Events

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

Becky Armstrong, Victoria University of Wellington

Analysis Seminar: Twisted groupoids that are not induced by continuous 2-cocycles

Twisted groupoids are generalisations of group extensions that play an important role in C*-algebraic theory: every classifiable C*-algebra has an underlying twisted groupoid model. It is well known that group extensions are in one-to-one correspondence with group 2-cocycles. Analogously, every groupoid 2-cocycle gives rise to a twisted groupoid. However, an example due to Kumjian shows that the converse is not true. Kumjian’s counterexample is a twisted groupoid consisting entirely of isotropy, but in this talk I will present a new example of a twisted groupoid that is not all isotropy, such that the twisted isotropy subgroupoid is not induced by a 2-cocycle. (This is joint work with Abraham C.S. Ng, Aidan Sims, and Yumiao Zhou.)

MC 5417

Carlo Pagano, Concordia University

Hilbert 10 via additive combinatorics

In 1900 Hilbert proposed a list of problems that have been very influential throughout the last century. In 1970 Matiyasevich, building on earlier work of Davis—Putnam—Robinson, proved that Hilbert's 10th problem is undecidable for Z. The problem of extending this result to any ring that is finitely generated over Z (eg ring of integers in number fields) has attracted significant attention since 1970 and, thanks to the efforts of many mathematicians, the task has been reduced to an arithmetic problem about elliptic curves. This problem so far had been solved only conditional on the BSD conjecture (one of the Millenium problems) by Mazur—Rubin.

In joint work with Peter Koymans we have combined additive combinatorics (Green—Tao’s celebrated theorem) with 2-descent (an old technique dating back to Fermat) to solve this problem about elliptic curves unconditionally. This shows that Hilbert 10 is undecidable over any finitely generated infinite commutative ring.

In this colloquium I will provide a gentle introduction to this undecidability result, giving a glimpse of how mathematical logic, number theory and additive combinatorics meet into one story.

MC 5501

Miao Gu, University of Michigan

On Triple Product L-functions

The Poisson summation conjecture of Braverman-Kazhdan, Lafforgue, Ngo and Sakellaridis is an ambitious proposal to prove analytic properties of quite general Langlands L-functions using vast generalizations of the Poisson summation formula. In this talk, we present the construction of a generalized Whittaker induction such that the associated L-function is the product of the triple product L-function and L-functions whose analytic properties are understood. We then formulate an extension of the Poisson summation conjecture and prove that it implies the expected analytic properties of triple product L-functions. Finally, we use the fiber bundle method to reduce this extended Poisson summation conjecture to a case of the Poisson summation conjecture in which spectral methods can be employed together with certain local compatibility statements. This is joint work with Jayce Getz, Chun-Hsien Hsu, and Spencer Leslie.

MC 5479

Clement Yung, University of Toronto

Weak A2 spaces, the Kastanas game and strategically Ramsey sets

In the past century, the insight behind the original Ramsey's theorem proved to be applicable to a wide range of mathematics, such as number theory, functional analysis and topology. This spurred two particular directions of Ramsey theory: The first one is known as topological Ramsey theory, a general procedure developed by Todorcevic to prove many seemingly unrelated Ramsey's theorem-like results. The second one is the Ramsey theory of Banach spaces, kickstarted by Gowers' shocking application of Ramsey theory to resolve a long-standing open problem in Banach space theory. In this talk, I introduce the theory of weak A2 spaces, which serves as a possible intersection between these two Ramsey theories and discuss how several infinite games that appeared in these Ramsey theories (the Kastanas game, the Gowers game and the asymptotic game) are closely related.

MC 5479