Cruz Castillo

Hello! My name is Cruz Castillo, and I am a fourth year PhD student at UIUC in Number Theory. I am also a Sloan Scholar and a NSF GRFP recipient. Modular forms, Maass forms, and L-functions are all of great interest to me. Scott Ahlgren is my advisor.

Research

Here is a list of my recent research projects. For more information such as slides and posters please click the research tab above.

• Surfaces Associated to Zeros of Automorphic L-functions (with Debmalya Basak & Alexandru Zaharescu), paper data companion
video
• An explicit version of Linik's Theorem.(with Michaela Cully-Hugill, Jewel Mahajan, Nathan Ng , and Chi Hoi (Kyle) Yip )
• Sign changes of the error term in the Piltz divisor problem. (with Siegfred Baluyot ) arxiv journal video
  International Mathematics Research Notices, 2024;, rnae189

I am also a co-organizer of the Graduate Number Theory Seminar.

Outreach

I really enjoy doing outreach programs. Fortunately, I have had the opportunity to present at two seminars whose audience is primarily undergraduate students. The first presentation was at Rose Hulman and the second at Lake Forest College. For these, I created two interactive websites using SageMath. I suggest clicking on the outreach tab above to see one of the websites.

Teaching

I was a TA for Calculus 1 from Fall 2021 to Spring 2022. I was ranked excellent by students all semesters.