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 5501
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
Sunil Naik, Queen's University
On a question of Christensen, Gipson and Kulosman
The study of irreducible polynomials in various polynomial rings is an important topic in mathematics. In this context, polynomials with restricted exponents have become the focus of considerable attention in recent years. Motivated by these considerations, Matsuda introduced the ring $F[X;M]$ of polynomials with coefficients in a field $F$ and exponents in a commutative, torsion-free, cancellative (additive) monoid $M$ and began an inquiry into the irreducibility of various polynomials in these rings. For any prime $\ell$, we say that $M$ is a Matsuda monoid of type $\ell$ if for each indivisible $\alpha$ in $M$, the polynomial $X^{\alpha}-1$ is irreducible in $F[X;M]$ for any field $F$ of characteristic $\ell$.
Let $M$ be the additive submonoid of non-negative integers generated by 2 and 3. In a recent work, Christensen, Gipson, and Kulosman proved that $M$ is not a Matsuda monoid of type 2 and type 3 and they have raised the question of whether $M$ is a Matsuda monoid of type $\ell$ for any prime $\ell$. Assuming the Generalized Riemann Hypothesis (GRH), Daileda showed that $M$ is not a Matsuda monoid of any positive type. In this talk, we will discuss an unconditional proof of the above result using its connection with Artin’s primitive root conjecture.
Anne Johnson, University of Waterloo
The Arc Space of the Grassmannian
We give a brief description of the arc space of a scheme and discuss a decomposition of the arc space of the Grassmanian given by Decampo and Nigro in 2016. To do so, we give just enough detail on Schubert calculus as is necessary to make sense of the decomposition. We present some of their related results on plane partitions and irreducibility and then discuss extensions of this work to flag varieties.
MC 5403
Facundo Camano, University of Waterloo
Gromov-Hausdorff Convergence
I will introduce Hausdorff and Gromov-Hausdorff distances on metric spaces. We will look at examples of calculating distances and convergent sequences of metric spaces. We will end off with proving Gromov’s precompactness theorem and a few pathological examples of convergence stemming from the result.
MC 5479
Tobias Shin, University of Chicago
Almost complex manifolds are (almost) complex
What is the difference topologically between an almost complex manifold and a complex manifold? Are there examples of almost complex manifolds in higher dimensions (complex dimension 3 and greater) which admit no integrable complex structure? We will discuss these two questions with the aid of a deep theorem of Demailly and Gaussier, where they construct a universal space that induces almost complex structures for a given dimension. A careful analysis of this space shows the question of integrability of complex structures can be phrased in the framework of Gromov's h-principle. If time permits, we will conclude with some examples of almost complex manifolds that admit a family of Nijenhuis tensors whose sup norms tend to 0, despite having no integrable complex structure (joint with L. Fernandez and S. Wilson).
MC 5417
Rizwanur Khan, University of Texas at Dallas
Eisenstein series and the Random Wave Conjecture
What do automorphic forms "look" like when plotted on the modular surface? Quantum chaos predictions say that they should tend to look more and more like random waves. We'll discuss the relevant conjecture and report on progress for a fundamental type of automorphic form - the Eisenstein series. This is joint work with Goran Djanković.