I am an AI scientist at XTX Markets.
My doctorate was on statistical foundations for learning on graphs and high-dimensional probability, co-advised by Prof Kimon Fountoulakis and Prof Aukosh Jagannath at the Cheriton School of Computer Science, University of Waterloo.
Before that, I did my M.Math. at UWaterloo with Jeffrey Shallit on algorithmic number theory and combinatorics on words, and my undergrad at IIT Jodhpur.
Fun fact: my Erdős number is 2 via Jeffrey Shallit.
Recent Posts
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Heisenberg uncertainty as Fourier duality
Posted on:The textbook framing makes the uncertainty principle sound like a measurement artifact. It isn't. It is a property of any wave: a packet narrow in x has a Fourier decomposition spread in p, with the bound σx · σp ≥ ℏ/2 saturated by a Gaussian. This post derives that statement from photoelectric-effect-level physics.
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Voronoi tessellations and Lloyd's algorithm
Posted on:A set of generators in the plane partitions it into regions, each closer to one generator than to any other. Lloyd's algorithm iterates "move each generator to the centroid of its region" and converges to a centroidal Voronoi tessellation. The same algorithm is k-means.
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Pólya's recurrence theorem
Posted on:Simple random walk on the integer lattice returns to the origin with probability one in 1D and 2D. In 3D and higher, there is a positive probability of never returning. The transition is exact, dimension-dependent, and reduces to convergence of a single harmonic-style series.
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High-dimensional Gaussians live on a sphere
Posted on:The bell-curve picture says Gaussian samples live near the mean. In high dimensions that picture is catastrophically wrong: almost all the mass lies in a thin spherical shell at radius √d. Density and mass are not the same thing.
Find all posts here.