Speaker:Guo Liang (SIMIS)
Time: 2025-10-24 14:30-15:30
Location: 1410, SIMIS
Abstract:
In this talk, I will use the K-theory of quotients of Roe algebras as index containers for elliptic operators to study the positive scalar curvature problem (PSC). We define a relative higher index for an elliptic operator, taking values in the quotient of the Roe algebra by a certain ideal. The non-vanishing of this index provides a precise obstruction to the existence of PSC metrics. To compute these indices, we formulate the relative coarse Baum-Connes and Novikov conjectures. Our main theorem shows that these conjectures hold for spaces admitting a relative fibred coarse embedding into Hilbert space. As a key application, we prove the maximal coarse Baum-Connes conjecture for products of certain expander graphs. This provides new examples where the conjecture holds beyond the classical setting of fibred coarse embedding. This is based on joint work with Qin Wang and Chen Zhang.
About Speaker:
Liang Guo is a Postdoctoral Fellow at the Shanghai Institute for Mathematics and Interdisciplinary Sciences. His research interests lie in higher index theory, coarse geometry, and noncommutative geometry. He has published several papers in internationally recognized journals such as J. Funct. Anal., J. Noncommut. Geom., etc.
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