**Monday, 24 October 2016, 1:30PM**-- DC 2568*Networks and Distributed Systems PhD Seminar*-- Computer Science*Speaker:*Nashid Shahriar, David R. Cheriton School of Computer Science*Title:**"Recovery from Node Failure in Virtual Network Embedding"*

*Abstract:*Network virtualization (NV) has evolved as a key enabling technology for offering the next generation network services. Recently, it is being rolled out in data center networks as a means to provide bandwidth guarantees to cloud applications. With increasing deployments of virtual networks (VNs) in commercial-grade networks with commodity hardware, VNs need to tackle failures in the underlying substrate network. In this talk, I will discuss the problem of recovering a batch of VNs affected by a substrate node failure. The combinatorial possibilities of alternate embeddings of the failed virtual nodes and links of the failed VNs makes the task of finding the most efficient recovery both non-trivial and intractable. Furthermore, any recovery approach ideally should not cause any service disruption for the unaffected parts of the VNs. I take into account these issues to design a recovery approach for maximizing recovery and minimizing the cost of recovery and network disruption. I will present an Integer Linear Programming (ILP) formulation of the recovery scheme. I will also discuss a fast and scalable heuristic algorithm to tackle the computational complexity of the ILP solution. Thereafter, I will discuss the evaluation results, and compare my solutions with a state-of-the-art solution. I will conclude the talk with some future research directions.

**Monday, 24 October 2016, 4:00PM**-- MC 5501*Colloquium*-- Pure Mathematics*Speaker:*Noah Giansiracusa, Department of Mathematics and Statistics, Swarthmore College*Title:**"“A matroidal view of algebraic geometry”"*

*Remarks:*Refreshments will be served in MC 5403 at 3:30 p.m.Everyone is welcome to attend.

*Abstract:*Tropical geometry is a rapidly developing subject that has touched upon many areas of math, emanating from the desire to represent complex manifolds with simpler, combinatorial models. I’ll give a brief overview and then discuss a recent effort to reinforce the connection to algebraic geometry by discussing an equations-based approach to tropical geometry built upon idempotent semirings and matroids.

**Tuesday, 25 October 2016, 3:30PM**-- MC 5417*Computability Learning Seminar*-- Pure Mathematics*Speaker:*Jonathan Stephenson, Department of Pure Mathematics University of Waterloo*Title:**"“Joins of r.i.c.e relations and r.i.c.e complete relations”"*

*Abstract:*We will show that there is a natural way to form both finite and infinite joins of subsets of a structure. We will also introduce r.i.c.e complete relations, and show that every structure has a r.i.c.e. complete relation. We will use this to define a jump operator on relations in structures.

**Tuesday, 25 October 2016, 4:00PM**-- MC 6486 true*Graduate Student Seminar Seminar*-- Combinatorics and Optimization*Speaker:*Speaker #1: Levent Tuncel, Speaker #2 Mehdi Karimi, University of Waterloo*Title:**"Speaker #1: A Brief, Unconventional Introduction to Convex Optimization, Speaker #2: How to Solve a Convex Optimization Problem"*

*Abstract:*Speaker #1 Abstract: We will start by touching on some fundamental concepts in convex optimization. Then, we will review some unconventional applications of is theory.Speaker #2 Abstract: In the first talk, you see some interesting applications of convex optimization. However, modeling a problem as a convex optimization problem would be useless without efficient algorithms for solving it. In the second talk, we see how to start solving a convex optimization problem.

**Wednesday, 26 October 2016, 1:00PM**-- MC 5403*Model Theory Seminar*-- Pure Mathematics*Speaker:*Steven Lazzaro, McMaster University*Title:**"“Metric Structures”"*

*Abstract:*In this talk, we begin the study of Continuous Model Theory following ”Model Theory for Metric Structures” (Ben Yaacov, Bernstein, Henson, Usvyatsov). We start by briefly providing the motivation for studying these so-called metric structures through examples. In particular, we will see that any first-order structure can be viewed as a metric structure in a natural way. Following this brief discussion, we will go on to outline the definitions for metric structures which are analogous to the basic definitions for first-order structures: metric structures and their signatures, embeddings and isomorphsims, and substructures.

**Wednesday, 26 October 2016, 1:00PM**-- DC 1331*Database Research Group PhD Seminar*-- Computer Science*Speaker:*Kareem El Gebaly, David R. Cheriton School of Computer Science*Title:**"In-Browser SQL Analytics with Afterburner"*

*Abstract:*This talk explores the idea of implementing an analytical RDBMS in pure JavaScript so that it runs completely inside a browser with no external dependencies. Our prototype, called Afterburner, generates compiled query plans that exploit typed arrays and asm.js, two relatively recent advances in JavaScript. On the TPC-H benchmark, we show that Afterburner achieves comparable performance to MonetDB running natively on the same machine. This is an interesting ?finding in that it shows how far JavaScript has come as an e?fficient execution platform. We also discuss how our techniques could support ubiquitous in-browser interactive analytics (potentially integrating with browser-based note-books) and also present interesting opportunities for split execution strategies where query operators are distributed between the browser and backend servers.

