Book talk
To book a talk, email frk23@cam.ac.uk.
To book a talk, email frk23@cam.ac.uk.
AI has changed mathematics permanently. The mindblowing progress has caused existential crisis for many mathematicians and raises a series of new questions.
Was intelligence always simple? How is maths in the future going to look? Why did we do maths in the first place?
The Danish election of 2022 was decided by the electoral system. For the first time since 1947 a party got more seats than their share of the votes.
How could that happen? What is the probability that this happens again? What considerations should go into changing the system?
Studying the Ising model using its graphical representations has been tremendously successful. These representations are coupled to each other using the uniform even subgraph, which is invariant under XOR. This trick enables simple proofs of equality of critical points between loop O(1) and Ising and exponential decay for the two-dimensional near-critical model. The scaling limit of the latter is famously conjectured to be related to the exceptional Lie Algebra E8.
Joint work with Ulrik Hansen, Jianping Jiang and Peter Wildemann.
We study the time evolution of single-particle quantum states described by a Lindblad master equation with local terms. By means of a geometric resolvent equation derived for Lindblad generators, we establish a finite-volume-type criterion for the decay of the off-diagonal matrix elements in the position basis of the time-evolved or steady states. This criterion is shown to yield exponential decay for systems where the non-hermitian evolution (and not the full Liouvillian) is either gapped or strongly disordered. The work thereby gives rigorous justification for the study of non-hermitian hamiltonians. The gap for the non-hermitian evolution exists for example whenever any level of local dephasing is present in the system. The result in the disordered case can be viewed as an extension of Anderson localization to open quantum systems.
Joint work with Simone Warzel.