Summer Al Hamdani

316 Van Vleck Hall,

480 Lincoln Dr,

Madison, WI 53705

I am a mathematics Ph.D. candidate at University of Wisconsin-Madison, studying harmonic analysis under the tutelage of Betsy Stovall. My doctoral minor is in statistics. I am incredibly fortunate for my graduate studies and research to be partially supported through the Analysis and PDEs Research Training Grant.

As of late, I spend most of my time thinking about problems at the intersection of harmonic analysis and geometry—specifically how things like underlying curvature and incidence relations will affect multilinear integral operators.

I am a co-organizer for Gender Minorities in Math at Wisconsin (GmMaW), which is the department’s graduate portion of our local AWM chapter; I’m also president of our chapter. I co-founded and previously co-organized for the Graduate Analysis and PDEs Seminar (GAPS). Prospective students¹ with interests in either GmMaW’s activities or research in analysis are welcome to reach out to me.

Before starting the doctoral program, I completed my undergraduate studies in Mathematics and Biomedical Physics along with a Master’s in Mathematics at California State University, Fresno (go Bulldogs!). My Master’s thesis studied the zero distribution of Chebyshev polynomials of the second kind with binomial-type coefficients. Afterwards, I briefly earned a living as a data analyst and mathematical statistician.

This website is sparingly updated—sorry! The best way to keep up with the happenings of my enthralling life is by email: alhamdani at math dot wisc dot edu. I usually try to respond within 24 ± 12 hours on business days.

I receive many emails from prospective students. I am, regretfully, not an appropriate person to ask about the activities of the other research caucuses. I strongly implore you to contact my colleagues who work in the field you are interested in, or (even better!) are advised by faculty whose research interests align with your own. ↩

news

Mar 30, 2026	There have been a few significant changes in my life since I last updated this site: I passed the differential topology qualifying exam, successfully defended my thesis prospectus, completed my doctoral minor, and am now (as of January) a dissertator. Where did the time go?
May 9, 2024	I received the Early Excellence in Teaching award for spreading the joys of calculus!
Feb 26, 2024	Allison Byars and I started a new graduate student seminar called GAPS, which held its first meeting on February 26th. Check out the UW-Math Wiki for further details.
Oct 6, 2023	I passed the analysis qualifying exam in August! I also received a “Superior” ranking for my teaching in the spring 2023 semester. Look at me go.
Jan 22, 2023	I updated this webpage! How exciting.

selected publications

Zeros of a binomial combination of Chebyshev polynomials

Summer Al Hamdani, and Khang Tran

International Journal of Number Theory, 2022

Abs arXiv HTML

For 0 < α< 1, we study the zeros of the sequence of polynomials { P_m(z) }_m=0^∞generated by the reciprocal of (1 − t)^α(1 − 2zt + t^2), expanded as a power series in t. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of P_m(z) outside the interval (−1, 1) is bounded by a constant independent of m.
Zero distribution of binomial combinations of Chebyshev polynomials of the second kind

Summer Al Hamdani

Master’s thesis, California State University, Fresno, May 2021

Abs PDF

For α∈\mathbbR such that 0 < α≤1, we can construct a sequence of real polynomials { P_m(z) }_m=0^∞that is generated by 1/(1-t)^α(1-2zt+t^2) = \sum_m=0^∞P_m(z)t^m . The sequence { P_m(z) }_m=0^∞is a binomial combination of the well-known Chebyshev polynomials of the second kind, which have all real zeros on the interval (−1, 1). We prove that there exists a constant C (independent of m) such that the number of zeros of P_m(z) outside of the interval (−1, 1) is at most C for all m ∈\mathbbN.