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Francisco Villacis, University of Waterloo

A Deep Dive into Mathematicians’ Questionable Outfits

Being able to prove the most impressive theorems and having a good sense of fashion need not be mutually exclusive - except it might be? This will be up to you to judge in this talk. Together, we’ll apply the most unscientific of methodologies to create a tier list of mathematicians based solely on their dressing style - from Euclid’s timeless toga to Grothendieck’s "I’ve been living in a forest for five years" aesthetic. Be sure to bring your best outfits, otherwise you might end up in a bored grad student's tier list one day.

MC 5479

(snacks from 4:00pm)

Alex Pawelko, University of Waterloo

The Formal Kaehler Structure of the G2 Knot Space

We will explore the usual suspects of the moduli space of knots embeddable in a G2 manifold, based upon the work of Brylinski for the analogous space corresponding to the 3-dimensional cross product. This gives an infinite-dimensional "formally Kaehler" manifold, which one can consider Kaehler reduction on. If time permits, we will gesture vaguely at considerations from gauge theory and geometric quantization that motivate many interesting questions in the case of G2 manifolds.

MC 5403

Faisal Romshoo, University of Waterloo

Symmetry groups, moment maps and cohomogeneity one special Lagrangians in C^m

We will discuss the relationship between symmetries and moment maps as explained in arXiv:math/0008021 and how this allows us to construct cohomogeneity one special Lagrangians in C^m. Time permitting, we will discuss some examples of SL m-folds in C^m.

MC 5403

Facundo Camano, University of Waterloo

Convergence Results for Taub-NUT and Eguchi-Hanson spaces

We define multi-Taub-NUT and multi-Eguchi-Hanson spaces and look at Gromov-Hausdorff convergences involving these spaces.

MC 5403

Justin Fus, University of Waterloo

The KKS Form and Symplectic Geometry of Coadjoint Orbits

A compact Lie group acts on its Lie algebra dual via the coadjoint representation. In this talk, we will explore how the coadjoint orbits of this representation carry a natural symplectic structure called the Kirillov-Kostant-Souriau (KKS) form. The KKS form is preserved by the action. If time permits, we will show that there is a moment map for the action that coincides with the inclusion map of the orbit. A worked example for SU(2) will be performed.

MC 5403

Joey Lakerdas-Gayle, University of Waterloo

Effective Algebra 1

We will begin learning about recursive groups following Chapter 8 of Yuri Manin's "A Course in Mathematical Logic for Mathematicians".

MC 5417

Jiahui Huang, University of Waterloo

Motivic integration for schemes, DM stacks, and Artin stacks.

We give an overview of motivic integration and its generalization to stacks. Early motivations for motivic integration involve singularity theory and the monodromy conjecture. We will explain how the change of variable formula works, and how it generalizes to the stack case. Motivic integration for stacks will use twisted or warped arcs, and we shall give a summary of the construction of the twisted arc space for DM stacks.

MC 5403

Zhenchao Ge, University of Waterloo

An additive property for product sets in finite fields.

Lagrange's Four Square Theorem states that every natural number can be written as a sum of four squares, i.e. squares form an additive basis of order 4. Cauchy observed that in a finite field F with q elements, squares form an additive basis of order 2. Bourgain further generalized the problem and proved that for any subset A in F, writing AA={aa': a,a'∈ A}, we have 3AA=F whenever |A|>q^{3/4}. 

In general, for subsets A,B in F with |A||B|>q, one might ask that how many copies of AB are enough to cover the entire space? The current record of this problem is due to Glibichuk and Rudnev. Using basic Fourier analysis tools, they achieved 10AB=F unconditionally and 8AB=F assuming symmetry (or anti-symmetry).

In this talk, we will (hopefully) go through the paper of Glibichuk and Rudnev.

MC 5417

Mark Poor, Cornell University

Some results about the pseudoarc and its homeomorphism group

It is known that the so called pseudoarc can be represented as a quotient of a zero-dimensional compact "prespace" under an appropriate equivalence relation (which is an inverse limit of linear graphs), and the automorphisms of this prespace densely embeds into the homeomorphism group of the pseudoarc. Although this embedding is only continuous, not a homeomorphic embedding, we can actually characterize the topology inherited from the homeomorphism group intrinsically, only in terms of the prespace. Using this characterization we show that not all homeomorphisms are conjugate to an automorphism, and we give a second proof to Kwiatkowska's conjecture, namely that there exists a homeomorphism with a dense conjugacy class.

This is joint work with S. Solecki.

MC 5479

Amanda Wilkens, Carnegie Mellon University

Poisson–Voronoi tessellations and fixed price in higher rank

We briefly define and motivate the Poisson point process, which is, informally, a "maximally random" scattering of points in space, and discuss the ideal Poisson–Voronoi tessellation (IPVT), a new random object with intriguing geometric properties when considered on a semisimple symmetric space (the hyperbolic plane, for example). In joint work with Mikolaj Fraczyk and Sam Mellick, we use the IPVT to prove a result on the relationship between the volume of a manifold and the number of generators of its fundamental group. We give some intuition for the proof. No prior knowledge on fixed price or higher rank will be assumed.

MC 5417