**Monday, 17 July 2017, 10:00AM**-- MC 5403*Seminar*-- Pure Mathematics*Speaker:*Stephen Wen, Department of Pure Mathematics, University of Waterloo*Title:**"An analog of Sarkozy's theorem on squares in difference sets"*

*Abstract:*We will follow a paper by Yu-Ru Liu and Thai Hoang Le in which we examine the difference sets of subsets of $\mathbb{F}_q[t]$. We will find a sufficient condition on the density of a subset $A$ in the set of polynomials of degree strictly less than $N$, denoted $\mathbb{G}_N$, so that $A-A$ must contain a perfect square. We will do this by bounding the density of sets $A$ such that $A-A$ has no perfect square. We will use the polynomial Hardy-Littlewood circle method along with density increment technology developed by Pintz, Steiger, and Szemeredi.

**Monday, 17 July 2017, 1:30PM**-- MC 2009*PhD Defence*-- Pure Mathematics*Speaker:*Adam Dor On, Department of Pure Mathematics, University of Waterloo*Title:**"Techniques in operator algebras: Classification, dilations and non-commutative boundaries"*

*Abstract:*In this talk we will see various techniques in operator algebras and operator systems. We begin with classification of non-self-adjoint and self-adjoint operator algebras constructed from certain Markov chains. We then transition to the study of non-commutative boundaries in the sense of Arveson, and use them to get interesting dilation results for families of operators associated to directed graphs. Finally, we discuss connections between operator systems, matrix convex sets and dilation theory, and use them to obtain scaled inclusion results for matrix convex sets.

**Tuesday, 18 July 2017, 3:30PM**-- MC 5403*Seminar*-- Pure Mathematics*Speaker:*Matthew Harrison-Trainor, Department of Pure Mathematics, University of Waterloo*Title:**"Computable Categoricity"*

*Abstract:*We will continue our discussion of computable categoricity by characterizing it for structures with some amount of decidability, and then separating it from relative computable categoricity.

**Wednesday, 19 July 2017, 10:00AM**-- MC 6460*Master's Thesis Presentation*-- Applied Mathematics*Speaker:*Shawn Corvec, Department of Applied Mathematics, University of Waterloo*Title:**"A modelling investigation into the impacts of the convective parameterization on the tropical circulation"*

*Abstract:*Many studies have shown that the tropical circulations (Walker and Hadley circulations) will weaken in a warmer world. This is sometimes attributed to changes in the tropical mean water cycling rate (driven by convective mass flux), which does not increase as fast as boundary layer water vapour in the tropics. However, this theory is only valid for the large scale upward convective mass flux in the tropics, not necessarily to the local circulations, which are not as energetically constrained. Here, we show that there is also a potential regime in which this argument does not hold by simply changing the convective scheme in a climate model. This regime is one in which the tropical mean convective mass flux can actually increase with warming, provided the precipitation efficiency decreases significantly. Our work supports the theory that the uniform tropical mean static stability increase is the physical driver of the weakening of the tropical circulations with climate change, which is mainly driven by the tropical mean SST increase, regardless of the change in strength of convective mass flux. The local changes in tropospheric diabatic heating from heating are shown to influence the magnitude of the weakening of the Walker circulation.We find that the precipitation efficiency decreases in an increased sea surface temperature AMIP-type experiment using the CAM4 AGCM with an alternate convective scheme using a unique mass flux closure, leading to a plausible scenario where tropical mean convective mass flux may increase, while the large-scale tropical circulations still weaken. While large-scale upward motion and convective mass flux are closely correlated spatially, the nature of this relationship can change in a warmer world if the precipitation efficiency changes. A decrease in precipitation efficiency can allow for increased upward convective mass flux, but the same tropospheric heating rate response, as the increased rate of condensational heating is offset by increased evaporational cooling. A decrease in precipitation efficiency leads to a lower heating rate per unit of upward mass flux due to a compensating increase in evaporation. The large tropical mean evaporation response seen with this scheme allows for stronger tropical mean convective updrafts, especially of the shallow variety, to balance where the evaporational cooling response is maximized.

**Wednesday, 19 July 2017, 4:00PM**-- DC 2314*Computer Graphics Research Group PhD Seminar*-- Computer Science*Speaker:*Lesley Istead, David R. Cheriton School of Computer Science*Title:**"Nonphotorealistic Rendering of Stereoscopic 3D Media"*

*Abstract:*We present a method for stylizing stereoscopic 3D images that guarantees consistency between the left and right views. Our method decomposes the left and right views of an input image into discretized disparity layers and merges the corresponding layers from the left and right views into a single layer where stylization takes place. We then construct new stylized left and right views by compositing portions of the stylized layers. Because the left and right views come from the same source layers, our method eliminates common artifacts that cause viewer discomfort. We also present a stereoscopic 3D painterly rendering algorithm tailored to our layer-based approach. This method uses disparity information to assist in stroke creation so that strokes follow surface geometry without ignoring painted surface patterns.

**Thursday, 20 July 2017, 9:30AM**-- MC 2009*PhD Defence*-- Pure Mathematics*Speaker:*Jaspar Wiart, Department of Pure Mathematics, University of Waterloo*Title:**"Four Years in Thirty Minutes"*

*Abstract:*In my four years at UW I completed two research projects. For the first project I computed the C*-envelopes of a family of isometric semicrossed products arising from number theory. In the second I characterized the Jacobson radical of certain semicrossed products of simple unital C*-algebras with sufficiently nice semigroups. In this talk I will briefly summarize what I did in reverse chronological order.

