Abstract:

We will begin with a quick reminder of algebraic K-theory, and a few classical, vanishing results for negative K-theory. The talk will then focus on a striking 2019 article by Antieau, Gepner and Heller - it turns out that there are K-theoretic obstructions to the existence of bounded t-structures.

The result suggests many questions. A few have already been answered, but many remain open. We will concentrate on the many possible directions for future research.

Short bio:

Education and employment: Received my PhD from Harvard University in 1983, postdoc positions at Institute for Advanced Study (1983/84), Princeton University (1984-87). Tenure at the University of Virginia (1987-98), then at the Australian National University (1999-2023), and the University of Milan (from 2023).

Honors: Australian Laureate Fellowship (2011-2016), invited speaker at ICM 2022,  European Research Council Advanced Grant (2023-2027).

Recording: https://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Vanishing_negative_K_theory_and_bounded_t_structures.html