Events

Candace Bethea, Duke University

The local equivariant degree and equivariant rational curve counting

I will talk about joint work with Kirsten Wickelgren on defining a global and local degree in stable equivariant homotopy theory. We construct the degree of a proper G-map between smooth G-manifolds and show a local to global property holds. This allows one to use the degree to compute topological invariants, such as the equivariant Euler characteristic and Euler number. I will discuss the construction of the equivariant degree and local degree, and I will give an application to counting orbits of rational plane cubics through 8 general points invariant under a finite group action on CP^2. This gives the first equivariantly enriched rational curve count, valued in the representation ring and Burnside ring. I will also show this equivariant enrichment recovers a Welchinger invariant in the case when Z/2 acts on CP^2 by conjugation.

MC 5417

Valeriya Kovaleva, University of Montreal

Correlations of the Riemann Zeta on the critical line

In this talk we will discuss the behaviour of the Riemann zeta on the critical line, and in particular, its correlations in various ranges. We will prove a new result for correlations of squares, where shifts may be up to size T^{3/2-\epsilon}. We will also explain how this result relates to Motohashi’s formula for the fourth moment, as well as the moments of moments of the Riemann Zeta and its maximum in short intervals.

MC 5479

Francisco Villacis, University of Waterloo

Integrable Systems and Applications

Completely integrable systems and toric moment maps form an important set of tools for symplectic geometers. These give rise to Lagrangian fibrations, which in turn play an important role in quantization problems and are the main object of study in the SYZ formulation of mirror symmetry. In this talk I will give a brief overview of (completely) integrable systems and toric moment maps, how these appear in the context of mirror symmetry, and some of my work these past couple of years.

MC 5403

Sumun Iyer, Carnegie Mellon University

Knaster continuum homeomorphism group

Knaster continua are a class of compact, connected, metrizable spaces. Each Knaster continuum is indecomposable-- it cannot be written as the union of two proper nontrivial sub continua. We consider the group Homeo(K) of all homeomorphisms of the universal Knaster continuum; this is a non-locally compact Polish group. We will describe some "large" topological group phenomena that occur in this group, in relation to the group's universal minimal flow and its generic elements.

MC 5479

Kyle Pereira, University of Waterloo

Fundamentals of Computability Theory 5

We will look at Post's Theorem and related hierarchies, following Robert Soare's textbook.

MC 5403

Zev Friedman, University of Waterloo

N-cohomologies on non-integrable almost complex manifolds

I will define an N-cohomology and compute some interesting examples, showing the different isomorphism classes on certain almost complex manifolds.

MC 5479

Camila Sehnem, University of Waterloo

A characterization of primality for reduced crossed products

In this talk I will discuss ideal structure of reduced crossed products by actions of discrete groups on noncommutative C*-algebras. I will report on joint work with M. Kennedy and L. Kroell, in which we give a characterization of primality for reduced crossed products by arbitrary actions. For a class of groups containing finitely generated groups of polynomial growth, we show that the ideal intersection property together with primality of the action is equivalent to primality of the crossed product. This extends previous results of Geffen and Ursu and of Echterhoff in the setting of minimal actions.

MC 5417 

Tristan Collins, University of Toronto

A free boundary Monge-Ampere equation with applications to Calabi-Yau metrics.

I will discuss a free boundary Monge-Ampere equation that arises from an attempt to construct complete Calabi-Yau metrics. I will explain how this equation can be solved and its connections with optimal transport. This is joint work with F. Tong and S.-T. Yau.

MC 5417

Diophantine Results for Shimura Varieties

Welcoming remarks: Dean Mark Giesbrecht (University of Waterloo)

Laudation: Professor Peter Sarnak (Institute for Advanced Study and Princeton University)

Ostrowski Lecture: Professor Jacob Tsimerman (University of Toronto)

Shimura Varieties are higher dimensional analogues of modular curves, and they play a foundational role in modern number theory. The most familiar Shimura varieties are the moduli spaces of Abelian varieties, and in this context we have a wealth of diophantine results, both in the number field and function field setting: Finiteness of S-rational points, the Tate conjecture, the Shafarevich conjecture, semisimplicity of Galois representations, and others. These results constitute a blueprint for what we expect to be true in other settings but is largely out of reach.

DC1302