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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 $Q_n$.

Thursday, July 9, 2020 2:30 pm - 2:30 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Olya Mandelshtam

Title: Formulas for Macdonald polynomials arising from the ASEP

Speaker: Olya Mandelshtam
Affiliation: Brown University
Zoom: Contact Karen Yeats

Abstract:

The asymmetric simple exclusion process (ASEP) is a one-dimensional model of hopping particles that has been extensively studied in statistical mechanics, probability, and combinatorics. It also has remarkable connections with orthogonal symmetric polynomials in many variables such as Macdonald and Koornwinder polynomials.

Friday, July 10, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Felix Leditzky

Title: Symmetries and asymptotics of port-based teleportation

Speaker: Felix Leditzky
Affiliation: University of Waterloo
Zoom: Please email Emma Watson

Abstract:

Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. The original teleportation protocol is an exact protocol and amazingly simple, but it requires a non-trivial correction operation to make it work. Port-based teleportation (PBT) is an approximate variant of teleportation with a simple correction operation that renders the protocol unitarily covariant.

Monday, July 13, 2020 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Sebastian Cioaba

Title: On the flip graph on perfect matchings of complete graphs and sign reversal graphs

Speaker: Sebastian Cioaba
Affiliation: University of Delaware
Zoom: Contact Soffia Arnadottir

Abstract:

In this talk, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties including connections to the signed reversal graph and we improve a previous upper bound on its chromatic number.

Thursday, July 16, 2020 2:30 pm - 2:30 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Oliver Pechenik

Title: Dynamics of plane partitions

Speaker: Oliver Pechenik
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

Abstract:

Consider a plane partition P in an a X b X c box. The rowmotion operator sends P to the plane partition generated by the minimal elements of its complement. We show rowmotion resonates with frequency a+b+c-1, in the sense that each orbit size shares a prime divisor with a+b+c-1. This confirms a 1995 conjecture of Peter Cameron and Dmitri Fon-Der-Flaass. (Based on joint works with Kevin Dilks & Jessica Striker and with Becky Patrias.)

Friday, July 17, 2020 1:30 pm - 1:30 pm EDT (GMT -04:00)

Combinatorial Optimization Reading Group - Nishad Kothari

Title: Two unsolved problems: Birkhoff--von Neumann graphs and PM-compact graphs

Speaker: Nishad Kothari
Affiliation: CSE Department, Indian Institute of Technology Madras
Zoom: Contact Sharat Ibrahimpur

Abstract:

A well-studied object in combinatorial optimization is the {\it perfect matching polytope} $\mathcal{PMP}(G)$ of a graph $G$ --- the convex hull of the incidence vectors of all perfect matchings of $G$. A graph $G$ is {\it Birkhoff--von Neumann} if $\mathcal{PMP}(G)$ is characterized solely by non-negativity and degree constraints, and $G$ is {\it PM-compact} if the combinatorial diameter of $\mathcal{PMP}(G)$ equals one.

Friday, July 17, 2020 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Shachar Lovett

Title: Point Location and Active Learning - Learning Halfspaces Almost Optimally

Speaker: Shachar Lovett
Affiliation: UC San Diego
Zoom: Please email Emma Watson

Abstract:

The point location problem is a central problem in computational geometry. It asks, given a known partition of R^d by n hyperplanes, and an unknown input point, to find the cell in the partition to which the input point belongs. The access to the input is via linear queries. A linear query is specified by an hyperplane, and the result of the query is which side of the hyperplane the input point lies in.