Kaleb Domenico Ruscitti, University of Waterloo
Organization Meeting
We will be scheduling talks for the term, please join us!
MC 5403
Cy Maor, Hebrew University of Jerusalem
Stability of isometric immersions and applications
An isometric immersion f:M→N between two Riemannian manifolds of the same dimension is very rigid—the values of f(p) and Df(p) at one point p∈M completely determine f. But what can be said about maps that are "almost" isometries (in a precise sense)—must they be close to true isometries? In this talk, I will survey this question from its origins in the 1960s to recent developments, and discuss its applications to non-Euclidean elasticity, where one seeks the “most isometric” immersion even when exact isometric immersions do not exist. Based on joint works with Raz Kupferman.
MC 5417
Xuemiao Chen, University of Waterloo
The Sphere
I will make a long story regarding the two dimensional sphere.
MC 5403
Laura DeMarco, Harvard University
The (algebraic) geometry of the Mandelbrot set
One of the most famous -- and still not fully understood -- objects in mathematics is the Mandelbrot set. By definition, it is the set of complex numbers c for which the recursive sequence defined by x_1 = c and x_{n+1} = (x_n)^2+c is bounded. This set turns out to be rich and complicated and related to many different areas of mathematics. I will present an overview of what's known and what's not known about the Mandelbrot set, and I'll describe recent work that (perhaps surprisingly) employs tools from number theory and algebraic geometry.
MC 5501
Enric Solé-Farré, University College London
The Hitchin and Einstein indices of cohomogeneity one nearly Kahler manifolds
Nearly Kähler manifolds are Riemannian 6-manifolds admitting real Killing spinors. They are the cross-sections of Riemannian cones with holonomy G2. Like the Einstein equation, the nearly Kähler condition has a variational interpretation in terms of volume functionals, first introduced by Hitchin in 2001.
The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption.
MC 5417
Joaco Prandi, University of Waterloo
Bounding the Local Dimension of the Convolution of Measures
Let mu be a finite measure on a metric space X. Then the local dimension of the measure mu at the point x in the support of mu is given by
dim_{loc}mu(x)=lim_r ln(B(x,r))}\ln(r)
In a sense, dim_{loc}mu(x) represents how much mass there is around the point x. The bigger the local dimension, the less mass there is. In this talk, we will explore how the local dimension of the convolution of two measures mu and nu can be bounded by the local dimension of one of the measures. This is based on joint work with Kevin Hare.
MC5417
Annie Lafrance, University of Waterloo
Introduction to p-approximation property for locally compact groups
We will introduce the p-approximation property and show that if G has the p-approximation property, then the algebra of convoluters is the algebra of pseudomeasures.
MC 5403
Spiro Karigiannis, University of Waterloo
Organizational Meeting
We will plan out the DG working seminar for the May to August summer period. The plan is to have two talks per week, from 1:00pm to 2:15pm and from 2:30pm to 3:34pm.
MC 5403
Elizabeth Cai, University of Waterloo
Mirror Symmetry Seminar: Isomorphism Between Small Analytical Neighborhoods of Points on (n − s − 1)-dim Stratum, Open Ball and Affine Toric Variety
In Batryrev's construction on dual polyhedra and mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties, when he introduces regularity conditions for hypersurfaces, he proposes a theory implied by the definition of ∆-regular, in which sugguests that there exists an analytical isomorphism from small analytical neighbourhoods of points on a (n − s − 1)-dimensional stratum Zf,σ ⊂ Zf,Σ to products of a (s − 1)-dimensional open ball and a small analytical neighbourhood of the point pσ on the (n − s)-dimensional affine toric variety Aσ,N(σ). This theory and its corollaries help obtain a simultanious resolution of all members of the family F(∆).
MC 2017
Soham Chakraborty, École Normale Supérieure
Measured groupoids and the Choquet-Deny property
A countable discrete group is called Choquet-Deny if for every non-degenerate probability measure on the group, the corresponding space of bounded harmonic functions is trivial. Recently a complete characterization of Choquet-Deny groups was obtained by Frisch, Hartman, Tamuz and Ferdowsi. In this talk, we will look at the extension of the Choquet-Deny property to the framework of discrete measured groupoids. Our main result gives a complete characterisation of this property in terms of the associated measured equivalence relation and the isotropy groups of the groupoid. This talk is based on a joint work with Tey Berendschot, Milan Donvil, Mario Klisse and Se-Jin Kim.
MC 5417 or Join on Zoom