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Events happening on March 14, 2023

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Mar. 14, 2023 12:10pm (MATH …	Kempner David Renfrew (Binghamton University) X I will describe the limiting behavior of the eigenvalues of minors of large biunitarily random matrices and the roots of derivatives of polynomials with independent, random coefficients, by giving a convolution semi-group which relates the two processes together. Eigenvalues of minors of random matrices and roots of derivatives of random polynomials
Mar. 14, 2023 1:25pm (Online)	Algebra/Logic Dmitriy Zhuk (Charles University, Prague, Czechia) View Online:https://cuboulder.zoom.us/j/96896272260 X In 2017 Moiseev found 2 079 040 clones on 3 elements definable by binary relations using a computer. It is clear that only computer can deal with so many clones but another result from 2019 showed that even computers have their limitations. Moore proved that they cannot check whether a clone given by generating operations is finitely related (definable by a relation). These results made us believe that even a computer description of all the clones on 3 elements would never appear. However, not all clones are essentially different, and one might try to characterise clones modulo clone homomorphisms or minor preserving maps (only h1-identities are preserved). In 2022 we showed that there are only countably many clones of self-dual operations on 3-elements modulo a minor preserving map. Then using a computer we collapsed 2 079 040 into a very small number and now we hope that a complete characterization of all clones on 3 elements modulo minor preserving maps is possible. Joint work with Libor Barto, Jan Adam Zah\'alka, Albert Vucaj, and Florian Starke. Clones on 3 Elements: A New Hope
Mar. 14, 2023 3:30pm (MATH 3…	Topology Howy Jordan (CU Boulder) X When first encountering manifolds, there are basic examples of non-manifolds that should be met. In particular, simple constructions like the wedge product of two manifolds immediately give spaces with points which fail to have appropriate neighborhoods. These spaces fail to have nice properties of manifolds such as Poincare duality. But these spaces are mostly manifolds after all. Much of the theory of manifolds can be recovered by observing how the space is naturally decomposable into manifolds and respecting this decompostion. This is the starting point for the theory of stratified spaces, spaces equipped with decompositions into manifolds. We will see that the tools familiar from the theory of manifolds, like tangent bundles and vector fields, allow one to refine the theory of stratified spaces further. Thom's first isotopy lemma for instance gives sufficient conditions for when a stratified space is locally a product of a manifold and a lower dimensional stratified space. If time permits, we will also consider the basics of the theories of intersection homology and perverse sheaves on stratified spaces, which allow even Poincare duality to be recovered. Stratified Spaces

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