LECTURERS 2025

CELSIUS LECTURE

Two and a Half Millennia of Irrationality in Mathematics

The discovery of irrational numbers - especially the fact that √2 is not rational - is often attributed to the Pythagorean philosopher Hippasus. According to legend, this revelation so disturbed his fellow Pythagoreans that they drowned him in a lake. In this talk, we will explore the long (often unsuccessful) history of our attempts to understand irrationality, with the goal of explaining how mathematicians really think about these questions. Our journey will span from ancient Greece to the ancien régime, from 17th-century Basel to the present day.

Here you can read an article about the lecture.

Professor Francesco Calegari

Frank Calegari was born in Australia in 1975 where he attended the University of Melbourne. Frank was a graduate student of Ken Ribet at Berkeley. After a postdoctoral position at Harvard, Frank was a professor at Northwestern University until he moved to the University of Chicago in 2015 where he has been ever since. Frank was an American Institute of Mathematics five year fellow, a Sloan fellow, and was elected as a fellow of the American Mathematical Society in 2013. In 2022, Frank gave a plenary address at the (virtual) International Congress of Mathematicians.

Frank has played the piano for many years, and studied at the University of Melbourne under a student of Alfred Brendel. He has appeared live with Zubin Mehta and the Israeli Philharmonic, although, fortunately for everyone involved, as a choir boy and not as a pianist.

Symposia Lecture: Diophantine Tales

Reading a copy of the book “Arithmetica” by Diophantus of Alexandria, next to the paragraph where Diophantus discusses how to express a square number as a sum of two squares of factions, Pierre de Fermat added a now famous note: This is possible for squares, but not for cubes or higher powers. It took a further 300 years until a proof of this fact was completed.

In this talk, we will explore the stories of various equations of similar kind, and explore what is known about numbers that can be written as sums of squares, cubes, or higher powers. Many of these equations have stories that go back for centuries, and trying to understand them has led to deep insights connecting number theory with algebra, geometry and analysis. I will explain some of the heuristics behind these equations, what is known and what is still unknown.

Senior Lecturer Julia Brandes

Born in 1986 in the German city of Göttingen, Julia Brandes studied Mathematics in Göttingen and Stuttgart, before completing her PhD in Bristol under the supervision of Trevor Wooley, FRS, in 2014. After this followed postdoctoral appointments in Göttingen, Gothenburg and Waterloo (Canada), as well as a Viterbi postdoctoral position at MSRI in Berkeley (California). Since 2018, she has worked as an Associate Senior Lecturer and now Senior Lecturer at the University of Gothenburg and Chalmers University of Technology.

Symposia Lecture: How heat distribution in networks leads to new formulas for certain important values in number theory

In 1734, Euler rose to prominence by discovering a remarkable formula for certain seemingly simple sums, which correspond to special values of the Riemann zeta function. This function is still today a central tool in the study of prime numbers, and the distribution of its zeros is arguably the most important unsolved problem in all of mathematics.

In this talk, I will introduce a novel approach to zeta functions, leading to new expressions for Euler’s sums. Additionally, this perspective offers a reinterpretation of formulas for the circumference, area, and volumes of circles and spheres known since antiquity.

Professor Anders Karlsson

A.K. was born outside Stockholm in 1972. After completing teknisk fysik at KTH in 1994 receiving the Wallquists studiemedalj, he began studies in mathematics at Yale University which led to a doctoral degree awarded in 2000. Since then he worked as a mathematician in Switzerland, Sweden, and the USA, currently holding professorships in Uppsala and in Geneva. Among his awards are an Alfred P. Sloan Foundation fellowship in 1999 for the Ph.D. thesis, the Wallenberg Prize 2008 (Svenska matematiker-samfundet), Edlund Prize 2015 (KVA) and Gårding Prize 2017 (Kungl. fysiografiska sällskapet i Lund).