In the summer of 2019, Havi Ellers (Harvey Mudd College, California) and Xiaomin Li (University of Illinois Urbana-Champaign, Illinois) participated in the FUSRP program at the Fields Institute for Research in Mathematical Sciences and succeeded in formulating interesting conjectures on a special family of multi-variate symmetric polynomials: Jack Polynomials. Havi and Xiaomin formulated their conjectures by sifting through a large amount of numerical data generated by a Python-like code that they wrote in SageMath. The duo resided in Toronto, as required by the FUSRP; therefore, the majority of their exchanges with Professor Salmasian took place via videoconference. Professor Salmasian shares, “The remote supervision was initially a challenge, but the final result ended up being one of the best undergraduate research projects under my supervision.” In the end, he was incredibly impressed by how quickly Havi and Xiaomin were able to understand the research problem and convert it into a fast SageMath code to produce their data. Havi and Xiaomin are immensely grateful to the many professors and mentors who guided and motivated them in their research, particularly Prof. Salmasian.
Even after completing her collaborative work with Prof Salmasian, Havi continued studying these concepts throughout the 2019–2020 academic year. In fact, for her senior thesis, she proved several combinatorial formulas related to the interpolation Jack polynomials. Now, both Havi and Xiaomin have completed their undergraduate studies and will soon begin PhDs in leading American universities. Havi, a recent graduate from Harvey Mudd College in California, will enter a PhD program in pure mathematics at the University of Michigan. She plans to take courses to solidify her mathematical background, work in a TA position, and eventually study representation theory. On his side, Xiaomin, graduated from the University of Illinois Urbana-Champaign and will join the Harvard John A. Paulson School of Engineering and Applied Sciences.
Finally, Havi wishes to share the following with future students who are pursuing similar goals to her own: “Find what you like and pursue it. Don't worry if you don't like the same things as others, there are so many ways to participate, engage and contribute to Mathematics!”
Read more:
- Havi and Xiaomin’s final report from the FUSRP program is on Prof. Salmasian’s website, under ‘My CV, in the Undergraduate Students section.
- Havi Ellers' thesis
- Xiaomin’s recent paper: Webster Sequences, Apportionment Problems, and Just-In-Time Sequencing
