# Mindeord: Johan P. Hansen

Johan P Hansen, Algebraic Geometer and Former Department Head at MATH, dies at 68

Niels Lauritzen has written the following memorial tribute to Johan P Hansen.

Johan was destined from an early age to take over his father's farm in Southwest Jutland, but an early aptitude and interest in mathematics made him pursue studies at first as an engineer at the Danish Technical University in Lyngby. After a semester, he resolutely changed his mind and showed up at Aarhus University knocking on Svend Bundgaard's door to talk mathematics and late admission. Bundgaard was impressed and Johan was admitted to the mathematics studies at Aarhus University in 1971.

In 1976-77, the American algebraic geometer William Fulton visited Aarhus. At that time, Johan was finishing his master's thesis ensuring his lasting legacy in mathematics by codiscovering with Fulton what has become known as the Fulton-Hansen connectedness theorem. It naturally found its way to the Annals of Mathematics (and later to Wikipedia). Johan went on to Brown University to get his PhD with Fulton in 1980. Fulton, learning of Johan's untimely death, writes *»I have fond memories of the beautiful mathematics that Johan did when we were together in Aarhus and Providence«*. In retrospect, this pointed to Johan's deep love for mathematics in a career later turning to more applied topics in algebraic geometry such as coding theory and cryptography, in particular advanced elliptic curve arithmetic and geometry used in quantum resistant cryptography.

After postdocs at Brown and Aarhus with a stint at *Institut Des Hautes Études Scientifiques* in Paris, Johan was hired as associate professor (lektor) at Aarhus, August, 1983. A position he kept until his death on January 22, 2020. He held numerous visiting positions and developed a love for French culture during his many visits to Luminy.

Johan P Hansen in MatLab, 2013. Photo: MATH.

On many levels, Johan was an exceptional colleague. I remember being warmly welcomed by him coming to Aarhus as a newly minted PhD many years ago. Originally from the Copenhagen area, I had to adjust to the Jutlandish mindset, but immediately felt at ease with Johan. We soon found out that we shared a deep passion for the teaching of mathematics. Teaching my first course on algebraic geometry, I often sought out Johan for advice. I distinctly remember his comment: *»Do it. It will challenge them and make them grow«* talking me into assigning a harder project to a group of students.

Before being hired by Aarhus in 1983, Johan spent half a year completing the pedagogical course for high school teachers (pædagogikum) at Hobro Gymnasium. He often said, with a smile on his face, that he was one of the few people at Aarhus formally trained to teach students, even though he had a profound dislike for unhinged pedagogy forced on the classroom. Johan was extremely popular as a teacher and advisor on all levels ranging from the bachelor studies to the PhD. In a year, Johan would typically advise ten bachelor projects and eight master's theses.

Johan was a team player with a remarkable sense of loyalty and responsibility towards the Department of Mathematics and Aarhus University in general. He acted as the department head for ten years from 2001 to 2011. This was a period with many challenges ranging from the introduction of the University Law of 2003, a major study reform in 2004 to the establishment of several larger research centers. One memorable contribution by Johan during this period was the introduction and implementation of the Mathematics Laboratory (MatLab) in 2004. Politically this was no small feat, since it required talking the other department heads into allocating more time to Calculus and breaking with the traditional one-way teaching of mathematics. To this day MatLab thrives and is used by more than a thousand students per year.

On the national scene, Johan was chairman of the Danish Mathematical Society from 2002 to 2006.

After retiring as department chair in 2011, Johan returned to teaching and research. Just a few years ago Johan's research interests turned to the newly discovered properties of the isogeny graph for (supersingular) elliptic curves in post-quantum cryptography. He pursued this deep and interesting topic until his death.

In teaching his legacy is firmly rooted in the first year course *Perspektiver* (especially his book *Tal og Polynomier*) and his graduate course *Elliptic Curves and Cryptography*. These courses consistently scored top evaluations and were extremely popular among students.

Johan will be deeply missed as a wonderful colleague, brilliant expositor and inspiring researcher.

*The eulogy can freely be shared or cited elsewhere provided that (1) you link back to this page and (2) the image is not reused.*