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Friday, September 27, 2019 — 3:30 PM EDT

**Title:** Countable weighted graphs with no unfriendly partitions

Wednesday, September 25, 2019 — 2:00 PM EDT

**Title:** Improving Implementations of CSIDH

Speaker: | Jason LeGrow |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

I will present on some papers related to implementations of CSIDH [1].

Friday, September 20, 2019 — 3:30 PM EDT

**Title:** Undermining key exchange

Speaker: | Douglas Stebila |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

There are many ways to undermine systems that rely on cryptography. An attacker could of course try to find flaws in the hardware and software implementing the system, or find mathematical weaknesses in the cryptographic algorithms.

Friday, September 20, 2019 — 1:00 PM EDT

**Title: **Submodular function maximization

Speaker: | Chaitanya Swamy |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract**:

I will give the introductory talk for this term's topic for the Combinatorial-Optimization Reading group, namely submodular function maximization. Submodular functions arise in diverse contexts in combinatorial optimization.

Thursday, September 19, 2019 — 4:00 PM EDT

**Title:** The sparsest matroids omitting an independent flat

Speaker: | Peter Nelson |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

Given integers $k,r \ge 1$, what is the smallest a rank-$r$ matroid can be that does not contain a $k$-element independent set that is also a flat? I will answer this question, characterize the extremal examples, and draw parallels with a problem in graph theory.

Thursday, September 19, 2019 — 3:30 PM EDT

**Title:** When are two Schur functions the same?

Speaker: | Nick Olson-Harris |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

A pair of skew shapes are said to be (skew) equivalent if they admit the same number of semistandard tableaux of any weight; i.e. if their associated skew Schur functions are equal.

Thursday, September 19, 2019 — 1:00 PM EDT

**Title****: **Orthogonal Polynomials and the Addition Formula

Speaker: | Chris Godsil |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

Many questions about designs and codes in the unit sphere can be reduced to questions about members of a family of orthogonal polynomials, the so-called Gegenbauer polynomials.

Friday, September 13, 2019 — 3:30 PM EDT

**Title:** Monochromatic cycle partitions

Speaker: | Richard Lang |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

A classic result of Erdős, Gyárfás, and Pyber states that the vertex set of every complete graph, whose edges have been coloured with r colours, can be covered by r^{2} log r disjoint monochromatic cycles.

Thursday, September 12, 2019 — 3:30 PM EDT

**Title:** Combinatorial questions motivated by Invariant Theory

Speaker: | Matthew Satriano |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

We begin the talk by discussing a question in Invariant Theory: given a representation $V$ of a Lie group $G$, when if the invariant ring $k[V]^G$ a polynomial ring? We give a conjectural answer which we have verified for $SL_n$ and discuss some combinatorial questions motivated by the proof. This is joint work with Dan Edidin.

Thursday, September 12, 2019 — 1:00 PM EDT

**Title:** Polynomial Spaces

Speaker: | Chris Godsil |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

We describe some simple machinery that enables us to derive upper bounds on the size of codes, and lower bounds on the size of designs in a quite general setting.

Friday, September 6, 2019 — 3:30 PM EDT

**Title:** Approximation Algorithms for Minimum-Norm Optimization Problems

Speaker: | Chaitanya Swamy |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

In many optimization problems, a feasible solution induces a multidimensional cost vector. For example, in k-clustering, opening k facilities induces an assignment-cost vector indexed by the clients; in load-balancing, a schedule induces a load vector across the machines.

Thursday, September 5, 2019 — 1:00 PM EDT

**Title:** Signings and induced subgraphs of the Hypercube

Speaker: | Maxwell Levit |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

Just over a month ago, Hao Haung resolved the sensitivity conjecture, a 30 year-old question about the complexity of boolean functions.

Tuesday, September 3, 2019 — 3:30 PM EDT

**Title: **Independence Polynomials and Their Roots

Speaker: | Jason Brown |

Affiliation: | Dalhousie University |

Room: | MC 5417 |

**Abstract:**

Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph G.

