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content/posts/consuelo-poem/index.md

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eres mi corazón.
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```
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content/posts/delia-poem/index.md

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calor solar.
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```
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content/posts/lucy-poem/index.md

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Pronto nos veremos otra vez.
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```
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content/posts/occidental-poem/index.md

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es información que se filtra entre la materia.
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```
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---
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title: "Perspectives into Tensors, Signals, and Kernel Methods"
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category: technical
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date: 2025-09-08
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math: true
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draft: true
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---
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{{< toc >}}
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## Abstract
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[Linear algebra](https://linear.axler.net/LADR4e.pdf), [signal processing](https://en.wikipedia.org/wiki/Signal_processing), and [machine learning](https://en.wikipedia.org/wiki/Machine_learning) are (one of many groups of) topics that enjoy a beautiful relationship protected by a nutshell of mathematics. Inside we can find a kernel of perspectives which are simply a pleasure to entertain. Here, I provide the [linear-operator](https://en.wikipedia.org/wiki/Linear_map) perspective into [systems of many dimensions](https://en.wikipedia.org/wiki/Multidimensional_system), characterizing properties like [time-invariance](https://en.wikipedia.org/wiki/Time-invariant_system) and [causality](https://en.wikipedia.org/wiki/Causal_system) via [tensor](https://en.wikipedia.org/wiki/Tensor) representations. I finish with an original perspective that connects the [convolution kernel](https://en.wikipedia.org/wiki/Convolution) to the [reproducing kernel](https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space#:~:text=then%20called%20the-,reproducing%20kernel,-%2C%20and%20it%20reproduces).
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---
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## Background
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This section is no more than a refresher on select topics. I will not make an attempt to explain them completely. If this is what you need, I recommend you explore these (completely free) resources:
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1. **Vector spaces.** [_Linear Algebra Done Right_](https://linear.axler.net/) by Axler.
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2. **Signals and Systems.** [_Signals & Systems: Theory and Applications_](https://ss2-2e.eecs.umich.edu/) by Ulaby and
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Yagle.
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3. **Kernel methods.** [_Foundations of Machine Learning_](https://cs.nyu.edu/~mohri/mlbook/) by Mohri, Rostamizadeh, and Talwalkar.
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### Vector Spaces
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### Signals and Systems
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### Kernel Methods
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---
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content/resume.md

