Events

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

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

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

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

Francisco Villacis, University of Waterloo

Integrable Systems and Applications

Completely integrable systems and toric moment maps form an important set of tools for symplectic geometers. These give rise to Lagrangian fibrations, which in turn play an important role in quantization problems and are the main object of study in the SYZ formulation of mirror symmetry. In this talk I will give a brief overview of (completely) integrable systems and toric moment maps, how these appear in the context of mirror symmetry, and some of my work these past couple of years.

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