Thursday, August 15, 2019 — 2:30 PM EDT

**Title**: Upsetting Matrices

Speaker: | Chris Godsil |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

If $A$ and $P$ are $n\times n$ matrices and the entries of $B$ are small, we may view $A+B$ as a perturbation of $A$, and expect that the spectral properties of $A+B$ should be related to those of $A$.

Thursday, August 8, 2019 — 2:30 PM EDT

**Title:** Continuous Quantum Walks

Speaker: | Soffia Arnadottir |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

Continuous quantum walks are of considerable interest in quantum physics and quantum computing.

Tuesday, August 6, 2019 — 3:30 PM EDT

**Title:** Feynman graphs, ribbon graphs and tensor graphs

Speaker: | Adrian Tanasa |

Affiliation: | Université de Bordeaux |

Room: | MC 5479 |

**Abstract:**

In this talk I will define the so-called Feynman graphs, which are a particular class of graphs appearing in quantum field theory.

Friday, August 2, 2019 — 3:30 PM EDT

**Title:** Optimization and Cryptography in Generalized Physical Theories

Speaker: | Jamie Sikora |

Affiliation: | Perimeter Institute |

Room: | MC 5501 |

**Abstract:**

In this talk, I will discuss three important cryptographic tasks in the quantum and post-quantum world. I will discuss the impossibility of bit-commitment and coin-flipping, and also the possibility of physically unforgeable money in the framework of Generalized Physical Theories (GPTs).

Friday, August 2, 2019 — 1:00 PM EDT

**Title:** Stable marraige with general preferences

Speaker: | Matthew Louis Gerstbrein |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

This week, we discuss a generalization of the standard stable marriage problem, in which one side has a complete, totally ordered, strict preference list while the other has preferences given in terms of arbitrary binary relations.

Thursday, August 1, 2019 — 3:30 PM EDT

**Title:** Counting subdivergence-free gluing of trees

Speaker: | Clair Dai |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

If we take two rooted trees with the same number of leaves and form a graph by gluing the leaves of one tree to the other, then we say the graph is subdivergence-free if no 2-edge cut have been generated.

Thursday, August 1, 2019 — 3:30 PM EDT

**Title:** The combinatorics of nearest and furthest values

Speaker: | Lily Wang |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

A classical problem asks us to find, for each element $*A*[*i*]$ of an array of integers, the position of the nearest smallest element.

Thursday, August 1, 2019 — 3:30 PM EDT

**Title: **Bijections among symmetric tableaux via folding and mixed insertion

Speaker: | Yuval Ohapkin |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

A standard Young tableau with entries $-*M* < \cdots -1 < 1 < \cdots < *M*$ can be "folded" by performing certain conversions and rectifications in sequence.

Thursday, August 1, 2019 — 2:30 PM EDT

**Title:** Non-Commutative Algebras and Graphs

Speaker: | Chris Godsil |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

I will discuss some of the non-commutative algebras that arise naturally in graph theory.

Friday, July 26, 2019 — 1:00 PM EDT

**Title:** New and Simple Algorithms for Stable Flow Problems

Speaker: | Justin Toth |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

In the previous reading group talk we defined stable flows and saw that they always exist by a reduction to the stable allocation problem.

Thursday, July 25, 2019 — 3:30 PM EDT

**Title:** Lewis Carroll and the Red Hot Potato

Speaker: | Melanie Dennis |

Affiliation: | Dartmouth College |

Room: | MC 5417 |

**Abstract:**

The Lewis Carroll identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns.

Thursday, July 25, 2019 — 2:30 PM EDT

**Title:** Kemeny's Constant for Markov Chains

Speaker: | Steve Kirkland |

Affiliation: | University of Manitoba |

Room: | MC 5479 |

**Abstract:**

Markov chains are a much-studied class of stochastic processes, and it is well-known that if the transition matrix A associated with a Markov chain possesses a certain property (called primitivity), then the long-term behaviour of the Markov chain is described by a particular eigenvector of A, known as the stationary distribution vector.

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