**Thursday, 20 July 2017, 2:30PM**-- MC 5403*Seminar*-- Pure Mathematics*Speaker:*Nickolas Rollick, Department of Pure Mathematics, University of Waterloo*Title:**"Categorizing schemes in the wild"*

*Abstract:*Last time, we laid the groundwork necessary to make sense of the category of schemes. This week, we get a feel for this category via some examples and structural facts. In particular, we will learn what the final object is, construct non-trivial morphisms from a one-point scheme to itself, and look at the seemingly odd notion of scheme-valued points of a scheme. It's truly a wild world these schemes live in...

**Thursday, 20 July 2017, 4:00PM**-- MC 5479*Seminar*-- Pure Mathematics*Speaker:*Brandon Doherty, Department of Pure Mathematics, University of Waterloo*Title:**"Goodstein sequences and the Hydra game"*

*Abstract:*G\"odel's incompleteness theorem proves the existence of certain statements about the natural numbers that can be neither proven nor disproven using basic first-order arithmetic. The kinds of statements constructed in the standard proof of the incompleteness theorem, however, are extremely technical, and not very interesting in and of themselves.This raises the question: are there any natural, interesting statements about the natural numbers that are neither provable or disprovable in first-order arithmetic? In 1982, Kirby and Paris provided examples of easily understandable theorems which are true, and can be stated in the language of first-order arithmetic, but cannot be proven. One of these states that every one of a class of sequences known as Goodstein sequences, which initially grow extremely quickly, eventually decays to zero and terminates. The other states that a graph-theoretic game involving rooted trees, known as the Hydra game, eventually terminates regardless of the player's strategy.

**Friday, 21 July 2017, 10:00AM**-- MC 6460*PhD Defence*-- Applied Mathematics*Speaker:*Mikhai Panine, Department of Applied Mathematics, University of Waterloo*Title:**"On Perturbative Methods in Spectral Geometry"*

*Abstract:*The goal of spectral geometry is to establish how much information about the geometry of compact Riemannian manifolds is contained in the spectra of natural differential operators, especially Laplacians, defined on them. Ideally, one would like to be able to recover the Riemannian manifold, up to isometry, from the spectra of one or several such operators. This would be a very powerful result, as it would introduce an invariant way to describe the shape of Riemannian manifolds. The consequences of such a result would range from practical applications to shape recognition to theoretical insights into quantum gravity.However, the most general form of such statements is known to be false. There is a number of known counterexamples, that is isospectral but not isometric manifolds. Indeed, there are even techniques to construct such counterexamples. Nonetheless, it is believed that almost all Riemannian manifolds can be identified by their spectra. In other words, the counterexamples are expected to be exceedingly rare special cases. This has been shown to be the case in some restricted classes of manifolds. The proof in the general case has remained elusive.

The main goal of this thesis is to move towards such a proof by studying the structure of isospectral sets of metrics. The main tool we use for this purpose is perturbation theory, a method ubiquitous in physics, but strangely underused in spectral geometry. Consequently, a secondary goal of this work is to demonstrate the usefulness of perturbation theory to the study of spectral geometry. We begin by a numerical exploration of spectral geometry in a perturbative regime. Then, we show that sets of isospectral conformally equivalent metrics on boundaryless manifolds of dimension two contain no convex subsets. This is an entirely new type of result in spectral geometry. We argue that it could lead to a proof of the rarity of counterexamples to the program of identifying shapes by their spectra.

The thesis also includes reviews of the fundamentals of the spectral theory of Laplace-type operators, of major results in spectral geometry and of perturbation theory.

**Friday, 21 July 2017, 11:00AM**-- DC 2306C*Artificial Intelligence Lab PhD Seminar*-- Computer Science*Speaker:*Nabiha Asghar, David R. Cheriton School of Computer Science*Title:**"Deep Active Learning for Dialogue Generation"*

*Abstract:*We propose an online, end-to-end, neural generative conversational model for open-domain dialogue. It is trained using a unique combination of offline two-phase supervised learning and online human-in-the-loop active learning. While most existing research proposes offline supervision or hand-crafted reward functions for online reinforcement, we devise a novel interactive learning mechanism based on hamming-diverse beam search for response generation and one-character user-feedback at each step. Experiments show that our model inherently promotes the generation of semantically relevant and interesting responses, and can be used to train agents with customized personas, moods and conversational styles.Published as a short paper in the Proceedings of the 6th Joint Conference on Lexical and Computational Semantics (*SEM), 2017.

*This work was done in Collaboration with Xin Jiang, Hang Li from Huawei Noah's Ark in Hong Kong and Pascal Poupart.*

**Friday, 21 July 2017, 2:00PM**-- MC 5417*Seminar*-- Pure Mathematics*Speaker:*Adam Morgan, Department of Applied Mathematics, University of Waterloo*Title:**"Finite Element Exterior Calculus, Part 3"*

*Abstract:*We will finish covering the concepts intended for the previous week's lecture, introducing discretizations of de Rham complexes and some rudimentary definitions in finite element analysis.

**Friday, 21 July 2017, 3:30PM**-- QNC 0101*Tutte Colloquium Colloquium*-- Combinatorics and Optimization*Speaker:*Dr. Maria Chudnovsky, Princeton University*Title:**"Coloring graphs with forbidden induced subgraphs"*

*Abstract:*The problem of testing if a graph can be colored with a given number k of colors in NP-complete for every k > 2. But what if we have more information about the input graph, namely that some xed graph H is not present in it as an induced subgraph? It is known that the problem remains NP-complete even for k = 3, unless H is the disjoint union of paths. We consider the following two questions:1) For which graphs H is there a polynomial time algorithm to 3-color (or in general k-color) an H-free graph?

2) For which graphs H are there nitely many 4-critical H-free graphs?

This talk will survey recent progress on these questions, an in particular give a complete answer to the second one.

* ...... WebNotice*