Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext 33038
PDF files require Adobe Acrobat Reader.
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Title: Quantum walks do not like bridges
Speaker: Emanuel Juliano Affiliation: Universidade Federal de Minas Gerais Zoom: Contact Sabrina LatoAbstract:
In this talk we consider graphs with two cut vertices joined by a bridge, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has no other vertex.
Title: EdgeDisjoint Linkage in Infinite Graphs
Speaker: Amena Assem Affiliation: University of Waterloo Zoom: http://matroidunion.org/?page_id=2477 or contact Shayla RedlinAbstract:
In 1980 Thomassen conjectured that, for odd k, an edgeconnectivity of k is enough for a graph to be weakly klinked, meaning any k pairs of terminals can be linked by k edgedisjoint paths. The best known result to date for finite graphs is from 1991, by Andreas Huck, and assumes an edgeconnectivity of k+1 for odd k.
Title: A New Adaptive Attack on SIDH
Speaker: Valerie Gilchrist Affiliation: University of Waterloo Zoom: Please email Jesse ElliottAbstract:
The SIDH key exchange is the main building block of SIKE, the only isogeny based scheme involved in the NIST standardization process. In 2016, Galbraith et al. presented an adaptive attack on SIDH. In this attack, a malicious party manipulates the torsion points in his public key in order to recover an honest party's static secret key, when having access to a key exchange oracle.
Title: Crystal invariant theory and geometric RSK
Speaker: Gabriel Frieden Affiliation:Université du Québec à Montréal (UQAM)
Zoom: Contact Olya MandelshtamAbstract:
The original problem of classical invariant theory was to describe the invariants of SL_m acting on a polynomial ring in an m \times n matrix of variables. One way to solve this problem is to consider the polynomial ring as a GL_m \times GL_n representation, and decompose this representation into its irreducible components.
Title: Laplacian States
Speaker: Chris Godsil Affiliation: University of Waterloo Zoom: Conatact Sabrina LatoAbstract:
It is customary to assume that the initial state of a continuous quantum walk on a graph $X$ is a vertex. However the Laplacian matrix of a graph with vertex set $V(X)$ is positive semidefinite, and can be scaled to produce a density matrix, and so provides an initial state for a walk on $X$.
Title: Enumerating Matroids and Linear Spaces
Speaker: Mehtaab Sawhney Affiliation: MIT Zoom: Please email Shayla RedlinAbstract:
We show that the number of linear spaces on a set of $n$ points and the number of rank3 matroids on a ground set of size $n$ are both of the form $(cn+o(n))^{n^2/6}$, where $c=e^{\sqrt 3/23}(1+\sqrt 3)/2$. This is the final piece of the puzzle for enumerating fixedrank matroids at this level of accuracy: there are exact formulas for enumeration of rank1 and rank2 matroids, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant $r\ge 4$ there are $(e^{1r}n+o(n))^{n^{r1}/r!}$ rank$r$ matroids on a ground set of size $n$.
Title: Guessing with little data
Speaker: Manuel Kauers Affiliation: Johannes Kepler University Zoom: Please email Emma WatsonAbstract:
A popular and powerful technique in experimental mathematics takes as input the first few terms of an infinite sequence and returns plausible candidates for recurrence equations that the sequence may satisfy. In a way, the search for such candidates is a generalization of polynomial interpolation. For polynomial interpolation, it is well known and easy to see that d+1 sample points are needed in order to recover a polynomial of degree d. Similarly, it turns out that (r+1)*(d+2) consecutive terms of a sequence are needed in order to detect a linear recurrence of order r with polynomial coefficients of degree at most d.
Title: Minimal relations for an algebra inspired by algebraic graph theory
Speaker: Erika Pirnes Affiliation: University of WisconsinMadison Zoom: Contact Sabrina LatoAbstract:
The balanced algebra has two generators, R and L, and its defining relations are that any pair of balanced words commutes. For example, RL and LR are balanced (contain the same number of both generators), so in the balanced algebra, (RL)(LR)=(LR)(RL).
Title: A Matching Theoretic Flat Wall Theorem
Speaker: Archontia Giannopoulou Affiliation: University of Athens Zoom: http://matroidunion.org/?page_id=2477 or please email Shayla RedlinAbstract:
One of the key theorems in Graph Minors is the Flat Wall Theorem which asserts the existence of a large wall under certain conditions. In this talk, we discuss about graphs with perfect matchings and their relationship with digraphs. Our main focus is on a matching theoretic analogue of the Flat Wall Theorem for bipartite graphs excluding a fixed matching minor.
Title: Random Selfreducibility of IdealSVP via Arakelov Random Walks
Speaker: Pravek Sharma Affiliation: University of Waterloo Zoom: Please email Jesse ElliottAbstract:
Fixing a number field, the space of all ideal lattices, up to isometry, is naturally an Abelian group, called the *Arakelov class group*. This fact, well known to number theorists, has so far not been explicitly used in the literature on latticebased cryptography. Remarkably, the Arakelov class group is a combination of two groups that have already led to significant cryptanalytic advances: the class group and the unit torus.
Title: Springer fibers and the Delta Conjecture at t=0
Speaker: Sean Griffin Affiliation: UC Davis Zoom: Please email Olya MandelshtamAbstract:
Springer fibers are a family of varieties that have remarkable connections to combinatorics and representation theory. Springer used them to geometrically construct all of the irreducible representations of the symmetric group (Specht modules). Moreover, they give a geometric meaning to HallLittlewood symmetric functions.
Title: Traveling Salesman Problems: Approximation Algorithms and BlackBox Reductions
Speaker: Jens Vygen Affiliation: University of Bonn Zoom: Please email Emma WatsonAbstract:
We survey the recent progress on approximation algorithms and integrality ratios for variants of the traveling salesman problem, with a focus on blackbox reductions from one problem to another. In particular, we explain recent results for the Path TSP and the Capacitated Vehicle Routing Problem, which are joint works with Vera Traub and Rico Zenklusen and with Jannis Blauth and Vera Traub.
Title: Hadamard diagonalizable graphs of small order
Speaker: Steve Butler Affiliation: Iowa State University Zoom: Contact Sabrina LatoAbstract:
A graph whose Laplacian matrix has a full set of eigenvectors with entries in {1,1} is said to be Hadamard diagonalizable (i.e. there exists a Hadamard matrix which diagonalizes the Laplacian matrix). We demonstrate that the only diagonalizable graphs on n=8k+4 vertices are K_n and K_{n/2,n/2}.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.