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Events for the weeks of November 17th – 29th

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Mon (Nov 18)	Tue (Nov 19)	Wed (Nov 20)	Thu (Nov 21)	Fri (Nov 22)
	Algebra/Logic 1:25pm @ online Max Hadek (Charles University Prague) X An algebra is called minimal Taylor if its clone satisfies a non-trivial minor condition, but no proper subclone does so. Recently, Barto, Brady, Bulatov, Kozik and Zhuk initiated the systematic study of minimal Taylor algebras, intending to build a unified theory to understand the complexity of constraint satisfaction problems. They conjecture that every minimal Taylor algebra is finitely related, which we disprove by giving a counterexample. This result can be interpreted as follows: there is an infinite sequence of tractable finite domain CSPs, such that every CSP harder than all problems in the sequence, is already NP-complete. A non-finitely related minimal Taylor algebra Lie Theory 2:30pm @ Math 350 Spencer Daugherty (CU Boulder) X The q,t-Catalan numbers can be described elegantly in terms of pairs of statistics on Dyck paths: area and bounce, or area and dinv. Mahonian permutation statistics, such as coinversion, disorder, and the sorting index, are some of the most thoroughly studied statistics on permutations. Using bijective methods, we prove new expressions of the q,t-Catalan numbers over subsets of permutations in terms of at least one Mahonian statistic. In the process, we develop new Catalan subsets of permutations, new bijections from Dyck paths to these subsets, and new permutation statistics. Mahonian Statistics and the q,t-Catalan Numbers Topology 3:30pm @ MATH 350 Andrew Doumont X We will construct Lagrangian Floer homology. Time permitting, we will also discuss Fukaya categories and the homological mirror symmetry conjecture. Lagrangian Floer Homology	Kempner 1:30pm @ MATH 350 Rodrigo Ribeiro (Denver University) X Networks are everywhere, from social media platforms to intricate systems in nature. But how do we study and understand them? Different fields like computer science, math, and statistics offer their own tools and views. In this talk, we'll explore how these areas approach network analysis and how mathematicians formalize intuition and results from other areas. The talk will cover joint works with Rémy Sanchis (UFMG), Roberto I. Oliveira (IMPA) and Caio Alves (Oak Ridge National Lab). Interdisciplinary Perspectives on Network Analysis: A Confluence of Computer Science, Mathematics, and Statistics	Algebraic Geometry 2pm @ CSU Carl Lian (Tufts Univerisity) X Let Gr(k,n) be the Grassmannian of k-planes in C^n. The standard torus action on C^n induces a torus action on Gr(k,n), whose orbits encode interesting combinatorial and geometric invariants. I will describe an explicit degeneration of the “generic” torus orbit closure into a union of Richardson varieties (intersections of two Schubert varieties). This gives a new proof of a formula of Berget-Fink for the Chow class of this subvariety of X, and the technique has further (but not yet fully realized) applications in enumerative geometry. The method also works for the variety of full flags in C^n, giving a new proof of an earlier result of Anderson-Tymoczko. Via the toric moment map, the combinatorial shadow of this degeneration is a polyhedral decomposition of the permutohedron due to Harada-Horiguchi-Masuda-Park. Time-permitting, I will mention some ongoing work with Grace Chen extending this story to type B. Degenerations of torus orbits

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