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

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

Amanda Petcu, University of Waterloo

Some results on hypersymplectic structures

A conjecture of Simon Donaldson is that on a compact 4-manifold X^4 one can flow from a hypersymplectic structure to a hyperkahler structure while remaining in the same cohomology class. To this end the hypersymplectic flow was introduced by Fine-Yao. In this thesis the notion of a positive triple on X^4 is used to define a hypersymplectic and hyperkahler structure. Given a closed positive triple one can define either a closed G2 structure or a coclosed G2 structure on T^3 x X^4. The coclosed G2 structure is evolved under the G2 Laplacian coflow. This descends to a flow of the positive triple on X^4, which is again the Fine-Yao hypersymplectic flow. In the second part of this thesis we let X^4 = R^4 \0 with a particular cohomogeneity one action. A hypersymplectic structure invariant under this action is introduced. The Riemann and Ricci curvature tensors are computed and we verify in a particular case that this hypersymplectic structure can be transformed to a hyperkahler structure. The notion of a soliton for the hypersymplectic flow in this particular case is introduced and it is found that steady solitons give rise to hypersymplectic structures that can be transformed to hyperkahler structures. Some other soliton solutions are also discussed.

MC 5403

Elisabeth Werner, Case Western Reserve University

The $L_p$-Floating Area and Isoperimetric Inequalities on the Sphere

Euclidean convex bodies in spaces of constant positive curvature. We introduce the family of $L_p$-floatingareas for spherical convex bodies, as an analog to $L_p$-affine surface area measures from Euclidean geometry.We investigate a duality formula, monotonicity and isoperimetric inequalities for this new family of curvaturemeasures on spherical convex bodies. Based on joint works with Florian Besau.

MC 5417