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## Introduction
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I am a fourth-year undergraduate at [UC Berkeley](https://www.berkeley.edu/) invested in mathematics and computer science. Primarily, I am a systems programmer and machine learning practitioner. I apply these aptitudes to research projects within computational game theory, advised by [Prof. Garcia](https://people.eecs.berkeley.edu/~ddgarcia/). I have also spent a few summers at [Meta](https://about.meta.com/) working on ML infrastructure among other things, and accrued significant leadership experience in two years as an engineering lead at [UC Berkeley SAIT](https://technology.berkeley.edu/SAIT).
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I am graduating from [UC Berkeley](https://www.berkeley.edu/) intellectually invested in mathematics and computer science. I am a systems programmer and machine learning practitioner by trade. With these aptitudes, I pursue projects in the intersection of machine learning and game theory. I also spent four summers at [Meta](https://about.meta.com/) (working on ML infrastructure, among other things) and have two years of leadership experience as an engineering lead at [UC Berkeley SAIT](https://technology.berkeley.edu/SAIT).
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---
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## Academic History
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### University of California, Berkeley
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_**B.A. Computer Science** - In progress_
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**B.A. Computer Science** -- Aug 2021 to Dec 2025
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{{< collapse "summary"="Coursework..." >}}
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* `CS 70` _Discrete Mathematics & Probability Theory_ ([Prof. Rao](https://www2.eecs.berkeley.edu/Faculty/Homepages/rao.html#main-content), [Prof. Ayazifar](https://www2.eecs.berkeley.edu/Faculty/Homepages/ayazifar.html#main-content))
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* `CS 61A` _Structure & Interpretation of Computer Programs_ ([Prof. DeNero](https://denero.org/))
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* `CS 61B` _Data Structures & Algorithms_ ([Prof. Hilfinger](https://www2.eecs.berkeley.edu/Faculty/Homepages/hilfinger.html#main-content))
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* `CS 61A` _Structure & Interpretation of Computer Programs_ ([<u>Prof. DeNero</u>](https://denero.org/))
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* `CS 61B` _Data Structures & Algorithms_ ([<u>Prof. Hilfinger</u>](https://www2.eecs.berkeley.edu/Faculty/Homepages/hilfinger.html#main-content))
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* `CS 61C` **_Great Ideas in Computer Architecture_** ([Prof. Garcia](https://people.eecs.berkeley.edu/~ddgarcia/))
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* `CS 170` **_Efficient Algorithms & Intractable Problems_** ([Prof. Haghtalab](https://people.eecs.berkeley.edu/~nika/), [Prof. Wright](https://www2.eecs.berkeley.edu/Faculty/Homepages/jswright.html#main-content))
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* `CS 170` **_Efficient Algorithms & Intractable Problems_** ([<u>Prof. Haghtalab</u>](https://people.eecs.berkeley.edu/~nika/), [Prof. Wright](https://www2.eecs.berkeley.edu/Faculty/Homepages/jswright.html#main-content))
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* `CS 186` _Introduction to Database Systems_ ([Prof. Cheung](https://people.eecs.berkeley.edu/~akcheung/))
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* `CS 162` **_Operating Systems & Systems Programming_** ([Prof. Kubiatowicz](https://people.eecs.berkeley.edu/~kubitron/))
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* `CS 189` **_Introduction to Machine Learning_** ([Prof. Listgarten](http://www.jennifer.listgarten.com/), [Prof. Saremi](https://www.linkedin.com/in/saeed-saremi-71935916/))
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* `CS C182` **_Deep Neural Networks_** ([Prof. Sahai](https://www2.eecs.berkeley.edu/Faculty/Homepages/sahai.html))
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* `CS 162` **_Operating Systems & Systems Programming_** ([<u>Prof. Kubiatowicz</u>](https://people.eecs.berkeley.edu/~kubitron/))
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* `CS 189` **_Introduction to Machine Learning_** ([<u>Prof. Listgarten</u>](http://www.jennifer.listgarten.com/), [Prof. Saremi](https://www.linkedin.com/in/saeed-saremi-71935916/))
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* `CS 182` **_Designing, Visualizing and Understanding Deep Neural Networks_** ([<u>Prof. Sahai</u>](https://www2.eecs.berkeley.edu/Faculty/Homepages/sahai.html))
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* `CS 272` **_Foundations of Learning, Decisions, and Games_** [Audited] ([<u>Prof. Haghtalab</u>](https://people.eecs.berkeley.edu/~nika/))
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<!-- -->
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* `EE 126` _Probability and Random Processes_ ([Prof. Khanna](https://www2.eecs.berkeley.edu/Faculty/Homepages/pkhanna.html))
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* `EE 120` **_Signals and Systems_** ([<u>Prof. Dimakis</u>](https://people.eecs.berkeley.edu/~alexdimakis/))
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<!-- -->
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* `MATH 1A` _Calculus I_ ([Prof. Vojta](https://math.berkeley.edu/~vojta/))
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* `MATH 1B` _Calculus II_ ([Prof. Paulin](https://math.berkeley.edu/~apaulin/))
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* `MATH 1B` _Calculus II_ ([<u>Prof. Paulin</u>](https://math.berkeley.edu/~apaulin/))
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* `MATH 54` **_Linear Algebra & Differential Equations_** ([Prof. Lott](https://math.berkeley.edu/~lott/))
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* `MATH 110` **_Abstract Linear Algebra_** ([Prof. Frenkel](https://www.edwardfrenkel.com/))
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* `MATH 110` **_Abstract Linear Algebra_** ([<u>Prof. Frenkel</u>](https://www.edwardfrenkel.com/))
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* `MATH 113` _Abstract Algebra_ [Audited] ([Prof. Utiralova](https://math.berkeley.edu/~sashau/))
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**Courses **in bold** are favorites of mine!*
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**Courses **in bold** and professors <u>underlined</u> are favorites of mine!*
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{{< /collapse >}}
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### Software Engineer Intern @ [Meta](https://about.meta.com/)
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New York, NY -- Since May 2025
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New York, NY -- May 2025 to Aug 2025
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{{< collapse "summary"="Details..." >}}
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Part of the Systems Experimentation team.
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Experimentation products at Meta (e.g. [ServiceLab](https://www.usenix.org/system/files/osdi24-chow.pdf)) rely on common experimentation infrastructure in the form of a unified platform. This platform underwent migration to a modularized alternative in the interest of extensibility into the use cases of new experimentation products (among other things).
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As part of the Systems Experimentation team, I migrated a feature that allowed experimentation products to track the status of collections of individual trials under an SLA of eventual consistency and retry-based fault tolerance. This required the design and implementation of distributed workflows written in Python and Rust, extensions to our external API, and close rollout monitoring via internal observability tooling.
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I also detailed a state log data pipeline and model-predictive workflow controller to optimize actions (such as retries) according to our SLOs. This took the form of a ~15 page RFC that I presented to the team.
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[]() <!-- This is for rendering the above as a <p> element -->
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public/categories/index.xml

