The outline of Cezar's and my work will be to show (1) $\hat{H}(a,b)$ is equal to a certain rational zeta series, and (2) $H(a,b)$ is equal to that same raitonal zeta series. Thus $H(a,b) = \hat{H}(a,b)$ independent of Don Zagier's proof. Cezar has proven (2) for $b=0$. In this talk, I will prove (1) for all $a,b$.
Abstract:
A topological group is extremely amenable if it has a fixed
point under every continuous action on a compact Hausdorff space. The
group of measure preserving transformations of the standard
probability space is extremely amenable by a result of Giordano and
Pestov applying analytical techniques. This in turn implies that the
class of finite measure algebras posseses the approximate Ramsey
property. Via discretization, Giordano and Pestov's result would
follow from (an exact) Ramsey property for finite measure algebras
Abstract:
Forcing is a technique for constructing new models of set theory where certain statements are "forced" to be true or false, e.g. the axiom of choice, or the continuum hypothesis. We describe a formalization of forcing using Boolean-valued models in the Lean 3 theorem prover. As an application of our framework, we specialize our construction to a Boolean completion of the Cohen poset and formally verify in the resulting model the failure of the continuum hypothesis. This is joint work with Floris van Doorn.
I will review the endeavors of many great mathematicians of the late 19th century and beginning of the 20th century, and their motivating philosophies in pursuing a consistent and complete axiomatic system for mathematics. On the way, they encountered many paradoxes, such as Russell's, with important implications for our mathematical understanding.
Abstract:
Large (and moderate) deviations principle identifies the exponential rate of decay of probabilities for rare events in the context of small noise asymptotics. For a class of nonlinear stochastic partial differential equations that arise in fluid dynamics, I will present weak convergence approach to identify the exponential rate.