Mathematics & Finance

Hi, I’m
Rignesh.

I like a problem that takes a while.

I work through number theory and set theory, study currency-market data, and write about what happens beneath a price chart.

I want to study pure mathematics deeply. I’m also exploring a future in execution trading.

Away from
my desk.

I’ve played table tennis for eight years. I like playing, and I can also spend a long time talking through the technique and strategy of a match.

Outside that: the gym with friends, Scotland Yard, horror films, and documentaries about athletes. I also get drawn into long conversations about hypothetical situations.

Usually, there are friends involved.

One week from my notebook

Small cases.
Then a very long week.

I spent a week trying small cases, modular arithmetic, and algebra on IMO 1988 Problem 6. None of those attempts gave me a proof. I eventually learned the method of Vieta jumping.

I want more time with difficult proofs, and people to work through them with.

If ab + 1 divides a² + b², why is
a² + b²ab + 1
always a perfect square?
For positive integers a and b.
Try the original problem ↗

There are mistakes in my notes, too. Here’s one I’ve kept, with the correction.

Where I’m
headed.

I want to study pure mathematics deeply: spend longer with abstract ideas, write better proofs, and understand why an argument works. Some questions interest me even when I can’t see an application for them.

Execution trading is another direction I want to explore. Once there’s a decision to trade, how should it be carried out? I’m interested in how timing, available liquidity, and the orders themselves affect what happens next.

I don’t have a fixed endpoint yet. These are the questions I want to spend more time with.

My currency-market research

What could I
have known then?

In my EUR/USD study, I ask what I could actually know when unusual quote activity first becomes detectable. A price move that has already happened is different from one a model still needs to predict.

Most of the average signed movement was already recorded at detection. The forecast extensions I tested did not improve their benchmarks. I’ve kept those results, and the limits of the study, in the account of the work.

Things I try
to explain.

On Invisible Market Currents, I write about the mechanics behind foreign-exchange prices.

All essays

Order Flow Imbalance

What should a measure of pressure count when orders can be added, executed, or cancelled?

If you have a problem worth thinking about,
I’d like to hear it.

The Cardinality of the Continuum

Original page 2 · 1 of 3

Original page 2: encoding sets as sequences, then switching from binary to ternary.

From sets to sequences. Base three avoids the duplicate binary expansions.

Download the three-page excerpt ↗

Pages from my research

Page 14 · Main results

Page 14 of the working paper, showing Table 3 and Figure 2.
Open this page image ↗