This page contains some of my work and other professional activities.

## Interests

As an industry mathematician, I have a wide range of interests. I currently work in venture capital and am interested in learning more about this space; I am especially interested in traditional and non-traditional financial data and how it can be used to make better investment decisions. As a part of this work, I also care about machine learning, data engineering, devops, and other tools that can help build better decision support systems.

For fundamental research, I primarily work on dynamic networks, i.e., graphs that change over time. While I do work on various applications of dynamic networks, I am also interested in theoretical questions, including perspectives from algebraic topology, algorithms, stochastic processes, optimization, and graph theory.

As a coder, I am interested in cool, ergonomic, and powerful devops and data engineering tools. I also love functional programming, immutable data structures, and type systems. I have also been thinking about:

- parallel and distributed computing
- crypotographically-guaranteed data privacy
- classical music
- aerospace technology and other vehicles

## Current Research Projects

I am currently working on a variety of research projects, primarily supported by my firm, Level Ventures. I like cataloging my active areas of work, even if they do not lead to specific publications or other outputs. If you’re interested in any of these projects or have a project you’d like to collaborate on, please reach out!

**Basketball data analysis**: with Erin Taylor, we’re studying the geometry and topology of basketball plays: given movement data, we want to summarize the relevant geometric information from trajectories and induced topological information (e.g. player passing networks). With this data, we want to classify plays, predict outcomes, and propose possible strategies for optimal play.**Multiset metric spaces**: As a part of the basketball work, we ran into a problem: given a metric space \((X, d)\), we want to define a new metric on the multisets of fixed size \(n\) from \(X\), which we can do based on bijections between multisets. While it’s straightforward to prove that we can construct a metric, we want to explain this metric’s relationship to the discrete Wasserstein metric and Hölder means.**Ecosystem federalism and compartmental disease models with dynamic networks**: with Julie Blackwood, I’m studying the spread of disease in the context of mutliscale governance models. We’re trying to understand the effects of different policies at multiple scales of governments with dynamic interaction networks.**Spatiotemporal clustering**: with Olga Dorabiala, I’m working on problems in spatiotemporal clustering, both in the general setting, and for dynamic networks specifically. We have published in this area already [1, 2] and have two additional pre-prints [3, 4], so this research thrust is realtively mature. We’re currently working on applying the general method to ML problems with foundation models and we’re thinking of ways to extend the technique for multiscale analysis in dynamic networks.**Gradient descent learning rate and error in convex functions**: as part of a working group in QCAM led by Andre Wibisono, we have been investigating the relationship between learning rate and error in gradient descent for convex functions. More precisely, given a (strongly) convex and sufficiently smooth function, we ask:*is it better to take \(k\) steps with learning rate \(\eta\) or \(2k\) steps with learning rate \(\eta/2\)?*As long as the learning rate is sufficiently small, we strongly suspect that the former is better; it is straightforward to prove for quadratic functions and in the 1-D case. We are trying to generalize this result to \(\mathbb{R}^d\) and, as a consequence, prove a more general conjecture about the relationship between gradient descent, gradient flow, and proximal gradient descent.

## Publications

**2024 – pre-print**(PDF)*Spatiotemporal \(k\)-means*[3]**2024 – pre-print**(PDF)*Vertex clustering in diverse dynamic networks*[4]**2023 – Complex Networks**(PDF)*A Novel Method for Vertex Clustering in Dynamic Networks*[2]**2023 – ComNets @ NetSci**(PDF)*Spatiotemporal Graph \(k\)-means*[1]**2023 – Bioinformatics Advances**(PDF)*Network-Augmented Compartmental Models to Track Asymptomatic Disease Spread*[5]**2023 – Princeton U. | Ph.D. Dissertation**(PDF)*On Systems of Dynamic Graphs: Theory and Applications*[6]

Adviser: Bernard Chazelle, Reader: Robert Kassouf-Short.**2022 – IEEE AeroConf**(PDF)*Introducing Tropical Geometric Approaches to Delay Tolerant Networking Optimization*[7]**2022 – IEEE AeroConf**(PDF)*A Survey of Mathematical Structures for Lunar Networks*[8]**2021 – Complex Networks**(PDF)*Extracting Semantic Information from Dynamic Graphs of Geometric Data*[9]**2016 – SIURO**(PDF)*Rumors with Personality: A Differential and Agent-Based Model of Information Spread through Networks*[10]

