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Contact

leticiam[at]mit[dot]edu

About me

I'm a Ph.D. candidate at MIT, where I research numerical methods for nonlinear PDE and other associated dynamical problems, under the supervision of Justin Solomon. The goal of my work is to advance applications of these PDE in the fields of geometry processing and computer graphics.

 

My research is supported by a 2023 MathWorks Fellowship. In the past, I had the generous support of a 2022 Schwarzman College of Computing Fellowship funded by Google and a 2021 MIT Distinguished Fellowship in EECS.

 

Before coming to MIT, I graduated cum laude with a bachelor's degree in mathematics at the University of California, Los Angeles.

If you are a student from an underrepresented group looking for advice on pursuing research in mathematics or computer science, check out this section or reach out by email. I'd be happy to help you and share resources!

Research Interests

My research is focused on numerical methods for PDE, in particular nonlinear parabolic PDE and certain kinetic equations. I am also interested in algorithms to solve dynamical problems involving the stochastic counterparts to these nonlinear PDE, e.g., algorithms for the Schrödinger Bridge Problem. I'm mainly concerned with applications in geometry processing, computer graphics and vision.

Publications

2023

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A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains

Leticia Mattos Da Silva, Oded Stein, Justin Solomon

ACM Transactions on Graphics (invited to present at SIGGRAPH 2024)

PDF

2022

Breaking Good: Fracture Modes for Realtime Destruction

Silvia Sellán, Jack Luong, Leticia Mattos Da Silva, Aravind Ramakrishnan, Yuchuan Yang, Alec Jacobson

ACM Transactions on Graphics

PDF

UROP Information

Ph.D. students like me typically are the day-to-day mentors for UROPs in our lab. If you are a student interested in doing a UROP with me, please read this page for more information before emailing me.

Availability

Summer 2024: I am not available to take on a UROP.
Fall 2024: Email me if interested!

Potential UROP Project

I'm our lab's "local expert on parabolic PDE, Schrödinger bridges, and other problems in the dynamical universe." We can jointly figure out a research direction in this area, but here's an example of a UROP project we could work on together — it is quite open-ended!

Overview. The Schrödinger Bridge Problem (SBP) seeks to steer an initial probability distribution of a linear stochastic system to a terminal distribution using minimal energy. In this project, we will explore a generalization of the SBP with nonlinear prior dynamics. The goal is to design a numerical solver for a pair of PDE associated with this generalization of the problem. We will then investigate using this solver in a pipeline to recover the optimal variables for the SBP. Here is a good reference to start with, if you are interested in pursuing a project in this direction. 

Prerequisites. There are no requirements beyond understanding of linear algebra, but 6.8410 can be helpful. 

Resources

I am committed to bridging the gap between students from underrepresented or underserved backgrounds and academic opportunities. To this end, I have put together a collection of resources that I have benefited from, participated in, or found interesting in the past. I hope that sharing these will be useful to you! 

Any short descriptions or advice written in this section are my own and do not necessarily reflect the official views of the organizations or programs listed.

For Current Graduate Students

| Recipient of the 2023-24 MathWorks Fellowship

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The CommKit has various guides useful to current graduate students, including on how to write thesis proposals, fellowship statements, posters, professional bios, and much more. The CommKit is available for free to students outside MIT.

For MIT students. If you are a MIT student you can also schedule an appointment to receive feedback.

Applying to Graduate School

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GAAP is a student-run, volunteer based program that provides one-to-one mentorship to prospective Ph.D. applicants from underrepresented groups.

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The CommKit has guides including advice on how to write a statements of purpose. The CommKit is available for free to students outside MIT.

For MIT students. You can set up a coaching appointment to receive feedback in graduate school and fellowship applications.

Undergraduate Summer REUs

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MSRP is a program designed to encourage students from historically underrepresented backgrounds to pursue careers in academic research by providing them the opportunity to conduct summer research at MIT. Students in this 9-week program receive a weekly stipend, round-trip travel and housing at MIT.

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SGI is a program designed to introduce undergraduate and early graduate students to the field of geometry processing. Students in this 6-week remote program receive a stipend. 

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FUSRP matches students with faculty at sponsoring or affiliated universities to conduct mathematical research over the summer. 

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