Alejandro Vélez-Santiago

Associate Professor of Mathematics
University of Puerto Rico – Mayagüez (UPRM)


Alejandro Vélez-Santiago was born in San Juan, Puerto Rico, and is the third son of a family of six siblings. His life story is one full of challenges, but also of hope and miracles. He was born with two major conditions: autism and chronic asthma. Alejandro liked math and music since he was a kid, and his parents put him in violin classes at the age of 10 years. From there, Alejandro excelled in music, particularly in violin performance, and began to play violin with the Puerto Rico Symphony Orchestra when he was in 11th grade in high school. During that period Alejandro also experienced a great miracle: when he was 16 years old the Lord healed him from both his autism, and his condition of chronic asthma. Alejandro was a product of homeschooling, which he considers to be a special part of his life. Since he was so advanced in violin performance, he first wanted to pursue his career as a violinist, but after following the advice of his parents, he also completed a bachelor’s degree in Mathematics (2004) at the University of Puerto Rico – Río Piedras (UPRRP), and then completed his Ph.D. in Mathematics (2010) at the same institution. After two postdoctoral positions (2010-2011 at Iowa State University and 2013-2016 at the University of California Riverside), he was hired by the University of Puerto Rico – Mayagüez (UPRM), where he is currently an Associate Professor of Mathematics. Alejandro is very thankful to many who have influenced his life, especially to his parents and family for their love, sacrifice, and teachings. But among all, he is very thankful to the Lord Jesus Christ for healing him, loving him, and being with him during all the steps in his life.

Alejandro’s research lies in the combination of Analysis, Partial Differential Equations (PDEs), Measure Theory, Potential Theory, Operator Theory, and Fractal Geometry (among others). His primary research consists of the solvability and regularity theory of various boundary value problems over non-smooth regions, which at times include domains with fractal boundaries and rough-type domains. Alejandro has also investigated models of quasi-linear-type boundary value problems exhibiting a nonstandard growth structure, which is a consequence of the presence of variable exponent function spaces and PDEs. These emerging topics have been influential in a recent line of Alejandro’s research, and currently he holds a research grant from the Puerto Rico Science, Technology, and Research Trust (PR Trust), focusing on the solvability and regularity properties for such models of nonstandard growth structure over non-smooth and irregular regions. Alejandro loves to involve students (at both the undergraduate and graduate level) into his research projects. He has conducted undergraduate research with multiple undergraduate students and has mentored three graduate students who did their master’s thesis under his mentorship. Alejandro loves to help his graduate students as much as possible with gaining quality research experiences in order to increase their opportunities of success in the future after graduation. This is why he has published (or submitted) an original research paper with each of his graduate students and strives to publish a research article with every graduate student he works with. He has also been able to publish research papers with his undergraduate students.  

Outside of his university work, Alejandro is also a member of the group in charge of preparing and training students from all the schools in Puerto Rico for the Mathematical Olympiads (OMPR). He uses his research areas of expertise to create original problems for the training and examinations of students. These training and exams are used in order to select the teams that will represent Puerto Rico in the international competitions of Mathematics.

Alejandro advises students to work hard and in a responsible manner, never giving up. During his studies, he encountered many challenges and things that he did not know, but he worked hard and gave the extra effort to cover those gaps and do his very best in everything. He tells students, “Giving full efforts usually tends to give good results.” Above all, the main advice Alejandro gives is “love the Lord and keep His commandments, for in Him is where life has true meaning and purpose.”

“I am humbly honored to be selected as part of this year’s group of contributors of the Lathisms calendar. It is a privilege to be part of this community, and always remember the roots of our lives. I consider this month as a special occasion in which we can inspire and influence many individuals, especially Latinxs in our community to be successful, and to build an environment of respect, friendship, and integrity. Our testimony speaks louder than words.”