## Talks

- 2025 January –
**Joint Mathematics Meetings***TBA* - 2024 June –
**QCAM**(Slides)*Vertex clustering in diverse dynamic networks* - 2024 June –
**UCLA Mathematics***Queer in Math Panel* - 2024 April –
**Spectra @ U. of Kentucky***Career Panel* - 2024 January –
**Joint Mathematics Meetings**(Slides)*A Novel Method for Vertex Clustering in Dynamic Networks* - 2023 November –
**Complex Networks**(Poster)*Spatiotemporal Graph*Given by Olga Dorabiala.*k*-means - 2023 May –
**Spectra Survey of Mathematics @ U. of Kentucky**(Slides)

*Dynamic Graphs* - 2023 May –
**Princeton U. | Ph.D. Defense**(Slides)*On Systems of Dynamic Graphs: Theory and Applications*

Committee: Bernard Chazelle, Mona Singh, Jason M. Klusowski. - 2023 March –
**SIAM CSE**(Slides)*Inspired by Nature: Dynamic Graphs and their Applications* - 2022 Winter –
**Princeton U. | PICSciE Wintersession***Workshop: Now You*`git`

It! - 2021 December –
**Complex Networks***Extracting Semantic Information from Dynamic Graphs of Geometric Data* - 2021 Fall –
**Princeton U. | PICSciE***Workshop: Now You*`git`

It! - 2021 Summer –
**NASA | GlennTalk***Why everyone is a graph theorist (and some potpourri)* - 2021 Summer –
**NASA***Workshop:*`git`

It Together - 2021 January –
**Princeton U. | General Examination***Analyzing Basketball with Dynamic Networks*

Committee: Bernard Chazelle, Szymon Rusinkiewicz, Weinan E. - 2020 Spring –
**Princeton U. | PICSciE***Workshop: Now You*`git`

It! - 2019 Fall –
**Princeton U. | Research Computing Bootcamp 2019***Workshop: Version Control with Git* - 2019 June –
**U. of Waterloo | Anita T. Layton Research Group***Mathketball* - 2017 Fall –
**Duke U. | Focus Dinner Talk***Get Your Text out of the Clouds with Laplace* - 2016 November –
**HackDuke 2016***React* - 2016 November –
**HackDuke 2016***Workshop:*With Jiawei Zhang.`git`

your shit together - 2016 Fall –
**Duke U. | Focus Dinner Talk***Rumors with Personality* - 2015 Spring –
**Duke U. Dept. of Romance Studies | Undergraduate Research Symposium***Oubapo: La Distillation de l’Information*

## Other Writing

- 2024 February –
**Level Ventures Research Blog***Dynamic Networks and Machine Learning*[11]

## Other Research Projects

- 2017 Spring to 2018 Spring –
**Duke U. | Senior Thesis Work***Basketball Data Analysis*(note: I never formally submitted my senior thesis.) - 2015 Summer –
**Duke U. | Bass Connections***Feature Extraction and Quantitative Analysis of Large Scientific Document Corpora*

Supervised by Xiaobai Sun and Nikos Pitsianis

## Current Professional Service

*Profession Chair, Board Member*,**Spectra, the Association of LGBTQ+ Mathematicians***Board Member*,**New Muses Project***Board Member*,**Queer Prinecton Alumni***Board Member*,**Duke LGBTQ+ Network**

## References

*Proceedings of the communities in networks ComNets @ NetSci 2023*, 2023.

*Complex networks & their applications XII*, Springer, 2023, pp. 445–456. doi: 10.1007/978-3-031-53499-7_36

*Bioinformatics Advances*, 2023, doi: 10.1093/bioadv/vbad082

*et al.*, “Introducing tropical geometric approaches to delay tolerant networking optimization,” in

*2022 IEEE aerospace conference (AERO)*, 2022, pp. 1–11. doi: 10.1109/AERO53065.2022.9843242

*et al.*, “A survey of mathematical structures for lunar networks,” in

*2022 IEEE aerospace conference (AERO)*, 2022, pp. 1–17. doi: 10.1109/AERO53065.2022.9843305

*Complex networks & their applications X*, Springer, 2021, pp. 474–485. doi: 10.1007/978-3-030-93413-2_40

*SIAM Undergraduate Research Online*, vol. 9, pp. 453–467, Dec. 2016, doi: 10.1137/16S015103