BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthew Foreman (UC Irvine) DTSTART:20200410T230000Z DTEND:20200410T235000Z DTSTAMP:20260404T094834Z UID:UCLALogicC/1 DESCRIPTION:Title: Attacking Classical Problems in Dynamical Systems with Descripti ve Set Theory\nby Matthew Foreman (UC Irvine) as part of UCLA logic co lloquium\n\n\nAbstract\nIn his classical 1932 paper\, von Neumann asked 3 questions: Can you classify the statistical behavior of differentiable sys tems? Are there systems where time-forward is not isomorphic to time-backw ard? Is every abstract statistical system isomorphic to a differentiable s ystem? These questions can be addressed with some surprising consequences by embedding them in Polish Spaces. Indeed the tools answer other question s from the 60's and 70's such as the existence of diffeomorphisms with arb itrary Choquet simplexes of invariant measures. Moreover there are surpris ing analogues to Hilbert's 10th problem.\n\nIn a different category\, buil ding on work of Poincare\, Smale proposed classifying the qualitative beha vior of differentiable systems on compact manifolds. His 1967 paper explic itly argued that the equivalence relation of "conjugacy up to homeomorphis m" captures this notion and he proposes classifying it. Call this notion t opological equivalence. Very recent joint results with A. Gorodetski show: \n\n- The equivalence relation $E _ 0$ is Borel reducible to topological e quivalence of diffeomorphisms of any smooth 2-manifold.\n\n- The equivalen t relation of Graph Isomorphism is Borel reducible to topological equivale nce of diffeomorphisms of any smooth manifold of dimension 5 or above.\n\n As corollaries\, none of the classical numerical invariants such as entrop y\, rates of growth of periodic points and so forth\, can classify diffeom orphisms of 2-manifolds\, and there is no Borel classification at all of d iffeomorphisms of 5-manifolds.\n\nIn the same 1967 paper Smale asks (in di fferent language) whether there is a generic class that can be classified. This is still an open problem.\n LOCATION:https://stable.researchseminars.org/talk/UCLALogicC/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Towsner (University of Pennsylvania) DTSTART:20200522T230000Z DTEND:20200523T000000Z DTSTAMP:20260404T094834Z UID:UCLALogicC/2 DESCRIPTION:Title: Removal and amalgamation\nby Henry Towsner (University of Pe nnsylvania) as part of UCLA logic colloquium\n\n\nAbstract\nThe key step i n the proof of the triangle removal lemma can be viewed as saying that we can identify a small number of edges in a graph as being the "exceptional" edges\, and the remaining edges are sufficiently "representative of the n eighborhood around them" that\, if there are any triangles left\, there mu st have been many triangles. This can be viewed as a amalgamation problem in the sense of model-theory: given types p(x\,y)\, q(x\,z)\, and r(y\,z)\ , each of which indicates that there is an edge between the vertices\, whe n are the types p\,q\,r "large" in a way which guarantees that there are m any (x\,y\,z) extending each of these types?\n\nThe exceptional types can be characterized as the non-Lebesgue points - that is\, the points which f ail to satisfy the Lebesgue density theorem in the right measure space. We give a way to generalize this to types of higher arity and use this to pr ove a new generalization\, an "ordered hypergraph removal lemma"\, extendi ng the recent ordered graph removal lemma of Alon\, Ben-Eliezer\, and Fisc her.\n LOCATION:https://stable.researchseminars.org/talk/UCLALogicC/2/ END:VEVENT END:VCALENDAR