9:30-10:00 coffee 10:00-11:00 Yoshinori Gongyo: Rational points on log Fano threefolds over a finite field Abstract: We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, a klt Fano threefold over a finite field has a rational point. This is a joint work with Yusuke Nakamura and Hiromu Tanaka. 11:30-12:30 Jean-Louis Colliot-Thélène: Chow group of cycles of codimension two and third unramified cohomology Abstract: Algebraic K-theory provides relations between the third unramified cohomology group (with torsion coefficients) of a smooth projective variety and the Chow group of codimension 2 cycles. This is used to study the image of such cycles under various cycle class maps into integral cohomogy. It is also used to investigate rationality questions for Fano hypersurfaces and for homogeneous spaces of connected linear algebraic groups. There are many open questions. 14:00-15:00 Shenghao Sun: Title Abstract: 15:00-15:30 coffee 15:30-16:30 Kento Fujita: Optimal bounds for the volumes of Kahler-Einstein Fano manifolds Abstract: We show that any $n$-dimensional Kahler-Einstein Fano manifold $X$ satisfies that the anti-canonical volume is less than or equal to the value $(n+1)^n$. Moreover, the equality holds if and only if $X$ is isomorphic to the projective space.
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