Research

List of Published Works

1. Integral Motivic Cohomology of BSO4

   • • by Alexander Port

2. Mixing Constant Sum and Constant Product Market Makers 

   • • by Alexander Port and Neelesh Tiruviluamala 

3. A General Framework for Impermanent Loss in Automated Market Makers 

   • • by Neelesh Tiruviluamala, Alexander Port and Erik Lewis

4. Motivic Cohomology of BG2 (can be found at USC Libraries)

   • • by Alexander Port

5. Topological Analysis of Syntactic Structures (published link here)

   • • by Alexander Port, Taelin Karidi and Matilde Marcolli

6. Persistent Topology of Syntax (published link here)

   • • by Alexander Port, Iulia Gheorghita, Daniel Guth, John M.Clark, Crystal Liang, Shival Dasu and Matilde Marcolli

7. Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory (published link here)

   • • by Matilde Marcolli and Alexander Port

8. Thermodynamic insights into histone transfer among chaperones (published link here)

   • • by Wallace H. Liu, Sarah C. Roemer, Alex M. Port and Mair E. A. Churchill

9. CAF-1-induced oligomerization of histones H3/H4 and mutually exclusive interactions with Asf1 guide H3/H4 transitions among histone chaperones and DNA (published link here)

   • • by Wallace H. Liu, Sarah C. Roemer, Alex M. Port and Mair E. A. Churchill

10. Interactions of Anopheles gambiae Odorant-binding Proteins with a Human-derived Repellent (published link here)

    • • by Emma J. Murphy, Jamie C. Booth, Foteini Davrazou, Alex M. Port and David N. M. Jones

Experience

My current research as a Senior Data Scientist at Thrackle revolves around the study of Automated Market Markers (AMMs). Two common types of AMMs are Constant Sum Market Makers and Constant Product Market Makers (CSMMs and CPMMs); these are markets where asset exchanges are allowed as long as they preserve the total sum or product of asset quantities respectively. My work here primarily focuses on the geometric blending of these two types of markets in order to get the best of both worlds. CSMMs provide reliably stable prices for traders and CPMMs support all possible exchange rates; my "homotopy AMMs" completely parametrize the space between CSMMs and CPMMs and therefore allow for a wide variety of markets to be designed using this framework. I have also contributed to work involving a notion called "Exchange Rate Level Independence" and the nice properties that markets with this quality have. I'm proud to say that as of March 30, 2022 our company as posted its first two papers on arXiv!

My graduate work at the University of Southern California culminated in me completing a PhD in Mathematics with advisor Dr. Aravind Asok. This goal of this research was to compute the integral motivic cohomology of the classifying space BG2 using BSO4. Here exceptional simple Lie group G2 is taken to mean the automorphism group of the split-octonions. G2 is interesting in its own right but it, along with other Lie groups like F4, have ties to quantum mechanics and quantum computing. More generally, the study of the classifying spaces of these Lie groups is an ongoing process that has several important historical checkpoints:

1. Borel computed the singular cohomology rings of BG2 over Zp for all primes p

2. Field computed the Chow ring of BSO(2n,C)

3. Guillot computed the Chow ring of BG2

4. Yagita computed the mod-2 motivic cohomology of BSO4 and conjectured on the same for BG2

I'm very happy to say that as of August 27, 2021 my thesis demonstrating computation of the integral motivic cohomology of BSO4 and BG2 was successfully defended!

An additional area of research for me has been the study of syntactic language databases using Topological Data Analysis (TDA). This work has been ongoing under the guidance of Dr. Matilde Marcolli at the California Institute of Technology. TDA is a powerful tool that allows for analysis of high dimensional data without the need for direct visualization of the data; it extracts abstract information about the shape of the data that is robust against the existence of noise. In our case, the data are syntactic parameters of natural languages around the world. Centuries of work exists in the field of historical linguistics but these syntactic parameter databases lie in the field of computational linguistics; an important goal in our work is to determine the relations between the historical and computational fields. Our latest paper on the subject was published on January 27, 2022.

I have also had research experience previous to graduate work. I spent three summers volunteering in the lab of Dr. David Jones at the University of Colorado School of Medicine. During my freshmen year at Caltech, I applied for and received a Summer Undergraduate Fellowship (SURF) in the lab of Dr. Mair Churchill, another structural biologist at the University of Colorado. Each of these endeavors resulted in my being a co-author in published journals. After my sophomore year at Caltech, I felt that I was finally ready to pursue research projects in pure math.  During the summer between my sophomore and junior years, I studied under the guidance of Dr. Alexander Kechris with the support of an NSF REU fellowship. For my second summer of mathematics research, after my junior year, I was awarded a SURF at Caltech to study with Dr. Marcolli.