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Title: Total Dual Integrality for Convex, Semidefinite and Extended Formulations
Speaker: Levent Tuncel Affiliation: University of Waterloo Zoom: Please email Emma WatsonAbstract:
Within the context of characterizations of exactness of convex relaxations of 0,1 integer programming problems, we present a notion of total dual integrality for Semidefinite Optimization Problems (SDPs), convex optimization problems and extended formulations of convex sets.
Title: Efficient $(j,k)$Domination
Speaker: Brendan Rooney Affiliation: Rochester Institute of Technology Zoom: Contact Soffia ArnadottirAbstract:
A function $f:V(G)\rightarrow\{0,\ldots,j\}$ is an efficient $(j,k)$dominating function on $G$ if $\sum_{u\in N[v]}f(u)=k$ for all $v\in V(G)$ (here $N[v]=N(v)\cup\{v\}$ is the closed neighbourhood of $v$).
Title: Factorization problems in complex reflection groups
Speaker: Alejandro Morales Affiliation: University of Massachusetts Amherst Zoom: Contact Karen YeatsAbstract:
The study of factorizations in the symmetric group is related to combinatorial objects like graphs embedded on surfaces and noncrossing partitions. We consider analogues for complex reflections groups of certain factorization problems of permutations first studied by Jackson, Schaeffer, Vassilieva and Bernardi.
Title: Generalization bounds for rational selfsupervised learning algorithms
Speaker: Boaz Barak Affiliation: Harvard University Zoom: Please email Emma WatsonAbstract:
The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples.Modern deep learning algorithms typically have large generalization gaps, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous.
Title: Pretty Good State Transfer and Minimal Polynomials
Speaker: Christopher van Bommel Affiliation: University of Manitoba Zoom: Contact Soffia ArnadottirAbstract:
We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out.
Title: The Hepp bound of a matroid: flags, volumes and integrals
Speaker: Erik Panzer Affiliation: University of Oxford Zoom: Contact Rose McCartyAbstract:
Invariants of combinatorial structures can be very useful tools that capture some specific characteristics, and repackage them in a meaningful way. For example, the famous Tutte polynomial of a matroid or graph tracks the rank statistics of its submatroids, which has many applications, and relations like contractiondeletion establish a very close connection between the algebraic structure of the invariant (e.g. Tutte polynomials) and the actual matroid itself.
Title: On the Theory of the Analytical Forms called Trees
Speaker: Nick OlsonHarris Affiliation: University of Waterloo Zoom: Contact Maxwell LevitAbstract:
Trees are among the most fundamental of combinatorial structures. Nowadays they appear all over mathematics and computer science, but this has not always been the case. Trees were first introduced, at least under that name, in an 1857 paper of Cayley by the same title as this talk.
Title: Coxeter combinatorics and spherical Schubert geometry
Speaker: Reuven Hodges Affiliation: University of Illinois Zoom: Contact Karen YeatsAbstract:
This talk will introduce spherical elements in a finite Coxeter system. These spherical elements are a generalization of Coxeter elements, that conjecturally, for Weyl groups, index Schubert varieties in the flag variety G/B that are spherical for the action of a Levi subgroup.
Title: Semidefinite Programming Relaxations of the Traveling Salesman Problem
Speaker: David P. Williamson Affiliation: Cornell University Zoom: Please email Emma WatsonAbstract:
Finding a polynomialtime solvable relaxation of the traveling salesman problem whose integrality gap better matches what is seen in practice has been an outstanding open problem in combinatorial optimization for some time. We study several semidefinite programming relaxations of the traveling salesman problem proposed in the literature and show that all known relaxations have an unbounded integrality gap.
Title: Pseuodrandom Cliquefree Graphs, Finite Geometry, and Spectra
Speaker: Ferdinand Ihringer Affiliation: Ghent University, Belgium Zoom: Contact Soffia ArnadottirAbstract:
A regular graph is called optimally pseudorandom if its second largest eigenvalue in absolute value is, up to a constant factor, as small as possible. Determining the largest degree of an optimally pseudorandom graph without a clique of size s is a wellknown open problem in extremal graph theory.
Title: qRSt: A probabilistic RobinsonSchensted correspondence for Macdonald polynomials
Speaker: Florian Aigner Affiliation: Université du Québec à Montréal Zoom: Contact Karen YeatsAbstract:
The RobinsonSchensted (RS) correspondence is a bijection between permutations and pairs of standard Young tableaux which plays a central role in the theory of Schur polynomials. In this talk, I will present a (q,t)dependent probabilistic deformation of RobinsonSchensted which is related to the Cauchy identity for Macdonald polynomials.
Title: The Tutte Symmetric Function
Speaker: Logan Crew Affiliation: University of Waterloo Zoom: Please email Emma WatsonAbstract:
The Tutte polynomial is one of the most celebrated and most wellstudied graph functions, in part because it specializes to every graph polynomial with a linear deletioncontraction relation, such as the chromatic polynomial. In the 1990s, Stanley generalized the Tutte polynomial to a symmetric function, but at the cost of the deletioncontraction relation.
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