Model Theory Working Seminar
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
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