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**Title: **Simplicial Reaction Networks and Dynamics on Graphs

**Date:**Thursday, May 11th, 2023

**Time:**11:00 AM – 12:00 PM PDT

**Location (In Person):**Soda 405, Berkeley CA

**Abstract: **Reaction networks are a powerful tool for modeling the behavior of a wide variety of real-world systems, including population dynamics and chemical processes, as well as algorithms for sampling combinatorial objects. While many such systems have well-understood equilibrium states, the long-standing conjecture that these states will always be achieved remains open.

This talk presents the class of simplicial reaction networks, which includes a wide variety of natural combinatorial examples. I will show how simplicial structures can be used to understand and control the equilibrium behavior of the network as a whole, and discuss related progress towards the Global Attractor Conjecture. Finally, I will present additional work exploring combinatorial approaches to the Inverse Eigenvalue Problem on graphs, including the randomized Zero Forcing algorithm and a lower bound for the Minimum Rank problem.

I’ll be at the JMM ILAS special session to speak about my recent work on the Computational Hardness of the Minimum Rank Problem on Graphs.

My coauthor Sam will also be presenting our joint work on Zero Forcing with Random Sets!

New on the arXiv: Zero Forcing with Random Sets.

Given a graph G and a real number 0 ≤ p ≤ 1, we define the random set Bp(G) ⊂ V(G) by including each vertex independently and with probability p. We investigate the probability that the random set Bp(G) is a zero forcing set of G. In particular, we prove that for large n, this probability for trees is upper bounded by the corresponding probability for a path graph. Given a minimum degree condition, we also prove a conjecture of Boyer et. al. regarding the number of zero forcing sets of a given size that a graph can have.

The Berkeley EECS Department was kind enough to award me with the EECS Outstanding TA award this year! I’m very grateful to the colleagues who nominated me, and to all the wonderful students who made teaching discrete math and probability a delightful experience.

**ze·nith**

*noun*

- The time at which something is most powerful or successful.
- The point in the sky or celestial sphere directly above an observer.

I was fortunate to receive the D.E. Shaw Zenith Fellowship award this year! Despite the name, here’s hoping that my most successful days are still ahead.

I’m starting a series of blog posts based on the notes I take when I read papers. The first one is about a paper I’m presenting in my Neural Network Mathematics reading group on 4/5: Adversarial Examples from Computational Constraints by Bubeck, Price, and Razenshteyn.

This semester, I participated in Berkeley’s 2-day PhD workshop on Communications for Engineering Leaders! We were challenged to design 5-minute lightning research talks, accessible to a broad audience of engineers and scientists.

I’m turning my talk into a blog post: coming soon!

Last year, I was accepted to the 2020-21 AMS research community on the Inverse Eigenvalue Problem. Since then, we’ve had an intensive learning workshop, and now a special session at the 2021 Joint Mathematics Meetings, leading up to our (virtual) collaboration this summer.

Check out our session at the 2021 JMM site for more information!

I also attended ITCS for the first time, and I highly recommend the short talk format. This is definitely a great conference for Theory students to attend and absorb new ideas!

I started off the new year by participating in a thought-provoking new mini course from Harvard GSAS: *Disrupting the New Jim Code: Applying Principles of Anti-Racism to Algorithmic Fairness, Accountability, and Ethics*.

We talked about many different lenses on ethical development of algorithms and machine learning, and read from literature spanning social science to law to computer science.

I highly recommend this course to researchers and practicioners alike, and to anyone in a position to work towards anti-racist, ethical decisionmaking.