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A loosely sorted and lightly annotated catalogue of through the music posts on this blog.

A large, opaque resale market for frontier LLM APIs has emerged to serve users blocked from OpenAI, Anthropic and Google endpoints (somewhat like a VPN). Two independent papers in the past two months provide the first systematic evidence that a substantial fraction of these intermediaries silently substitute models, truncate context, or misreport billing. Apart from inflated price, the shadow market maybe more chaotic than ideal: for example, shadow-API providers would steal tokens by using fake educational accounts. The claim to provide expensive good models while quietly substituting for cheaper ones. ...

Our empirical analysis course is really cool. Here’s what we covered last week: The setup is quite clean. There is one agents. Four objects: Object Symbol Role Likelihood $\ell(x\mid\theta)$ family of probability models for data $x$, indexed by parameter $\theta\in\Theta$ Prior $\pi(\theta)$ your subjective beliefs over which $\theta$ is true Utility $U(\gamma,\theta)$ what you care about; $\gamma$ is a “prize rule” mapping data into an outcome Decision rule $\delta(z)$ what you actually choose, as a function of observed $z$ Split the data: $x=(w,z)$, where $z$ is observed before act and $w$ is realized after—the decision $\delta$ may only use $z$. The prize is then $\gamma_\delta(x)=\Psi(\delta(z),x)$. ...

On May 9, 2026, the University of Chicago’s University Symphony Orchestra (USO) and our Alumni Orchestra are celebrating music director Barbara Schubert’s 50-year tenure with two landmark performances: Brahms — Academic Festival Overture (Alumni Orchestra) Mahler — Symphony No. 2, “Resurrection” (USO) I’m playing in both pieces across the May 9 and May 10 performances — roughly two hours of music in total, with the Mahler alone clocking in as an eighty-minute marathon. Wish me luck. ...

I was invited by my pianist friend to a Music of the Spring music appreciation event at our International House. We covered music from around the world related with Spring spirit. This was my favourite:

Today is Tchaikovsky’s birthday (1840 May 7 - 1893 Nov 6). Happy birthday to my most favorite composer! The Seasons [Op 37b, a piano miniature collection] were commissioned from Tchaikovsky by the publisher Nikolay Bernard, for publication in his journal Nuvellist (Нувеллист), which was issued on the first day of each month. It was composed almost same time with Swan Lake. Each piece is a different month of a year of Russia. ...

Professor Ryota Iijima came over to give a talk of his recent work Auctions as Experiments. Great paper. Great insights. You can find the full paper at Professor Ryota’s Google Site. Here are some notes jotted down during the talk, along with some thoughts from discussions with fellow phd students: Setup $n$ buyers, one indivisible good, quasi-linear preferences. Values $v_i \stackrel{iid}{\sim} F_\theta$ given state $\theta \in \Theta \subseteq \mathbb{R}$, prior $q_0$. $(F_\theta)$ has MLRP in $\theta$; each $F_\theta$ has continuous, strictly positive density on a compact $I_\theta$. Information asymmetry. Buyers observe $(\theta, v_i)$. The decision-maker (DM) observes only the $n$ realized bids. Canonical interpretation: $v_i = u(\theta, \varepsilon_i)$ — $\theta$ is a common-value component, $\varepsilon_i$ idiosyncratic. Class of auctions (“standard auctions”) Sealed bids $b_i$, ranked $b^{(1)} \ge \dots \ge b^{(n)}$; highest wins. Payment functions $\psi = (\psi_\ell)_{\ell=1}^n$, increasing and symmetric in bids; $\psi_\ell = 0$ when $b^{(\ell)} = 0$. Examples: $k$-th price ($\psi_1 = b^{(k)}$, others $0$); all-pay ($\psi_\ell = b^{(\ell)}$); own-pay-$\alpha$ ($\psi_\ell = \alpha_\ell b^{(\ell)}$). Restrict to symmetric, monotone equilibria $b_\theta^\psi$. Bid CDF: $G_\theta^\psi(b) = F_\theta((b_\theta^\psi)^{-1}(b))$. All standard auctions are revenue-equivalent at each $\theta$ (private values, i.i.d.). Remak: why does the auction format matter? If buyers observed only $v_i$ (not $\theta$), all formats would be informationally equivalent — DM could invert the bidding function and back out $v_i$. Knowing $\theta$ is what creates the competition effect: at fixed $v$, the equilibrium bid $b_\theta(v)$ shifts with $\theta$ in a way that depends on $\psi$. This is the channel of differential informativeness. ...

Professsor Virginia Minni speaks at the BFI student lunch series covering 3 papers in 45 minutes. One o fthe paper in particular I found very interesting Making the Invisible Hand Visible: Managers and the Allocation of Workers to Jobs QJE 2026. Virginia Minni. ABSTRACT Abstract: Why do managers matter for firm performance? This paper provides evidence of the critical role of managers in matching workers to jobs within the firm using the universe of personnel records from a large multinational firm. The data covers 200,000 white-collar workers and 30,000 managers over 10 years in 100 countries. I identify good managers by their speed of promotion and leverage exogenous variation induced by the rotation of managers across teams. I find that good managers cause workers to reallocate within the firm through lateral and vertical transfers and generate large and persistent gains in workers’ career progression and productivity. My results imply that the visible hands of managers match workers’ specific skills to specialized jobs, leading to an improvement in the productivity of existing workers that outlasts the managers’ time at the firm. ...

Bar 500. Still resting. The piccolos are about to come in and I am going to lose another decibel of hearing for Gustav Mahler. You are not allowed to say you don’t like Mahler. Try it sometime — in a lobby, on a forum, at dinner with people who own seasonal orchestra subscriptions. Watch the faces. Conductors love him. Critics love him. Audiences pay good money to weep through eighty minutes of him. To dissent is to out yourself as stupid amateurs. ...

A note from a Tuesday night with the swans of Hyde Park Before I went, my musician friends tried to spare me: The technique might not be there. You know what Swan Lake demands. You love Tchaikovsky fine and don’t go and disappoint yourself. But I went anyway. Well I had to — I take ballet courses at the University — which is to say, badly and with great affection — half the swans on that stage were people I know. People I’ve stretched next to at the barre, people who borrowed me their bobby pins. They studied for midterms last week and then, somehow, also learned to be a corps. And I know was never going to be about technique. ...