Events

Kain Dineen, University of Waterloo

Gromov's non-squeezing theorem

I will discuss Gromov's non-squeezing theorem. We will prove the affine version of the theorem and discuss a potential generalization of it for maps preserving some power of the symplectic form. We will then discuss the general non-squeezing theorem and, as an application, prove the classical rigidity result that the symplectomorphism group of any symplectic manifold is (C^0)-closed in the diffeomorphism group.

MC 5479

Nicolas Chavarria Gomez, University of Waterloo

MCurve Excluding Fields IV

We continue reading through Will Johnson's and Vincent Ye's paper on the theory of existentially closed fields excluding a curve.

MC 5403

Roy Zhao, Tsinghua University

Unlikely Intersection Problems and The Pila-Zannier Method

The Zilber-Pink Conjecture or the Mordell-Lang Conjecture predict that the unlikely intersections, be it for dimension reasons or other geometrical reasons, between a variety and families of special subvarieties can be completely explained by only finitely many special subvarieties. In the past twenty years, Pila and Zannier introduced a new method to prove these types of problems by utilizing tools from o-minimality and functional transcendence. In this talk, we will give an overview of this method in some simple cases of the Andre-Oort Conjecture. Then, we will discuss our recent work and how it plays a key role in the Pila-Zannier method proof of the full Andre-Oort Conjecture.

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Jiahui Huang, University of Waterloo

Deformation of Complex Structures in Mirror Symmetry

In the spirit of relating the complex geometry of a Calabi-Yau manifold to the Kahler geometry of its mirror, this talk considers how their deformations relate to each other. We study deformations of complex structures via Kodaira-Spencer theory and Kahler structures via Gromov-Witten invariants. We will also look at how they relate to homological mirror symmetry.

MC 5479

Adam Jelinsky, University of Waterloo

The Completing Technique for sums of periodic complex valued functions

In Iwaniec and Kowalski's book on analytic number theory, they detail what they call the "completing technique" to evaluate bounds on incomplete sums of periodic functions Z^n->C by "completing" it by finding an equivalent complete sum over all Z/qZ. In this talk we will discuss how this completion technique can be used to prove the Polya-Vinogradov inequality, which gives a nearly tight bound on all sums of Dirichlet characters over the interval [N,N+M]. From this we will discuss other applications of this method, and give examples where this method fails to give a bound that is nontrivial.

MC 5403

Roberto Albesiano, University of Waterloo

From division to extension

The L^2 extension theorem of Ohsawa and Takegoshi, and the L^2 division theorem of Skoda are two fundamental results in complex analytic geometry. They are also intimately related: in fact, Ohsawa showed that a version of the latter can be proved as a corollary of the former. I will explain the main idea of Ohsawa and how, conversely, a version of the L^2 extension theorem can be obtained as an easy corollary of a Skoda-type L^2 division theorem with bounded generators.

MC 5479

Nicolas Chavarria Gomez, Waterloo

Curve Excluding Fields V

We continue reading through Will Johnson's and Vincent Ye's paper on the theory of existentially closed fields excluding a curve.

MC 5403

Sourabh Das, University of Waterloo

Love, Life, and the Math Behind It -  Solving the Ultimate Equation

Finding love isn’t just about fate, chemistry, or the right swipe – it’s a problem. And if

there’s one thing math is great at, it’s solving problems (well, most of them). In this talk,

we’ll tackle the big questions of love using probability, and a touch of game theory:

- What are the odds of finding "The One"? (Spoiler: Finding aliens is actually more

likely.)

- When should you stop searching and settle down? (Mathematically, not emotionally.)

- How happy are you in your relationship? (A mathematical approach to the age-old

question: "Do they really know me?")

The first two parts will involve some surprisingly useful math to help you navigate the

dating world and optimize your love life. The final segment? A game designed to test your

compatibility with a "partner" – a friend, a crush, or your long-term love. To maximize

enjoyment (and potential awkwardness), attending in pairs is highly encouraged. In other

words: Bring a date. Or, if you’re feeling adventurous, let the math do the matchmaking!

MC 5417

(snacks at 5:00pm)

Kaleb D Ruscitti, University of Waterloo

Yukawa Coupling & the Mirror Map

The mirror map is a choice of co-ordinates on the moduli space of complex deformations Def(X) that come from natural co-ordinates on a moduli space of Kahler structures for X. In this presentation, we aim to introduce this map & the associated Yukawa couplings, in as much detail as possible given only one hour.

MC 2017

Jules Ribolzi, University of Waterloo

Nonstandard models of CCM

We start to consider elementary extensions of the standard model.

MC 5479