Events

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.

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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

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

Nathaniel Bannister, Carnegie Mellon University

Condensed Sets and the Solovay Model

We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the κ-pyknotic sets of Barwick--Haine and Clausen--Scholze. We then use the properties of this morphism andautomatic continuity in the Solovay model to outline a proof of Clausen--Scholze's resolution of the Whiteheadproblem for discrete condensed abelian groups. Joint work with Dianthe Basak.

MC 5417

Fateme Peimany, University of Waterloo

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