The present talk is a gentle introduction to the theory of cohomological Hall algebras and their relevance in the study of the topology of moduli spaces, such as the Hilbert schemes of points on a smooth surface.…
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The Beauville-Voisin conjecture for $\mathsf{Hilb}(K3)$ and the Virasoro algebra – Andrei Negut (MIT)
We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of $K3$ surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes.…
Dynamical Systems Stemming from a Family of Multi-dimensional Continued Fraction Algorithms – Thomas Garrity (Williams College)
The underlying dynamics behind classical continued fractions has been heavily studied. Attempts to generalize the many properties of continued fractions fall under the rubric of “multi-dimensional continued fractions.” As continued fractions can be…
Flanders’ theorem for many matrices under commutativity assumptions – Fernando De Terán (Universidad Carlos III de Madrid)
Given two matrices $A \in C^{m \times n}$ and $B \in C^{n \times m}$ , it is known [1] that theJordan canonical form of AB and BA can only differ in the sizes of theJordan blocks associated with the eigenvalue zero, and the difference in thesize of…