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.
Join on Zoom
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
Zev Friedman, University of Waterloo
4-dimensional U(m) structures
We will define the modified deRham operator D on U(m) structures, and prove that D^2=0 is equivalent to d \omega=0 in the 4-dimensional case.
MC 5479
Ryoya Arimoto, Kyoto University
Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries
Results of Archbold and Spielberg, and Kalantar and Kennedy assert that a discrete group admits a topologically free boundary if and only if the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. In this talk, I will show a similar result for totally disconnected locally compact groups.
MC 5417 or Join on Zoom
Faisal Romshoo, University of Waterloo
Constructing associatives in 7-manifolds
We will revisit the classical examples of Special Lagrangians invariant under some group G in SU(n) using a new method and check if we can use the same method to construct associative submanifolds, which are a type of calibrated 3-submanifolds in 7-manifolds, in R^7.
MC 5479
Spiro Karigiannis, University of Waterloo
Organizational Meeting
We will meet to plan out the Differential Geometry Working Seminar for the Winter 2025 term.
MC 5479
Rahim Moosa, University of Waterloo
Organisational meeting
We will meet to discuss the seminars taking place in the Winter term.
MC 5403
Dror Varolin, Stony Brook University
Extending sections of Holomorphic Vector Bundles
In 1987 Ohsawa and Takegoshi published their fundamental result on L2 extension of holomorphic functions. It did not take long for this result to be generalized to sections of holomorphic line bundles, and a spectacular array of applications appeared in a number of areas of complex analytic and algebraic geometry. By contrast, the L2 Extension of sections of holomorphic vector bundles has been much less considered. In particular, until recently optimal positivity conditions were not totally understood. In this talk I will present a result about L2 Extension in the higher rank case, and also an example showing that this type of positivity is optimal. I will also discuss the relevance to a question about deformation of spaces of holomorphic sections.
MC 5417