Speaker: Bannai Eiichi (Kyushu University) Title: On unitary t-designs
Abstract:
The purpose of design theory is for a given space $M$ to find good finite subsets $X$ of $M$ that approximate the whole space $M$ well. There are many design theories for various spaces $M$. If $M$ is the sphere $S^{n-1}$ then such $X$ are called spherical designs. If $M$ is the unitary group $U(d)$, then such $X$ are called unitary designs.
Timo Krisam will speal about distal theories and the type decomposition theorem. . Title: Distal Theories and the Type Decomposition Theorem
Abstract: The class of NIP-Theories is an important subject of study in pure model theory. It contains many interesting examples like stable theories, o-minimal theories or algebraically closed valued fields.
Abstract: The Bernoulli convolution with parameter 1/2 < t < 1 is the distribution of the random variable (+/-)t + (+/-)t^2 + (+/-)t^3 + ..., where the sequence of signs +/- form an unbiased i.i.d. random sequence. This distribution has been studied since the 1930s, and the main problem is to characterize those parameters t for which the distribution is absolutely continuous, or has full dimension. In these talks I will review the history and recent developments, leading up to P. Varju's proof a little over a year ago, that for all transcendental parameters the dimension is 1.
Abstract: The Bernoulli convolution with parameter 1/2 < t < 1 is the distribution of the random variable (+/-)t + (+/-)t^2 + (+/-)t^3 + ..., where the sequence of signs +/- form an unbiased i.i.d. random sequence. This distribution has been studied since the 1930s, and the main problem is to characterize those parameters t for which the distribution is absolutely continuous, or has full dimension. In these talks I will review the history and recent developments, leading up to P.
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.