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<item>
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<title>Poem 5. &#34;Zoe&#34;</title>
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<link>http://localhost:1313/poem-5.-zoe/</link>
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<pubDate>Mon, 28 Jul 2025 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/poem-5.-zoe/</guid>
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<description>&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;caudaloso río de la memoria;
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sacrificio, derrota clavada,
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memoria total, pensamiento
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que me abruma,
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te vas
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para regresar una vez más,
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siempre una vez más, nunca
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te vas,
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pero tampoco llegas;
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ya te fuiste, y aún sigues
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aquí, sigues en el instante,
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la hora te produce siempre,
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ya no sueño, recordar tu luz
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me despierta, me carcome,
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lo pagué todo para pensarte,
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símbolo del olvido,
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cara
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atorada siempre en el pasado,
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sólo te pienso en el pasado,
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palabras que escribo pensando
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en el pasado;
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ahí perteneces,
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que el instante es una nada;
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el futuro toca ya la puerta
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de mi alma, y no lo escucho;
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silencio que me abruma,
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pensamientos que me gritan,
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memorias que me ahogan
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en su caudal, río perdido
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que te busca siempre
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&lt;/code&gt;&lt;/pre&gt;</description>
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</item>
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<item>
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<title>Poem 4. &#34;Consuelo&#34;</title>
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<link>http://localhost:1313/poem-4.-consuelo/</link>
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<pubDate>Sun, 27 Jul 2025 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/poem-4.-consuelo/</guid>
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<description>&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;Ay, mijo,
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que te bendiga Dios.
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No eres de ule ni de fierro.
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Te amo con todo mi ser;
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eres mi corazón.
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&lt;/code&gt;&lt;/pre&gt;</description>
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</item>
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<item>
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<title>Poem 3. &#34;Lucy&#34;</title>
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<link>http://localhost:1313/poem-3.-lucy/</link>
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<pubDate>Sat, 12 Jul 2025 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/poem-3.-lucy/</guid>
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<description>&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;Marsupial madre de un amor tenaz
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que se resguarda entre mis costillas;
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me llena de un sentimiento líquido
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que se construye al cerrar mis ojos.
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Llueves gotas de ideas inmarcesibles.
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Toda la noche llueves sobre mi rostro;
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gotas de lluvia que veo ya sobre mi piel
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son transparentes, por tu transparencia.
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Cómo te extraño, querida amiga;
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que convertiste nuestra vivienda en hogar,
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y cuidas siempre de mí, así cómo yo de ti.
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Pronto nos veremos otra vez.
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&lt;/code&gt;&lt;/pre&gt;</description>
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</item>
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<title>Poem 2. &#34;Occidental&#34;</title>
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<link>http://localhost:1313/poem-2.-occidental/</link>
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<pubDate>Wed, 30 Apr 2025 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/poem-2.-occidental/</guid>
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<description>&lt;p&gt;El negro de la noche es el final del infinito;&lt;br&gt;
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la verdad me llega a la velocidad de la luz.&lt;br&gt;
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Son trayectorias que trazan entre los átomos,&lt;br&gt;
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son curvas que desnudan misterios paralelos.&lt;br&gt;
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Es hipótesis de tiempo escrita en el espacio,&lt;br&gt;
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es información que se filtra entre la materia.&lt;/p&gt;
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</description>
