Wed, 20 Nov 2024
11:00
L4

Quadratic and $p^\mathrm{th}$ variation of stochastic processes through Schauder expansions

Yuchen Fan
(University of Oxford)
Abstract
We present a class of stochastic processes which admit a unique quadratic variation along any sequence of partitions $(\pi^n)_{n\geq 1}$ with $\sum_{n\geq 1}|\pi^n|<\infty$, which generalizes the previous results for finitely refining partitions. This class of processes contains some signed Takagi-Landsberg functions with random coefficients and standard Brownian motions, and these processes admit $\frac{1}{4}$-Hölder continuous version. We study the quadratic and $p^\mathrm{th}$ variation of signed Takagi-Landsberg functions with random coefficients. Finally, we seek some generalizations and applications of our results.


 

Tue, 23 Jan 2024

11:00 - 12:00

[Rescheduled] A new axiom for Q_p^ab and non-standard methods for perfectoid fields

Leo Gitin
(University of Oxford)
Abstract

The class of henselian valued fields with non-discrete value group is not well-understood. In 2018, Koenigsmann conjectured that a list of seven natural axioms describes a complete axiomatisation of Q_p^ab, the maximal extension of the p-adic numbers Q_p with abelian Galois group, which is an example of such a valued field. Informed by the recent work of Jahnke-Kartas on the model theory of perfectoid fields, we formulate an eighth axiom (the discriminant property) that is not a consequence of the other seven. Revisiting work by Koenigsmann (the Galois characterisation of Q_p) and Jahnke-Kartas, we give a uniform treatment of their underlying method. In particular, we highlight how this method can yield short, non-standard model-theoretic proofs of known results (e.g. finite extensions of perfectoid fields are perfectoid).

Fridays@2 Week 2: How to Write a Good Maths Solution

 

In this interactive workshop, lead by Dr Luciana Basualdo Bonatto, we'll discuss what mathematicians are looking for in written solutions. How can you set out your ideas clearly, and what are the standard mathematical conventions? Please bring a pen or pencil!

The Invariants – Week 2 Events

Hey there! We're the Invariants, a.k.a. the Oxford University Student Society for Mathematics.

If you've not heard of us before, we're a hub for all things a Maths student would be interested in. We run a wide variety of events each term, including talks, socials, competitions, career events, and more.

Are you curious about maths PhDs?

Are you curious about maths PhDs? Or maybe you've never really thought about them before... but you'd like to know more? 

 

We're excited to invite you to PhD Your Way 2024 which is free to attend and hosted virtually on Wednesday November 6th 2pm - 4.30pm. 

Global PhD Datathon

Hosted by Citadel and Citadel Securities in partnership with Correlation One, we’re inviting top PhD students all over the world to compete at the PhD Datathon this November. Top performing students have the opportunity to win $25,000USD in cash prizes along with exclusive recruiting opportunities with Citadel.

 

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