Events

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.

Join on Zoom

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

Rachael Alvir, University of Waterloo

Introduction to Continuous Logic I

We begin with an introduction to continuous logic and metric structures following the manuscript "Model Theory for Metric Structures" by Berenstein, Ben Yaacov, Henson, and Iovino.

MC 5403

Almut Burchard, University of Toronto

On spatial monotonicity of heat kernels

The heat kernel on a manifold contains a wealth of global geometric information about the underlying space. It is of central importance for partial differential equations (describing diffusion of a unit of heat released from a point through the space) and for probability (giving the transition densities for Brownian motion).

On flat n-dimensional space, the heat kernel K_t(x,y) decreases with the distance between the points x and y (that is, temperature decreases as we move away from the heat source); the same is true on the sphere. Does the heat kernel on different Riemannian manifolds have similar properties?  In general, the answer is "No!" ... except sometimes ...

MC 5501

Refreshments available at 3:30pm