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Title: Factorial Schur Functions and Quantum Intergrability
Speaker: Timothy Miller Affiliation: University of Waterloo Zoom: Contact Karen YeatsAbstract:
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, ZinnJustin reproved the answer to a tiling problem (the puzzle rule) with a toy fermionic model, using techniques from physics to extract the result.
Title: Numbertheoretic methods in quantum computing
Speaker: Peter Selinger Affiliation: Dalhousie University Zoom: Please email Emma WatsonAbstract:
An important problem in quantum computing is the socalled \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 SolovayKitaev 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 longstanding open problem whether the exponent $c$ could be reduced to $1$.
Title: A covering graph perspective on Huang’s theorem
Speaker: Maxwell Levit Affiliation: University of Waterloo Zoom: Contact Soffia ArnadottirAbstract:
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 $Q_n$.
Title: Formulas for Macdonald polynomials arising from the ASEP
Speaker: Olya Mandelshtam Affiliation: Brown University Zoom: Contact Karen YeatsAbstract:
The asymmetric simple exclusion process (ASEP) is a onedimensional 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.
Title: Symmetries and asymptotics of portbased teleportation
Speaker: Felix Leditzky Affiliation: University of Waterloo Zoom: Please email Emma WatsonAbstract:
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 nontrivial correction operation to make it work. Portbased teleportation (PBT) is an approximate variant of teleportation with a simple correction operation that renders the protocol unitarily covariant.
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 ArnadottirAbstract:
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.
Title: Dynamics of plane partitions
Speaker: Oliver Pechenik Affiliation: University of Waterloo Zoom: Contact Karen YeatsAbstract:
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+c1, in the sense that each orbit size shares a prime divisor with a+b+c1. This confirms a 1995 conjecture of Peter Cameron and Dmitri FonDerFlaass. (Based on joint works with Kevin Dilks & Jessica Striker and with Becky Patrias.)
Title: Two unsolved problems: Birkhoffvon Neumann graphs and PMcompact graphs
Speaker: Nishad Kothari Affiliation: CSE Department, Indian Institute of Technology Madras Zoom: Contact Sharat IbrahimpurAbstract:
A wellstudied 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 Birkhoffvon Neumann} if $\mathcal{PMP}(G)$ is characterized solely by nonnegativity and degree constraints, and $G$ is {\it PMcompact} if the combinatorial diameter of $\mathcal{PMP}(G)$ equals one.
Title: Point Location and Active Learning  Learning Halfspaces Almost Optimally
Speaker: Shachar Lovett Affiliation: UC San Diego Zoom: Please email Emma WatsonAbstract:
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.
Title: Group Theory and the Erd\H{o}sKoRado (EKR) Theorem
Speaker: Karen Meagher Affiliation: University of Regina Zoom: Contact Soffia ArnadottirAbstract:
Group theory can be a key tool in sovling problems in combinatorics; it can provide a clean and effective proofs, and it can give deeper understanding of why certain combinatorial results hold. My research has focused on the famous Erd\H{o}sKoRado (EKR) theorem.
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