Matroids and Algebraic Cycles

A reading seminar

Spring 2026, Yale

Organizers: Junliang Shen and Siqing Zhang

Time and location: Fridays, 2:15 - 4:15 pm. KT 801

Objectives

The main goal is to study the recent paper "Matroids and the integral Hodge conjecture for abelian varieties" by Philip Engel , Olivier de Gaay Fortman , and Stefan Schreieder. This paper uses matroids to obtain constraints on algebraic cycles.

We are going to follow the outline of this seminar: GT Matroïdes et cycles algébriques

References

• "Matroids and the integral Hodge conjecture for abelian varieties" by Philip Engel , Olivier de Gaay Fortman , and Stefan Schreieder.

• "Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction" by Philip Engel, Olivier de Gaay Fortman, Stefan Schreieder

• "Matroid Theory" by James Oxley

• "Degenerations of cubic threefolds and matroids" by Tawanda Gwena

• "On the universal CH_0 group of cubic hypersurfaces" by Claire Voisin

Schedule

• Jan 30 (Junliang) Organizational meeting and introduction

• Feb 6 (Charlie) Matroids I

• Feb 13 (Vlad) Matroids II

• Feb 20 (David B.) Matroidal family and statement of theorem 1.6

• Feb 27 (David F.) Gwena's use of matroids

• Spring break

• Mar 27 (Soumik) Voisin's results on Integral Hodge Conjecture and stable rationality

• Apr 3 (Siqing) Structure of the proof of the main theorem

• Apr 10 (Vlad) Mumford construction

• Apr 17 (Siqing) Admissible resolutions, theorem 3.15

• Apr 24 (Junliang) More details on the proof