Events

Tommaso Pacini, University of Torino

Kahler techniques beyond Kahler geometry: the case of pluripotential theory

Classical pluripotential theory was introduced into complex analysis in the 1940's, as an analogue of the theory of convex functions. In the early 2000's, Harvey and Lawson showed that both pluripotential theory and many of its analytic applications make sense in a much broader setting.

Starting with the work of Calabi in the 1950's, however, it has become clear that pluripotential theory is central also to Kahler geometry. In particular, it is closely related to the cohomology of Kahler manifolds via Hodge theory and the ddbar lemma, and it provides one of the main ingredients in proving the existence of canonical metrics.

Work in progress, joint with A. Raffero, shows how parts of this "second life" of pluripotential theory extend to other geometries, hinting towards new research directions in the field of calibrated geometry and manifolds with special holonomy.

The goal of this talk will be to present a non-technical overview of some of these topics, aimed at non-specialists.

MC 5501

Chi Hoi Yip, Georgia Institute of Technology

Inverse sieve problems

Many problems in number theory boil down to bounding the size of a set contained in a certain set of residue classes mod p for various sets of primes p; and then sieve methods are the primary tools for doing so. Motivated by the inverse Goldbach problem, Green–Harper, Helfgott–Venkatesh, Shao, and Walsh have explored the inverse sieve problem: if we let S \subseteq N be a maximal set of integers in this interval where the residue classes mod p occupied by S have some particular pattern for many primesp, what can one say about the structure of the set S beyond just its size? In this talk, I will give a gentle introduction to inverse sieve problems, and present some progress we made when S mod p has rich additive structure for many primes p. In particular, in this setting, we provide several improvements on the larger sieve bound for |S|, parallel to the work of Green--Harper and Shao for improvements on the large sieve. Joint work with Ernie Croot and Junzhe Mao.

Join on Zoom

Rahim Moosa, University of Waterloo

Definable groups in CCM

I will survey what is known about the structure of definable groups in both the standard and nonstandard models of CCM.

MC 5479

Faisal Romshoo, University of Waterloo

Deformations of calibrations

We will look at a criterion for unobstructedness for calibrations and see when the corresponding moduli spacesform smooth manifolds, following the approach by Goto in https://arxiv.org/abs/math/0112197

MC 5403

Evan Sundbo, University of Waterloo

Broken Toric Varieties and Balloon Animal Maps

We will see the definition and some examples of broken toric varieties and balloon animal maps between them. After an overview of some of the many different areas in which they appear, we look at how their geometry can be studied via complexes of sheaves on an associated complex of polytopes. This yields results such as a version of the Decomposition Theorem and some explicit formulas for dimensions of rational cohomology groups of broken toric varieties.

MC 5417

Open Mic

Come listen to or contribute a minitalk (no longer than 15 minutes). Anything (as long as it vaguely relates tomathematics and is reasonably accessible) goes!

MC 5479

(Refreshments will start at 16:30)

Xiao Zhong, University of Waterloo

Bounds on the Greatest Common Divisors and a Dynamical Analogy

In this talk, I will discuss a dynamical analogue of a classical number-theoretic question concerning bounds on the greatest common divisors of two integer sequences. I will present some recent progress on this problem and highlight several open directions for future research. Finally, I will explain how this question relates to the Dynamical Mordell–Lang Conjecture, a central topic in algebraic and arithmetic dynamics.

MC 5501

(with snacks afterward)

Mathilde Gerbelli-Gauthier, University of Toronto

Equidistribution of Root Numbers

The root number of an L-function captures important arithmetic information, such as, conjecturally, the parity of the rank in the case of elliptic curves. As such, statistics of root numbers can tell us about the typical behavior of arithmetic objects. In joint work with Rahul Dalal, we prove an equidistribution result for root numbers of self-dual automorphic representations of GL_N as the weight varies. This is done in the framework of endoscopy and the stable trace formula.

MC 5479

Rahim Moosa, University of Waterloo

Definable groups in CCM

I will continue the compactification argument for complex manifolds that are compactifiable outside one point.

MC 5479

Facundo Camano, University of Waterloo

Moduli Space Degeneration via Monopole Deformation

In this talk, I will discuss the theory behind the deformation of monopoles. I will then apply the theory to show monopole moduli spaces degenerate as a singularity is sent off towards infinity.

MC 5403