17th(Monday)
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Lior SILBERMAN (University of British Columbia)
Title: Random groups and Spectral gaps
Abstract: I will describe Gromov's density and graphical models for random groups, and the connection between the spectral gap property of such groups ("Kazhdan property (T)") and the ordinary spectral gap property for associated graphs.
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Asuka TAKATSU （Nagoya University）
Title: Isoperimetric inequality for radial probability measure on Euclidean spaces
Abstract: The isoperimetric inequality compares the volume and the 'perimeter' of a set.
In this talk, I derive the Gaussian isoperimetric inequality for a certain radial probability measure on Euclidean spaces.
This is done by generalizing the Poincare limit which states that the Gaussian measure is approximated
by the projection of the uniform probability measure on the Euclidean sphere of appropriate radius as the dimension diverges to infinity.
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Takefumi KONDO （Tohoku University）
Title:On a question of Gromov about Wirtinger spaces
Abstract: In the study of measure concentration inequalities on CAT(0) spaces, Gromov proved the Wirtinger inequalities for CAT(0) spaces. He asked if a weaker condition Cycl_4(0) implies all the Wirtinger inequalities. The main purpose of my talk is to answer this question affirmatively. This talk is based on a joint work with Tetsu Toyoda and Takato Uehara.___________
18th(Tuesday)
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Lior SILBERMAN (University of British Columbia)
Title: Fixed points for random groups.
Abstract: I will describe results (some joint with Assaf Naor) on showing
that random groups have fixed-point properties when acting by isometries on suitable metric spaces. We note that non-positive curvature conditions are similar to uniform convexity conditions from the theory of Banach spaces, and all those support averaging constructions, controlled by Poincare inequalities. I will also discuss extending those results to non-isometric actions.
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Kazumasa KUWADA (Ochanomizu University)
Title: The entropic curvature-dimension condition and Bochner's inequality Abstract： This talk is based on a joint work with M. Erbar and K.-T. Sturm (Bonn). In this joint work, the curvature-dimension bounds of Lott-Sturm-Villani (via entropy and optimal transport) is shown to be equivalent to Bakry–\'Emery's one (via energy and $\Gamma_2$-calculus) in complete generality for infinitesimally Hilbertian metric measure spaces. In particular, we establish the full Bochner inequality on such metric measure spaces. In this talk, I will discuss some of other equivalent conditions and relations between them. They include an alternative curvature-dimension bound via optimal transport using the relative entropy, which we call the entropic curvature-dimension condition. I am planning to mention some of known applications, if time permits.
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Hiroyasu IZEKI （Keio University）
Title: Fixed-point property of random quotients by plain words
Abstract:Recent progress in geometric group theory tells us that groups with certain fixed-point property form an extensive class among the finitely generated groups. I would like to discuss a result along this line; certain random groups have fixed-point property for L^p spaces. This talk is based on a joint work with Marc Bourdon (Lille).
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Tetsu TOYODA （Suzuka National College of Technology）
Title: The path-method for nonlinear spectral gaps Abstract: As a nonlinear analogue of the linear spectral gap of a finite connected graph $G$, we can define the nonlinear spectral gap $\lambda_1 (G,X)$ with respect to any metric space $X$. Recently, estimates of these invariants are required in various contexts in geometric group theory and metric geometry. In this talk, we generalize the path-method to the nonlinear setting. The original path-method is well known in the context of random walks as one giving only rough estimates of linear spectral gaps. However, our generalization gives a kind of sharp estimates of the nonlinear spectral gaps. This talk is based on joint works with Takefumi Kondo.