Expositio
Create account Log in

EXPOSITIO

A home for expository scholarship

Expositio is a repository for expository papers in a wide range of academic disciplines, supporting preprints, revisions, optional peer review, saved papers, and overlay journals.

37 Public papers
Log in to submit Browse by date

What is Expositio?

A public repository for expository academic papers, with an integrated scholarly record.

Expositio is a place to read and cite expository work. Papers are published as stable, citable records, while remaining connected to later versions, editorial decisions, and related context.

Some papers are early drafts; others have been peer reviewed or formally published. Each paper remains readable on its own, while preserving the history behind it.

The result is both a reading room and a record: a place to browse by field, read papers in stable form, and follow their development over time.

Search Expositio

Published papers

Narrow the shelf by title or author words, public state, topic language, or submission date.

Start broad, then narrow by domain or deeper subject branches from the left rail.

37 results Sort: Recent
Refine this shelf
Return to full archive
Preprint
v1

Monolayer transition metal dichalcogenides (TMDs) host two inequivalent valleys at the K and K′ points of the Brillouin zone, offering a binary degree of freedom that can encode information. Lifting the degeneracy between these valleys is the central challenge of valleytronics. …

Physics / Electronic structure
Physics > Electronic structure > Valley degrees of freedom Primary
Physics > Electronic structure > Valleytronics
Public since Oct 25, 2026 0 saves
Read paper
Preprint
v1

Single-point airfoil optimization targets one operating condition, which limits how reliably a design performs across real flight conditions. This study presents a multi-point optimization of a NACA 4-digit airfoil, maximizing lift-to-drag ratio and lift coefficient while minimi…

Aerospace Engineering / Aerospace Engineering
Aerospace Engineering > Aerospace Engineering Primary
Public since Oct 21, 2026 0 saves
Read paper

Expositio paper

Kepler Towers (Catalan Objects)

Justin Cheong

Preprint
v1

In this paper, we will dive into the deep world of Catalan numbers, exploring interesting examples and why those are Catalan objects. There will be a special focus on Kepler Towers, one specific type of Catalan object that seems to be relatively unstudied and has a nonobvious …

Mathematics / Combinatorics
Mathematics > Combinatorics > Other designs, configurations Primary
Mathematics > Combinatorics > Combinatorial identities, bijective combinatorics
Mathematics > Combinatorics > Exact enumeration problems, generating functions
Public since Oct 20, 2026 0 saves
Read paper

Expositio paper

Hilbert's Third Problem

Simon Rubinstein-Salzedo

Preprint
v1

Hilbert's Third Problem asks whether, given two polyhedra of the same volume, it is possible to cut one into finitely many polyhedra and rearrange the pieces into the other one. In these notes, we will answer this question and study the surrounding mathematics. The notes conclud…

Mathematics / Geometry
Mathematics > Geometry > Polyhedra and polytopes; regular figures, division of spaces Primary
Public since Oct 14, 2026 0 saves
Read paper

Expositio paper

Central Limit Theorem

Justin Cheong

Preprint
v1

In this paper, we will prove a few different versions of the Central Limit Theorem: first, a weak one, then the Lindeberg and Liapunov Central Limit Theorems. Additionally, we will show the Central Limit Theorem in action and explain why it is one of the most useful theorems …

Mathematics / Probability theory and stochastic processes Mathematics / Statistics
Mathematics > Probability theory and stochastic processes > Central limit and other weak theorems Primary
Mathematics > Statistics > Asymptotic distribution theory in statistics
Public since Oct 12, 2026 0 saves
Read paper