Events

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

William Dan, University of Waterloo

Random Left C.E. Reals and Solovay Reducibility

In the last seminar we discussed how the halting probability of a universal prefix-free machine is left c.e. andrandom, and asked if the converse would hold. We then studied Solovay reducibility and the resulting concept ofSolovay completeness, which turns out to be key in proving the converse. In this seminar, we will use thisconcept to prove the two theorems giving the converse, a theorem from Calude et al. and the Kucera-Slamantheorem. Then, we will go back to expand further on the properties of Solovay reducibility and how it connectsto relative randomness, and relate this connection back to the theorems we proved. This seminar follows sections9.1 and 9.2 from the Downey and Hirschfeldt book.

MC 5403

Matthew Young, Rutgers University

The shifted convolution problem for Siegel modular forms

The shifted convolution problem for Fourier coefficients of cusp forms has seen a lot of attention due to applications towards moments of L-functions and the subconvexity problem. However, the problem for higher rank automorphic forms (beyond GL_2) has been a notorious bottleneck towards progress on the sixth moment of the Riemann zeta function. In this talk, I will discuss recent progress on the problem for Siegel cusp forms on Sp_4. This is joint work with Wing Hong (Joseph) Leung.

Join on Zoom

Rahim Moosa, University of Waterloo

Definable groups in CCM

I will continue totalk about “Strongly minimal groups in the theory of compact complex maniflds".

MC 5479

Fateme Peimany, University of Waterloo

Model Theory Working Seminar: Definable groups in CCM

We continue to study the structure of groups definable in CCM, toward showing that every strongly minimal group is either a complex torus or a (commutative) linear algebraic group.

MC 5479

Jules Ribolzi, University of Waterloo

On Two Model-Theoretic Approaches to Complex Analytic Geometry

There is a first-order multi-sorted structure for compact complex spaces which satisfies important model-theoretic properties (quantifier elimination, elimination of imaginaries, finiteness of Morley rank,…). We call this theory $CCM$. On the other hand, any compact complex manifold is definable in the O-minimal structure $\mathbb{R}_{an}$. In this talk, we will discuss the relation between these two structures (and also their elementary extensions).

MC 5417