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DTSTAMP:20261011T205828
DTSTART;TZID=America/Detroit:20261014T143000
DTEND;TZID=America/Detroit:20261014T153000
SUMMARY:Workshop / Seminar:Student Number Theory: An Introduction to Perfectoid Theory
DESCRIPTION:Nearly fifteen years ago\, Peter Scholze introduced perfectoid fields\, establishing a bridge between deeply ramified fields of characteristic zero and characteristic (p). Perfectoid theory has since found important applications in arithmetic geometry. In this talk\, I will follow Scholze’s original paper to give an introduction to perfectoid fields and\, if time permits\, perfectoid spaces.
UID:153543-21915987@events.umich.edu
URL:https://events.umich.edu/event/153543
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 3088
CONTACT:
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DTSTAMP:20261001T231756
DTSTART;TZID=America/Detroit:20261014T150000
DTEND;TZID=America/Detroit:20261014T160000
SUMMARY:Workshop / Seminar:Entropy-Regularized Finite-State Mean Field Control Problems
DESCRIPTION:We study an infinite-horizon discounted mean field control problem for finite-state nonlinear continuous-time Markov chains. Controls are locally integrable transition-rate matrices and are penalized by relative entropy with respect to a state-dependent reference generator. We prove that the value function is the unique bounded viscosity solution on the closed simplex of the Hamilton–Jacobi–Bellman equation by a direct dynamic-programming argument and a finite-state comparison principle. Under a uniform semiconvexity condition and C¹\,¹ regularity\, the value function is globally semiconvex and intrinsically C¹\,¹ on the closed simplex and yields a Gibbs feedback that is the unique Hamiltonian minimizer at interior states. For positive\, symmetric\, possibly state-dependent reference rates\, an entropy-plus-value free energy decays globally exponentially when the temperature parameter is compatible with the semiconvexity modulus. We also establish a discounted planner-to-game correspondence for potential mean field games under a state-independent reference generator.
UID:153194-21915402@events.umich.edu
URL:https://events.umich.edu/event/153194
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:Angell Hall - AHG128
CONTACT:
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