Friday, December 2, 2022
Time | Items |
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All day |
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10am |
12/02/2022 - 10:30am A relaxed-pace seminar on impromptu subjects related to the interests of the audience. Everyone is welcome. The subjects are geometry, probability, combinatorics, dynamics, and more! Location:
LOM 205
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12pm |
12/02/2022 - 12:00pm We introduce two models of consensus following a majority rule on time-evolving stochastic block models (SBM), in which the network evolution is Markovian or non-Markovian. Under the majority rule, in each round, each agent simultaneously updates his/her opinion according to the majority of his/her neighbors. Our network has a community structure and randomly evolves with time. In contrast to the classic setting, the dynamics is not purely deterministic, and reflects the structure of SBM by resampling the connections at each step, making agents with the same opinion more likely to connect than those with different opinions. In the Markovian model, connections between agents are resampled at each step according to the SBM law and each agent updates his/her opinion via the majority rule. In the non-Markovian model, a connection between two agents is resampled according to the SBM law only when some of the two changes opinion and is otherwise kept the same. We study the phase transition between the fast convergence to the consensus and a halt of the dynamics. Moreover, we establish thresholds of the initial lead for various convergence speeds. This is based on joint work with J. Wei and Z. Zhang. Location:
LOM
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2pm |
12/02/2022 - 2:00pm A static vacuum metric produces a Ricci flat manifold of one dimension higher and naturally arises on studying scalar curvature deformation and gluing. Originating from his quasi-local mass program in 1989, R. Bartnik conjectured that one can always find an asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. I will discuss well-posedness of this geometric boundary value problem and the recent progress toward the conjecture for large classes of boundary data. It is based on joint work with Zhongshan An. Location: |