Monday, March 27, 2023 — 8:00 PM EDT

Title: Inverse eigenvalue problem of a graph

Speaker: Jephian C.-H. Lin
Affiliation: National Sun Yat-sen University
Location: Please contact Sabrina Lato for Zoom link

Abstract:  We often encounter matrices whose pattern (zero-nonzero, or sign) is known while the precise value of each entry is not clear. Thus, a natural question is what we can say about the spectral property of matrices of a given pattern. When the matrix is real and symmetric, one may use a simple graph to describe its off-diagonal nonzero support.

Wednesday, March 29, 2023 — 2:30 PM EDT

Title: Distance-Regular and Distance-Biregular Graphs

Speaker: Sabrina Lato
Affiliation: University of Waterloo
Location: MC

Abstract: For a given diameter d and valency k, what is the maximum number of vertices a k-regular graph of diameter d can have, and what graphs meet that bound? Although there is a straightforward counting argument to bound the number of vertices using the structural information, the problem of characterizing the graphs that meet the bound turns out to be a problem in algebraic graph theory, and helps gives rise to the notion of distance-regular graphs.

Thursday, March 30, 2023 — 1:00 PM EDT

Title: Arrangements of Pseudolines, Tropical Grassmannians, and Generalized Scattering Amplitudes

Speaker: Freddy Cachazo
Affiliation: Perimeter Institute
Room: MC 6029

Abstract: For each arrangement of (pseudo)lines on the projective plane, it is possible to construct a differential form that captures its combinatorial structure. The forms have simple poles whenever triangles shrink to a point in the arrangement, and share the same residue when two arrangements are connected via a "triangle flip".

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