**Wednesday, 26 October 2016, 3:00PM**-- MC 5403*Geometry & Topology Seminar Seminar*-- Pure Mathematics*Speaker:*Martin Pinsonnault, University of Western Ontario*Title:**"TBA"*

**Wednesday, 26 October 2016, 7:30PM**-- St. Jerome's SJ2 1004*Bridges Lecture Lecture*-- Faculty of Mathematics*Speaker:*Matthew Scott and Soheila Esfahani, Matthew Scott is an Associate Professor of Applied Mathematics and co-director of the Mathematical Biology Laboratory at the University of Waterloo.*and*Soheila Esfahani is an artist and educator based in Waterloo Region. Her research and art practice navigates the terrains of cultural translation in order to explore the processes involved in cultural transfer and transformation.*Title:**"Pattern finding – popular expression of transcendent ideas"*

*Remarks:*Please register at https://www.eventbrite.ca/e/bridges-public-lecture-series-pattern-finding-popular-expression-of-transcendent-ideas-tickets-27131816995

*Abstract:*Jokes, prayers, stories, art all express our deep need to communicate experience beyond our immediate interactions with the material world. Delight in shape and pattern is found in all folk art traditions back to the farthest reaches of antiquity. Focusing on episodes drawn from all over the world, we will discuss how mathematics plays a vital role in codifying our common experiences of awe and wonderment.

**Thursday, 27 October 2016, 1:30PM**-- MC 5479*Number Theory Seminar Seminar*-- Pure Mathematics*Speaker:*Divyum Sharma, Department of Pure Mathematics University of Waterloo*Title:**"“Number of solutions of Thue Equations”"*

*Abstract:*LetF(X,Y)∈Z[X,Y]beabinaryformwithnon-zerodiscriminantanddegreer≥3. Lethbea non-zero integer. In 1909, Thue proved that the equation F (X, Y ) = h has only finitely many solutions in integers x and y. Since then, much work has been done to estimate the number of solutions of Thue equations from above. In this talk, we will consider forms F which are diagonalizable, i.e. forms which can be written as F (X, Y ) = (αX + βY )r − (γX + δY )r, where the constants α, β, γ and δ are such that F (X, Y ) ∈ Z[X, Y ] and αδ − βγ ̸= 0. Following the hypergeometric method of Thue and Siegel, we give upper bounds for the number of primitive solutions of the Thue inequality 0 < |F (X, Y )| ≤ h, where F is diagonalizable. This is joint work with S. Akhtari and N. Saradha.

**Thursday, 27 October 2016, 3:30PM**-- Math & Computer, Room 5479*Seminar*-- Combinatorics and Optimization*Speaker:*Dr. Peter Nelson, Dept. of Combinatorics & Optimization, University of Waterloo*Title:**"The probability that a random subgraph contains a circuit"*

*Abstract:*We show that if $G$ is a sufficiently large graph of average degree $d > 2$ and $p > 1/(d-1)$, then a set $X \subseteq E(G)$ obtained by randomly including each edge with probability $p$ contains a circuit with high probability.

**Friday, 28 October 2016, 3:30PM**-- MC 5417*Analysis Seminar Seminar*-- Pure Mathematics*Speaker:*Paul Skoufranis, York University*Title:**"Majorization in C*-Algebras"*

*Abstract:*A classical result in matrix theory characterizes the convex hull of the unitary orbit of a self-adjoint matrix using spectral data. The description of these convex hulls has many applications such as characterizing the possible diagonal n-tuples of a self-adjoint matrix based on its eigenvalues. As all of these questions have natural analogues in an arbitrary unital C*-algebra, it is natural to ask whether these results have generalizations.In this talk, using a notion of majorization against unbounded traces, we characterize the norm-closed convex hulls of the unitary orbits of self-adjoint operators in any unital C*-algebra. Furthermore, for several classes of C*-algebras, such as those satisfying Blackadar's strict comparison of positive elements, an upper bound for the number of unitary conjugates in a convex combination required to approximate an element in the closed convex hull within a given error is shown to exist. (Joint work with P. Ng and L. Robert.)

**Friday, 28 October 2016, 3:30PM**-- Math & Computer, Room 5501*Colloquium*-- Combinatorics and Optimization*Speaker:*Gabriel Coutinho, Dept. of Computer Science, University of Sao Paulo*Title:**"Quantum walks on irregular graphs"*

*Abstract:*In this talk, we discuss the continuous-time quantum walk model which is described as the solution of Schrodinger's equation. Despite its simple description, many fundamental questions about this model remain open, even when the underlying graph is quite small. I will talk about some of these questions, and then I will discuss some recent advances in understanding quantum walks in paths of arbitrary length.

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