Arithmetic geometry, at its core, investigates the rich interplay between number theory and geometry. In the context of unitary groups—algebraic groups defined as the symmetries of Hermitian forms—the ...
This paper studies generalizations of the classical Apollonian circle packing, a beautiful geometric fractal that has a surprising underlying integral structure. On the one hand, infinitely many such ...
We introduce the notion of a "crystallographic sphere packing," defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension. We exhibit an ...
Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...
Our research group is concerned with two lines of investigation: the construction and study of (new) cohomology theories for algebraic varieties and the study of various aspects of the Langlands ...
Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...
This project provides an interactive Streamlit application for simulating and visualizing both Geometric Brownian Motion (GBM) and Arithmetic Brownian Motion (ABM). It's a powerful tool for ...
This repository contains Pari and Sage code for calculating period matrices of genus 2 hyperelliptic curves by using the arithmetic-geometric mean. It will later be generalized to curves of higher ...
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