Speaker: Spencer Leslie (Duke)
Title: The endoscopic fundamental lemma for unitary symmetric spaces
Abstract: Motivated by the study of certain cycles in locally symmetric
spaces and periods of automorphic forms on unitary groups, I propose a
theory of endoscopy for certain symmetric spaces. The main result is the
fundamental lemma for the unit function. After explaining where the
fundamental lemma fits into this broader picture, I will describe its
proof.
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Abstract: A circle packing is a canonical way of representing a planar graph. There is a deep connection between the geometry of the circle packing and the proababilistic property of recurrence/transience of the simple random walk on the underlying graph, as shown in the famous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However, by using certain natural weights that arise from the circle packing for a weighted random walk, (at least) one of the directions of the He-Schramm Theorem remains true.
Abstract: A circle packing is a canonical way of representing a planar graph. There is a deep connection between the geometry of the circle packing and the proababilistic property of recurrence/transience of the simple random walk on the underlying graph, as shown in the famous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However, by using certain natural weights that arise from the circle packing for a weighted random walk, (at least) one of the directions of the He-Schramm Theorem remains true.
Joint E-seminar of Bar-Ilan University and the Hebrew University
Title: Transformations of the transfinite plane
Abstract: We discuss the existence of certain transformation functions turning pairs of ordinals into triples (or pairs) of ordinals, that allows reductions of complicated Ramsey theoretic problems into simpler ones. We will focus on the existence of various kinds of strong colorings. The basic technique is Todorcevic's walks on ordinals. Joint work with Assaf Rinot. The Zoom meeting ID is 243-676-331
Abstract: Let G be a countable group. A mutliorder is a collection of bijections from G to Z (the integers) on which G acts by a special "double shift". If G is amenable, we also require some uniform Folner property of the order intervals. The main thing is that mutiorder exists on every countable amenable group, which can be proved using tilings. For now, multiorder provides an alternative formula for entropy of a process and we are sure in the nearest future it will allow at produce
Abstract.I will outline some results in Algebraic Geometry obtained in our works withT.Ziegler. Our proofs are based on Analysis over finite fields which leads tonew results even for complex varieties.
