Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants
 Argüz, H Bousseau, P Annales de l'Institut Fourier volume 72 issue 4 1547-1620 (12 Sep 2022)
The higher-dimensional tropical vertex
 Argüz, H Gross, M Geometry & Topology volume 26 issue 5 2135-2235 (12 Dec 2022)
The flow tree formula for Donaldson–Thomas invariants of quivers with potentials
 Argüz, H Bousseau, P Compositio Mathematica volume 158 issue 12 2206-2249 (19 Dec 2022)
Equations of mirrors to log Calabi–Yau pairs via the heart of canonical wall structures
 ARGÜZ, H Mathematical Proceedings of the Cambridge Philosophical Society volume 175 issue 2 381-421 (11 Sep 2023)
Gromov–Witten theory of complete intersections via nodal invariants
 Argüz, H Bousseau, P Pandharipande, R Zvonkine, D Journal of Topology volume 16 issue 1 264-343 (17 Mar 2023)
Fock–Goncharov dual cluster varieties and Gross–Siebert mirrors
 Argüz, H Bousseau, P Journal für die reine und angewandte Mathematik (Crelles Journal) (22 Jul 2023)
Quivers and curves in higher dimension
 Argüz, H Bousseau, P Transactions of the American Mathematical Society (03 Sep 2024)

Short stories 1

The mathematical genius of birds with Christiana Mavroyiakoumou.

Mon, 13 Oct 2025
16:00
C3

Eigenvalues of non-backtracking matrices

Cedric Pilatte
(Mathematical Insitute, Oxford)
Abstract
Understanding the eigenvalues of the adjacency matrix of a (possibly weighted) graph is a problem arising in various fields of mathematics. Since a direct computation of the spectrum is often too difficult, a common strategy is to instead study the trace of a high power of the matrix, which corresponds to a high moment of the eigenvalues. The utility of this method comes from its combinatorial interpretation: the trace counts the weighted, closed walks of a given length within the graph.
 
However, a common obstacle arises when these walk-counts are dominated by trivial "backtracking" walks—walks that travel along an edge and immediately return. Such paths can mask the more meaningful structural properties of the graph, yielding only trivial bounds.
 
This talk will introduce a powerful tool for resolving this issue: the non-backtracking matrix. We will explore the fundamental relationship between its spectrum and that of the original matrix. This technique has been successfully applied in computer science and random graph theory, and it is a key ingredient in upcoming work on the 2-point logarithmic Chowla conjecture.
Fri, 24 Oct 2025
12:00
L3

Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry

Claude LeBrun
(SUNY at Stony Brook)
Abstract

In this talk, I will discuss my joint paper with Olivier Biquard and Paul Gauduchon on ALF Ricci-flat Riemannian  4-manifolds. My collaborators had previously classified all such spaces that are toric and Hermitian, but not Kaehler. Our main result uses an open curvature condition to prove a rigidity result of the following type: any Ricci-flat metric that is sufficiently close to a non-Kaehler, toric, Hermitian ALF solution (with respect to a norm that imposes reasonable fall-off at infinity) is actually  one of the  known Hermitian toric  solutions. 
 

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