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<description>&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;Son trayectorias que trazan entre los átomos,
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son curvas que desnudan misterios paralelos.
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Es hipótesis de tiempo escrita en el espacio,
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es información que se filtra entre la materia.
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&lt;/code&gt;&lt;/pre&gt;</description>
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<pubDate>Sun, 27 Apr 2025 00:00:00 +0000</pubDate>
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<guid>http://localhost:1313/poem-1.-delia/</guid>
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<description>&lt;p&gt;Madre que no te suelta el estandarte,&lt;br&gt;
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madre de selva que te cubre como yedra;&lt;br&gt;
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me arrulla desde la penumbra,&lt;br&gt;
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me susurra el nombre de Dios.&lt;br&gt;
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Ya quítame de aquí que me muero, madre,&lt;br&gt;
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dame las palabras que me corresponden,&lt;br&gt;
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sacude desde tu sigilo mi sangre,&lt;br&gt;
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hazme llegar tu amor.&lt;br&gt;
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Soledad eterna y vida corta,&lt;br&gt;
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no te vayas a olvidar de mí.&lt;br&gt;
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Madre que a ciegas todo lo ve;&lt;br&gt;
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corazón de parota, palabras de luz.&lt;br&gt;
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Eres la cumbre de este desierto,&lt;br&gt;
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autora del método mío,&lt;br&gt;
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madre de todo.&lt;br&gt;
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Mi primer amor, también el último,&lt;br&gt;
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mi castillo, mi escudo, mi ángel.&lt;br&gt;
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Águila de quinientas virtudes,&lt;br&gt;
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reguilete infinito de colores,&lt;br&gt;
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piedra de orgullo inexorable.&lt;br&gt;
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Arbol terrestre que toca el cielo,&lt;br&gt;
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sosiego inminente,&lt;br&gt;
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calor solar.&lt;/p&gt;
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</description>
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<description>&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;Madre que no me suelta el estandarte,
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madre de selva que me cubre como yedra,
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estás completamente marcada en mí;
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me arrullas desde mi penumbra,
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me susurras el nombre de Dios.
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Ya quítame de aquí que me muero, madre,
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dame las palabras que me corresponden,
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sacude desde tu sigilo mi sangre
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y hazme llegar tu amor.
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Soledad eterna y vida corta,
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nunca te me vayas a ir.
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Madre que a ciegas todo lo ve;
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corazón de parota, palabras de luz.
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Eres la cumbre de este desierto,
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autora del método mío;
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eres madre de todo.
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Águila de quinientas virtudes,
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reguilete infinito de colores,
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piedra de orgullo inexorable.
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Árbol terrestre que toca el cielo;
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sosiego inminente,
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calor solar.
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&lt;/code&gt;&lt;/pre&gt;</description>
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&lt;hr&gt;
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&lt;h2 id=&#34;materials&#34;&gt;Materials&lt;/h2&gt;
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&lt;p&gt;The slides I used during my talk can be found below. Anyone can use them without my permission.&lt;/p&gt;
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width: 100%;
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-webkit-animation: spin 1s ease-in-out infinite;
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margin: auto;
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padding: 0.3em 1em;
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border: solid 2px;
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border-radius: 12px;
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border-color: #00000030;
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text-decoration: none;
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height: clamp(1em, 2vw, 1.4em);
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&lt;div class=&#34;pdf-loading&#34; id=&#34;pdf-loading-de1ff50c&#34;&gt;&lt;/div&gt;
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&lt;/div&gt;

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<description>Recent content on Max Fierro</description>
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<generator>Hugo -- gohugo.io</generator>
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<lastBuildDate>Mon, 28 Jul 2025 00:00:00 +0000</lastBuildDate>
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<lastBuildDate>Mon, 08 Sep 2025 00:00:00 +0000</lastBuildDate>
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