multiple of a constant matrix or have only one non-zero column. Furthermore, we analyze this correspondence for co-Higgs fields over curves of genus greater or equal to one. Finally, we analyze how stability can be interpreted geometrically through the zeros of the induced Poisson structure, establishing connections between \Phi -invariant subbundles, Poisson subvarieties, and the spectral curve.
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Meeting ID: 971 4907 1044
Passcode: 776121
Ruiran Sun, University of Toronto
Rigidity problems on moduli spaces of polarized manifolds.
Motivated by Shafarevich’s conjecture, Arakelov and Parshin established a significant finiteness result: for any curve C, the set of isomorphism classes of non-constant morphisms C → M_g is finite for g≥2. However, for moduli stacks parametrizing higher-dimensional varieties, the Arakelov-Parshin finiteness theorem fails due to the presence of non-rigid families. In this talk, I will review recent advances in rigidity problems for moduli spaces of polarized manifolds, focusing on two main topics: an "one-pointed" version of Shafarevich’s finiteness theorem and the distribution of non-rigid families within moduli spaces.
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Thomas Bray, University of Waterloo
To b or Not to b: The Art of Generalizing Metric Spaces
Metric spaces form the foundation of many areas in mathematics, offering a rigorous framework for understanding distance and convergence. But what happens when we relax the triangle inequality? Enter b-metric spaces, where the triangle inequality is replaced by a more flexible inequality scaled by a constant. In this talk, we will explore how this generalization leads to surprising results and broadens the scope of classical fixed-point theory, topology, and functional analysis. Join me as we delve into the rich structure of b-metric spaces and uncover their role in contemporary mathematical research.
Snacks will be available from 4:00pm
MC 5417