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daniel lópez castaño daniel lópez castaño applied mathematician baltimore md cv about bio news projects blog published work teaching talks about i am a ph d candidate in applied mathematics and statistics at johns hopkins university advised by mateo díaz and soledad villar my research sits at the intersection of optimal transport riemannian optimization and manifold learning beyond research i dedicate time to teaching and mentoring my interests extend to cycling artisanal coffee and anime tv shows bio i obtained a m sc in applied mathematics and statistics from johns hopkins university in 2024 and a m sc in mathematics from the universidad nacional de colombia in 2020 where i worked on spectral geometry and noncommutative geometry under the supervision of prof sylvie paycha and prof carolina neira jiménez during the latter i did a research internship at the institute fur mathematik of the universität potsdam i also worked as a machine learning engineer at vozy a latin american startup specializing in conversational ai news august 31 september 4 2026 talk at inabag school conference presenting my research on estimation of morse indices from samples at the inabag school conference in applied algebraic geometry in siena italy more info august 17 25 2026 upcoming minicourse and talk at unal bogota in spanish more info june august 2026 internship i m interning at the interamerican development bank in the systemic risk group working on graph models and network analysis applied to financial systems december 9 12 2025 poster presentation presenting work on estimation of morse information on manifolds at the statistics and data science workshop universidad de los andes may 27 30 2025 optimization and learning theory and applications montreal canada projects systemic risk framework research consultant 2026 present developed a framework for systemic risk that models direct and cascading dependencies across both external drivers and institutional risk networks built a regularized graph autoregressive forecasting model combining temporal lags and high order network effects geometric factor analysis research 2024 present uncovering latent factors in data by mapping onto optimized orthogonal reference frames in the stiefel manifold combining optimal transport with riemannian optimization to address rotational ambiguity in high dimensional factor models vision guided drone mentor feb 2025 may 2025 mentored a team of three high school interns at johns hopkins university in developing an autonomous drone navigation system using computer vision and optimization techniques for safe and efficient flight path planning qudost research may 2023 may 2024 advances density estimation by transforming it into a supervised learning problem enabling real time inference via universal approximation research conducted at the johns hopkins university applied physics laboratory vobio machine learning engineer 2020 2021 voice biometrics authentication system developed in pytorch and tensorflow one of the first of its kind deployed for corporate use in latin america integrated into vozy s client authentication framework with real time inference capabilities blog december 4 2024 understanding factor analysis through geometric lenses exploring the intersection of geometry and statistical analysis to uncover hidden patterns in high dimensional data structures read more published work master s thesis 2020 a distributional approach to asymptotics of the spectral action daniel lópez castaño the spectral action introduced by chamseddine and connes in 1997 is the natural and appropriate notion of an action on the space of spectral triples after presenting key definitions and results from the cesàro theory of distributions and asymptotic analysis we discuss the asymptotic expansion of the spectral action in the distributional sense for a commutative spectral triple following estrada gracia bondía and várilly research conducted at universität potsdam under the supervision of prof sylvie paycha publication show abstract teaching johns hopkins university en 553 781 functional data analysis fall 2026 teaching assistant en 553 625 machine learning 2 spring 2025 teaching assistant en 553 620 machine learning 1 fall 2024 fall 2023 teaching assistant en 553 660 nonlinear optimization 2 spring 2024 teaching assistant en 553 513 directed reading in applied mathematics fall 2024 geometry of the space of probability distributions mentee shayaan emran mentor en 553 513 directed reading in applied mathematics spring 2024 symmetries and representations mentee minjae kim mentor en 553 513 directed reading in applied mathematics fall 2023 spectral geometry on triangles mentee sukriti gupta mentor universidad nacional de colombia cálculo diferencial calculus 1 2018 2 2019 1 instructor talks presentations 2025 estimating morse information from samples poster statistics and data science workshop universidad de los andes bogotá colombia 2024 geometric factor analysis runner up best poster poster optimization workshop universidad de los andes bogotá colombia 2024 geometric factor analysis poster siam mathematics of data science atlanta ga 2023 inference fast density estimation via universal approximators poster johns hopkins ai x foundry fall symposium baltimore md 2019 on vibrating strings drums and what can and cannot be heard conference colloquium mathematics department universidad nacional de colombia bogotá 2019 on the distributional asymptotic expansion of the spectral action seminar analysis group seminar universität potsdam germany 2019 sunada s technique for constructing isospectral manifolds short communication summer school on l² torsion and symmetric spaces universität göttingen germany 2019 a space of symbols and the cesàro behaviour at infinity seminar analysis group seminar universität potsdam germany 2019 notions of spectral action short communication uniandes sri 2019 on geometry and theoretical physics villa de leyva colombia 2018 spectral geometry and spectral action short communication cimpa school on noncommutative geometry and index theory cimat mérida mexico 2017 index formulas of an elliptic operator short communication school on geometric algebraic and topological methods for qft villa de leyva colombia 2017 the weak topology on distributions and calculation rules short communication top3 ud universidad distrital francisco josé de caldas bogotá 2017 radon measures an approximation of topological dual of l short communication vii encuentro nacional de matemáticas y estadística universidad del tolima ibagué tech stack python pytorch jax git docker flask html javascript sql bash 2026 daniel lópez castaño all rights reserved