Tate form and weak coupling limits in F-theory

Weak Coupling Theory

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Weak Coupling and Continuous Limits for Repeated Quantum Interactions

We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ , the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three asymptotic regimes of t...

Weak coupling limits in a stochastic model of heat conduction

Hodge-Tate Theory

This thesis aims to expose the amazing sequence of ideas, concerning p-adic representations coming from geometry, that form the heart of what was called Hodge-Tate theory. This subject, initiated by Tate in the late ’60s in analogy to classical Hodge theory, leads in to the now vast and highly fruitful program of p-adic Hodge Theory. The central result of the theory is the Hodge-Tate decomposit...

Lubin-Tate Theory

Motivation: We seek to understand the stable homotopy category by understanding the structure of the moduli stack of formal groups. Over algebraically closed fields, this is straightforward. If char(k) = 0, every formal group law is isomorphic to the additive one and we’ve described the group of automorphisms (coordinates changes) before. If char(k) = p > 0 every formal group law is classified ...