Joey Lakerdas-Gayle, University of Waterloo
Fundamentals of Computability Theory 4
We will continue working through some examples of injury arguments, following Robert Soare's textbook.
MC 5403
Faisal Romshoo, University of Waterloo
Special Lagrangian Geometry
I will talk about special Lagrangian submanifolds, which have garnered considerable interest in several areas in differential geometry and theoretical physics. In particular, I will describe some examples of special Lagrangian submanifolds explicitly.
MC 5479
Matthew Wiersma, University of Waterloo
Entropies and Poisson boundaries of random walks on groups with rapid decay
Let $G$ be a countable group and $\mu$ a probability measure on $G$. The Avez entropy of $\mu$ provides a way of quantifying the randomness of the random walk on $G$ associated with $\mu$. We build a new framework to compute asymptotic quantities associated with the $\mu$-random walk on $G$, using constructions that arise from harmonic analysis on groups. We introduce the notion of \emph{convolution entropy} and show that, under mild assumptions on $\mu$, it coincides with the Avez entropy of $\mu$ when $G$ has the rapid decay property. Subsequently, we apply our results to stationary dynamical systems consisting of an action of a group with the rapid decay property on a probability space, and give several characterizations for when the Avez entropy coincides with the Furstenberg entropy of the stationary space. This leads to a characterization of Zimmer amenability for stationary dynamical systems whenever the acting group has the property of rapid decay.
This talk is based on joint work with B. Anderson-Sackaney, T. de Laat and E. Samei.
MC 5417 or Zoom link below
https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09
Candace Bethea, Duke University
The local equivariant degree and equivariant rational curve counting
I will talk about joint work with Kirsten Wickelgren on defining a global and local degree in stable equivariant homotopy theory. We construct the degree of a proper G-map between smooth G-manifolds and show a local to global property holds. This allows one to use the degree to compute topological invariants, such as the equivariant Euler characteristic and Euler number. I will discuss the construction of the equivariant degree and local degree, and I will give an application to counting orbits of rational plane cubics through 8 general points invariant under a finite group action on CP^2. This gives the first equivariantly enriched rational curve count, valued in the representation ring and Burnside ring. I will also show this equivariant enrichment recovers a Welchinger invariant in the case when Z/2 acts on CP^2 by conjugation.
MC 5417
Valeriya Kovaleva, University of Montreal
Correlations of the Riemann Zeta on the critical line
In this talk we will discuss the behaviour of the Riemann zeta on the critical line, and in particular, its correlations in various ranges. We will prove a new result for correlations of squares, where shifts may be up to size T^{3/2-\epsilon}. We will also explain how this result relates to Motohashi’s formula for the fourth moment, as well as the moments of moments of the Riemann Zeta and its maximum in short intervals.
MC 5479
Sumun Iyer, Carnegie Mellon University
Knaster continuum homeomorphism group
Knaster continua are a class of compact, connected, metrizable spaces. Each Knaster continuum is indecomposable-- it cannot be written as the union of two proper nontrivial sub continua. We consider the group Homeo(K) of all homeomorphisms of the universal Knaster continuum; this is a non-locally compact Polish group. We will describe some "large" topological group phenomena that occur in this group, in relation to the group's universal minimal flow and its generic elements.
MC 5479
Kyle Pereira, University of Waterloo
Fundamentals of Computability Theory 5
We will look at Post's Theorem and related hierarchies, following Robert Soare's textbook.
MC 5403
Zev Friedman, University of Waterloo
N-cohomologies on non-integrable almost complex manifolds
I will define an N-cohomology and compute some interesting examples, showing the different isomorphism classes on certain almost complex manifolds.
MC 5479
Camila Sehnem, University of Waterloo
A characterization of primality for reduced crossed products
In this talk I will discuss ideal structure of reduced crossed products by actions of discrete groups on noncommutative C*-algebras. I will report on joint work with M. Kennedy and L. Kroell, in which we give a characterization of primality for reduced crossed products by arbitrary actions. For a class of groups containing finitely generated groups of polynomial growth, we show that the ideal intersection property together with primality of the action is equivalent to primality of the crossed product. This extends previous results of Geffen and Ursu and of Echterhoff in the setting of minimal actions.
MC 5417
Tristan Collins, University of Toronto
A free boundary Monge-Ampere equation with applications to Calabi-Yau metrics.
I will discuss a free boundary Monge-Ampere equation that arises from an attempt to construct complete Calabi-Yau metrics. I will explain how this equation can be solved and its connections with optimal transport. This is joint work with F. Tong and S.-T. Yau.
MC 5501