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Tuesday, February 15, 2022 4:00 pm - 4:00 pm EST (GMT -05:00)

Graphs and Matroids Seminar - Chun-Hung Liu

Title: Homomorphism counts in robustly sparse graphs

Speaker: Chun-Hung Liu
Affiliation: Texas A&M University
Zoom: Click here or please email Shayla Redlin

Abstract:

For a fixed graph H and for arbitrarily large host graphs G, the number of homomorphisms from H to G and the number of subgraphs isomorphic to H contained in G have been extensively studied when the host graphs are allowed to be dense.

Friday, February 18, 2022 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Chandra Chekuri

Title: Densest Subgraph: Supermodularity, Iterative Peeling, and Flow

Speaker: Chandra Chekuri
Affiliation: University of Illinois, Urbana-Champaign
Zoom: Please email Emma Watson

Abstract:

The densest subgraph problem in a graph (DSG), in the simplest form, is the following. Given an undirected graph G = (V, E) find a subset S of vertices that maximizes the ratio |E(S)|/|S| where E(S) is the set of edges with both endpoints in S. DSG and several of its variants are well-studied in theory and practice and have many applications in data mining and network analysis.

Tuesday, March 1, 2022 11:00 am - 11:00 am EST (GMT -05:00)

Graphs and Matroids Seminar - Louis Esperet

Title: Packing and covering balls in planar graphs

Speaker: Louis Esperet
Affiliation: G-SCOP Laboratory
Zoom: Join via http://matroidunion.org/?page_id=2477 or please email Shayla Redlin

Abstract:

The set of all vertices at distance at most r from a vertex v in a graph G is called an r-ball. We prove that the minimum number of vertices hitting all r-balls in a planar graph G is at most a constant (independent of r) times the maximum number of vertex-disjoint r-balls in G.

Thursday, March 3, 2022 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Federico Castillo

Title: Lineup polytopes and exclusion principles

Speaker: Federico Castillo
Affiliation: Universidad Catolica de Chile
Zoom link: Contact Logan Crew

Abstract:

The set of all possible spectra of 1-reduced density operators for systems of N particles on a d-dimensional Hilbert space is a polytope called hypersimplex and this is related to Pauli's exclusion principle. If the spectrum of the original density operators is fixed, the set of spectra (ordered decreasingly) of 1-reduced density operators is also a polytope.

Friday, March 4, 2022 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Mireille Bousquet-Mélou

Title: Counting planar maps, 50 years after William Tutte

Speaker: Mireille Bousquet-Mélou
Affiliation: CNRS, Université de Bordeaux
Location: MC 5501 or please contact Emma Watson for Zoom link

Abstract:

Every planar map can be properly coloured with four colours. But how many proper colourings has, on average, a planar map with $n$ edges? What if we allow a prescribed number of "monochromatic" edges, the endpoints of which share the same colour? What if we have $q$ colours rather than four?

Monday, March 7, 2022 11:30 pm - 11:30 pm EST (GMT -05:00)

Algebraic Graph Theory Seminar - Bill Martin

Title: Polynomial ideals, association schemes, and the Q-polynomial property

Speaker: Bill Martin
Afiliation: Worcester Polytechnic Institute
Zoom: Contact Sabrina Lato

Abstract:

Let X ⊆ S^{m−1} be a spherical code in C^m. We study the ideal I ⊆ C[z_1, . . . , z_m] of polynomials that vanish on the points of X: I = { F(z) | (∀a ∈ X) (F(a) = 0) }. The primary example of interest is where the Gram matrix of X is proportional to the first idempotent in some Q-polynomial ordering of an association scheme (X, R) defined on X.

Tuesday, March 8, 2022 4:00 pm - 4:00 pm EST (GMT -05:00)

Graphs and Matroids Seminar - Sang-il Oum

Title: Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k

Speaker: Sang-il Oum
Affiliation: Institute for Basic Science / KAIST
Zoom: Join via http://matroidunion.org/?page_id=2477 or please email Shayla Redlin

Abstract:

Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field $\mathbb F$, the list contains only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)].

Thursday, March 10, 2022 11:30 am - 11:30 am EST (GMT -05:00)

Cryptography Reading Group

Title: “Lattice-Based Zero-Knowledge Arguments for Integer Relations” by Benoit Libert, San Ling, Khoa Nguyen, and Huaxiong Wang

Speaker: Camryn Steckel
Affiliation: University of Waterloo
Zoom: Contact Jesse Elliott

Abstract:

We provide lattice-based protocols allowing to prove relations among committed integers. While the most general zero-knowledge proof techniques can handle arithmetic circuits in the lattice setting, adapting them to prove statements over the integers is non-trivial, at least if we want to handle exponentially large integers while working with a polynomial size modulus q.

Thursday, March 10, 2022 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Joshua Swanson

Title: Type B q-Stirling numbers

Speaker: Joshua Swanson
Affiliation: USC
Location: MC 6029 or contact Logan Crew for Zoom link

Abstract:

The Stirling numbers of the first and second kind are classical objects in enumerative combinatorics which count the number of permutations or set partitions with a given number of blocks or cycles, respectively. Carlitz and Gould introduced q-analogues of the Stirling numbers of the first and second kinds, which have been further studied by many authors including Gessel, Garsia, Remmel, Wilson, and others, particularly in relation to certain statistics on ordered set partitions.

Friday, March 11, 2022 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Walaa Moursi

Title: Strongly nonexpansive mappings revisited: uniform monotonicity and operator splitting

Speaker: Walaa Moursi
Affiliation: University of Waterloo
Location: MC 5501 or please contact Emma Watson for Zoom link

Abstract:

The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental role in the convergence analysis of the splitting methods. Indeed, the performance of some of these methods, e.g., Douglas–Rachford and Peaceman–Rachford methods hinges on iterating the so-called splitting operator associated with the individual operators.