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

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

Friday, September 27, 2019 — 1:00 PM EDT

**Title: **Submodular function maximization

Speaker: | Chaitanya Swamy |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**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 26, 2019 — 3:30 PM EDT

**Title:** Chord diagrams, generating functions, and qft

Speaker: | Karen Yeats |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

I'll talk about some joint work with Julien Courtiel where some nice enumerative combinatorics tells us something about how gauge theories are such special quantum field theories.

Thursday, September 26, 2019 — 1:00 PM EDT

**Title:** LP bounds and the addition formula

Speaker: | Chris Godsil |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

I will show how we can derive useful bounds on the size of codes and designs, using linear programming and the addition formula.

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.

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.

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