|Yi Shi||assistant professor, School of Mathematical Sciences, Peking University|
Bio: Yi Shi obtained PhD from Peking University and Universite de Bourgogne in 2014, and then did postdoc in IMPA. He is now an assistant professor in School of Mathematical Sciences at Peking University. His research field is differentiable dynamical systems, including partially hyperbolic dynamics and singular star vector fields.
Spectrum rigidity and integrability for Anosov diffeomorphisms.
Let f be a partially hyperbolic derived-from-Anosov diffeomorphism on 3-torus T3. We show that the stable and unstable bundle of f is jointly integrable if and only if f is Anosov and admits spectrum rigidity in the center bundle. This proves the Ergodic Conjecture on T3. In higher dimensions, let A∈SL(n,ℤ) be an irreducible hyperbolic matrix admitting complex simple spectrum with different moduli, then A induces a diffeomorphism on Tn. We will also discuss the equivalence of integrability and spectrum rigidity for f∈Diff2Tn which is C1-close to A.
|Lev Lokutsievskiy||Steklov Mathematical Institute (Moscow)|
Bio: Lokutsievskiy L.V. is a specialist in geometric optimal control theory. He proved his habilitation thesis in 2015. Starting from 2016 he works at Steklov Mathematical Institute as a leading researcher.
Аn application of algebraic topology and graph theory in microeconomics.
One of the important questions in mechanism design is the implementability of allocation rules. An allocation rule is called implementable if for any agent, benefit from revealing its true type is better than benefit from lying. I’ll show some illustrative examples. Obviously, some allocation rules are not implementable. Rochet’s theorem states that an allocation rule is implementable if it is cyclically monotone. During the talk, I’ll present a new convenient topological condition that guarantees that cyclic monotonicity is equivalent to ordinary monotonicity. The last one is easy to check (in contrary to cyclic one). Graph theory and algebraic topology appear to be very useful here.
The meeting will be held in the form of a webinar on the Zoom platform.
Pre-registration for the event is not required.
To join Zoom meeting（You can join in the meeting without a phone number):
Meeting ID: 674 4141 7410
Instructions for installing and using the Zoom platform are available here: