In Summer of 2022, I helped lead an REU along with Sanjay Kumar and Melody Molander at UC Santa Barbara (virtually) regarding the project on extending the polynomial invariants of links using the techniques of dimer models. (https://arxiv.org/abs/2408.13410)
In Summer of 2023, I led an REU at the Ohio State University where with Giovanni Ferrer and Jiaqi Lu, we worked on SL(4) webs and a four valent model for it. This was part of the ROMUS program at OSU. The project description can be found below:
In this project, we provide a four valent diagrammatic presentation for the representation category of SL(4) starting from Cautis-Kamnitzer-Morrison's trivalent model. We achieve this by constructing a more general diagrammatic quotient category generated by tagged oriented four valent graphs which contains as a subcategory the SL(4) representation category. Along the way, we also show how this general construction specializes to ribbon categories that encapsulate other well-known constructions due to Murakami-Ohtsuki-Yamada and also due to Kauffman-Vogel.
I co-organized the DRP in 2021-22.
As part of my first DRP project, I mentored Nyah J. Davis and led a project related to combinatorics (Pascal matrices and Young Tableaux).
Nyah is now getting a PhD in mathematics at Rice University.
More information regarding the University of Iowa Directed Reading program can be found here: https://math.uiowa.edu/graduate-program/directed-reading-program