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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 

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

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

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

Mark Hamilton, Mount Allison University

Toric degenerations and independence of polarization

In the theory of geometric quantization, one essential ingredient is the choice of a "polarization"; a natural question is then whether the resulting quantization depends on this choice.  One recent approach to the question of "independence of polarization" is using a deformation of complex structure to "deform" one polarization into another.  Originally applied to smooth toric varieties, this has also been applied to a broader class of examples, such as flag varieties, by using a toric degeneration. 

In this talk I will present an overview of this program (including a short introduction to the key ideas of geometric quantization), and mention several examples of its application, including flag manifolds, more general varieties, and moduli spaces of flat connections (work in progress).

MC 5403

Kunjakanan Nath, IECL Nancy, France

Circle method and binary correlation problems

One of the key problems in number theory is to understand the correlation between two arithmetic functions. In general, it is an extremely difficult question and often leads to famous open problems like the Twin Prime Conjecture, the Goldbach Conjecture, and the Chowla Conjecture, to name a few. In this talk, we will discuss a few binary correlation problems involving primes, square-free integers, and integers with restricted digits. The objective is to demonstrate the application of Fourier analysis (aka the circle method) in conjunction with the arithmetic structure of the given sequence and the bilinear form method to solve these problems.

Zoom: https://uwaterloo.zoom.us/j/94276302733?pwd=stZaTKvufL02c5UlpyubhpXYkTSDoN.1

Meeting ID: 942 7630 2733 Passcode: 144512

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

Anand Pillay, University of Notre Dame du Lac

On theories of "nice" fields equipped with a generic derivation

There is a growing body of work on differential fields which are NOT differentially closed but nevertheless have a tractable model theory. I will discuss various results, including a description of definable groups and analogues of algebraic D-groups.

MC 5479

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