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Friday, June 12, 2020 1:30 pm - 1:30 pm EDT (GMT -04:00)

Combinatorial Optimization Reading Group - Vishnu V. Narayan

Title: One Dollar Each Eliminates Envy

Speaker: Vishnu V. Narayan
Affiliation: McGill University
Zoom: Contact Sharat Ibrahimpur

Abstract:

We study the fair division of a collection of $m$ indivisible goods amongst a set of $n$ agents. Whilst envy-free allocations typically do not exist in the indivisible goods setting, envy-freeness can be achieved if some amount of a divisible good (money) is introduced.

Friday, June 12, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Courtney Paquette

Title: Halting Time is Predictable for Large Models: A Universality Property and Average-case Analysis

Speaker: Courtney Paquette
Affiliation: University of Waterloo
Zoom: Please email Emma Watson

Abstract:

Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in optimization. One difficulty is that the analysis can depend on the probability distribution of the inputs to the model.

Thursday, June 18, 2020 1:03 pm - 1:03 pm EDT (GMT -04:00)

Combinatorial Optimization Reading Group - Julián Romero

Title: Graph coloring of graphs with large girth is hard for the Nullstellensatz

Speaker: Julián Romero
Affiliation: University of Waterloo
Zoom: Contact Sharat Ibrahimpur

Abstract:

In this talk we will discuss a method to solve combinatorial problems using hierarchies of systems of linear equations using Hilbert's Nullstellensatz. In particular, we will study the behaviour of these hierarchies for deciding the non-$k$-colorabilty of graphs.

Thursday, June 18, 2020 2:30 pm - 2:30 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Victor Reiner

Title: Sandpiles and representation theory

Speaker: Victor Reiner
Affiliation: University of Minnesota
Zoom: Contact Karen Yeats

Abstract:

For an undirected graph, its sandpile group is an interesting isomorphism invariant-- it is a finite abelian group that describes the integer cokernel of the graph's Laplacian matrix.

Friday, June 19, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Nicolas Trotignon

Title: Widths in even-hole-free graphs

Speaker: Nicolas Trotignon
Affiliation: CNRS - LIP - École Normale Supérieure de Lyon
Zoom: Please email Emma Watson

Abstract:

Historically, the study of even-hole-free graphs is motivated by the analogy with perfect graphs. The decomposition theorems that are known for even-hole-free graphs are seemingly more powerful than the ones for perfect graphs: the basic classes and the decompositions are in some respect more restricted. But strangely, in an algorithmic perpective, much more is known for perfect graphs. 

Thursday, June 25, 2020 2:30 pm - 2:30 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Ali Mahmoud

Title: 2-Connected Chord Diagrams and Applications in QFT

Speaker: Ali Mahmoud
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

Abstract:

A functional equation for 2-connected chord diagrams is derived, then is used to calculate asymptotic information for the number of 2-connected chord diagrams by means of alien derivatives applied to factorially divergent power series.

Friday, June 26, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - David Wagner

Title: Discrete diffusion on graphs and real hyperplane arrangements

Speaker: David Wagner
Affiliation: University of Waterloo
Zoom: Please email Emma Watson
To view the slides: Click here

Abstract:

In 2016, Duffy, Lidbetter, Messinger, and Nowakowski introduced the following variation of a chip-firing model on a graph. At time zero, there is an integer number of "chips" at each vertex. Time proceeds in discrete steps.  At each step, each edge is examined (in parallel) -- one chip is moved from the greater end to the lesser end if the ends are not equal.

Thursday, July 2, 2020 2:30 pm - 2:30 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Timothy Miller

Title: Factorial Schur Functions and Quantum Intergrability

Speaker: Timothy Miller
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

Abstract:

I will introduce factorial Schur functions as they relate to my Master's thesis. Factorial Shur functions are a generalization of Schur functions with a second family of "shift" parameters. In 2009, Zinn-Justin reproved the answer to a tiling problem (the puzzle rule) with a toy fermionic model, using techniques from physics to extract the result.

Friday, July 3, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Peter Selinger

Title: Number-theoretic methods in quantum computing

Speaker: Peter Selinger
Affiliation: Dalhousie University
Zoom: Please email Emma Watson

Abstract:

An important problem in quantum computing is the so-called \emph{approximate synthesis problem}: to find a quantum circuit, preferably as short as possible, that approximates a given target operation up to given $\epsilon$. For nearly two decades, from 1995 to 2012, the standard solution to this problem was the Solovay-Kitaev algorithm, which is based on geometric ideas. This algorithm produces circuits of size $O(\log^c(1/\epsilon))$, where $c$ is a constant approximately equal to $3.97$. It was a long-standing open problem whether the exponent $c$ could be reduced to $1$.

Monday, July 6, 2020 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory seminar - Maxwell Levit

Title: A covering graph perspective on Huang’s theorem 

Speaker: Maxwell Levit
Affiliation: University of Waterloo
Zoom: Contact Soffia Arnadottir

Abstract:

Just about a year ago, Hao Huang resolved the sensitivity conjecture by proving that any induced subgraph on more than half the vertices of the hypercube $Q_n$ has maximum degree at least $\sqrt(n)$. The key ingredient in his proof is a special $\pm 1$ signing of the adjacency matrix of $Q_n$.