Andy Zucker, University of Waterloo
Dynamical Partite Construction
We revisit the partite construction using some of the dynamical ideas we have developed.
MC 5417
Cynthia Dai, University of Waterloo
Resolution of Singularities via Stacky Blow-ups
We follow Dan Abramovich and Ming Hao Quek’s paper on resolution of singularity by multi-weighted blowups. This line of work is first motivated to give a more natural and motivated proof of Hironaka’s result, and that leads to the notion of weighted blowup, where you repeatedly blowing up the worst singular locus via weighted blowups. The problem with this is at the end you do not get an ambient space that’s smooth DM, but log smooth(specifically it’s toroidal DM stack). Using the technique of multi-weighted blowup introduced by Satriano, we can improve this result to get a logarithmic resolution of singularity with a smooth ambient space.
MC 5403
Facundo Camano, University of Waterloo
A Gromov—Hausdorff Convergence Result for the Moduli Space of Singular Monopoles
I will introduce singular monopoles on R^3 and their moduli space. We will then focus on U(2) singular monopoles, which have known explicit expressions, and look at the Gromov—Hausdorff convergence of the moduli space as one singularity is sent off towards infinity.
MC 5403
Yash Singh, University of Waterloo
Vector Bundles on Toric Stacks
We give moduli interpretations of toric vector bundles and generalize this approach to a classification of bundles on arbitrary toric stacks.
MC 5403
Sean Lee, University of Waterloo
Topological dynamics of the Rado graph
We introduce some concepts from topological dynamics, in particular the universal minimal flow, with the goal of showing that the universal minimal flow of the automorphism group of the Rado graph is the space of linear orders of the Rado graph.
MC 5417
Rachael Alvir, University of Waterloo
More Torsion-Free Abelian Groups
We will continue learning about torsion-free Abelian Groups following the Monograph by Downey and Melnikov.
MC 5417
Faisal Romshoo, University of Waterloo
Constructing calibrated submanifolds through evolution equations
I will talk about how we can construct examples of calibrated submanifolds using the techniques of evolution equations. We will begin by defining the ideas involved in coming up with these evolution equations and then look at some of the examples of calibrated submanifolds that are constructed this way, following arXiv:math/0008021, arXiv:math/0008155, arXiv:math/0010036 and arXiv:math/0401123.
MC 5403
Xuemiao Chen, University of Waterloo
On the space of lines
I will make a story about the space of oriented lines in the three dimensional Euclidean space.
MC 5403
Sean Lee, University of Waterloo
Dynamics of the Rado graph II
We continue our discussion about the topological dynamics of the automorphism group of the Rado graph.
MC 5417
Jiahao Hu, Yau Mathematical Sciences Center, Tsinghua University
Homotopy theoretical holomorphic invariants of complex manifolds
In this talk, I will begin by presenting a method for extracting new holomorphic invariants of a complex manifold from its de Rham algebra of complex-valued differential forms. These invariants can be seen as refined versions of the complexified homotopy groups. I will then explore their potential connections with Hermitian geometry. Specifically: (1) the non-abelian part (refined fundamental group) should be related to a generalization of Higgs bundle; (2) the abelian part (refined higher homotopy) may provide new tools for studying the geometry of holomorphic mappings.
MC 5417