This Week in Mathematics


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Entries for this week: 2

Monday March 30, 2026

Colloquium
Structure in group-labeled graphs and its applications
- Youngho Yoo, Alaska Fairbanks
Time: 3:05 Room: LOV 101
Abstract/Desc: Can a cycle of length L modulo M be found in a given graph in polynomial time? This problem was first posed by Arkin, Papadimitriou, and Yannakakis (1991), motivated by periods of Markov chains, and reiterated in the study of graph databases and extremal graph theory. I will discuss recent work on the structure of group-labeled graphs that resolves this problem in a far more general form. Our work also provides a characterization of the topological obstructions to an approximate packing-covering duality for cycles of length L modulo M, resolving a problem of Dejter and Neumann-Lara (1988). I will further discuss applications of our work to other group-expressible length constraints.

Thursday April 02, 2026

Algebra seminar
Bands, Idylls, Valuated Matroids and Linear Spaces
- Jeffery Liu, FSU
Time: 3:05pm Room: LOV 0232
Abstract/Desc: Matroids encode dependencies among elements of a finite set. One class of examples are "realizable" matroids, those which come from linear dependence among an arrangement of vectors in a vector space. However, most matroids are not realizable. We survey the development of ring-like and field-like objects called "bands" and "idylls" respectively, and matroids with coefficients valued in a band or idyll. In particular, all matroids can be valued in the Krasner hyperfield, which is the terminal object in the category of idylls. Then, following the band/idyll-theoretic model we introduce a vector space-like object over an idyll whose vector arrangements realize matroids valued in that idyll.

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Department of Mathematics

This Week in Mathematics