## MATH+ Distinguished Fellow Bruno Klingler (HU Berlin)

**We are delighted that Bruno Klingler, Einstein-Professor for Algebra at the Department of Mathematics of Humboldt-Universität zu Berlin, has been awarded the MATH+ Distinguished Fellowship. The MATH+ Distinguished Fellowship Program recognizes outstanding contributions to the mathematical sciences and supports the work of world-leading mathematicians in Berlin. Congratulations!**

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Bruno Klingler is a French mathematician specializing in arithmetic and algebraic geometry. He is one of the most renowned mathematicians in arithmetic geometry worldwide. His academic career began in France, where he studied mathematics, physics, and philosophy, ultimately earning a double master’s degree in mathematics and philosophy. Klingler then focused on mathematics and described his attraction to the field: “The most important part of doing math is the beauty—it’s difficult to describe but the aesthetic feeling you get when you are inside a mathematical theory. Another decisive factor is the certainty that what you talk about is well-defined and correct.” Klingler earned his doctorate in discrete group theory under Yves Benoist at the University of Paris in 1997. In 2002, he was appointed Assistant Professor at Yale University, followed by a position at the University of Chicago in 2003, where he stayed for four years. Klingler considers his time at the University of Chicago a milestone in his career. Fascinated by the numerous high-level courses and the spirit of research fostered by world-famous mathematicians, he became familiar with other areas and shifted his research focus from discrete group theory to algebraic geometry.

In 2007, he returned to France as a full professor at Université Paris-Diderot, where he stayed for ten years. In 2017, he moved to Berlin as Einstein Professor of Algebra at Humboldt Universität zu Berlin. One of the highlights of his career was being an Invited Speakers at the International Congress of Mathematicians 2022 (ICM 2022) in the sections “Complex and Algebraic Geometry” and “Number Theory.“ Since 2022, he has served on the BMS committee of MATH+.

When asked about *MATH+ Distinguished Fellowship*, Bruno Klingler said, “This award is a sign of recognition and appreciation by the mathematical community in Berlin, which is a great pleasure for me. It shows that my work is of interest and that pure mathematicians will be supported. I will use the funding that comes with the award to support a postdoc and organize conferences in Berlin and elsewhere.”

Bruno Klingler’s research focuses on the topology of varieties in relation to their algebraic and arithmetic structures. In 2021, his project “Tame Geometry and Transcendence in Hodge Theory (TameHodge)” was awarded an ERC Advanced Grant, the most prestigious European research award, with over 1.8 million euros in funding. The goal of the project is to uncover links between Hodge theory and tame geometry and to address fundamental questions in Hodge theory using tools from mathematical logic. Hodge theory, developed around the 1970s, is crucial for understanding the geometry and arithmetic of complex algebraic varieties. It linearizes complex algebraic varieties into finite-dimensional complex vector spaces that encode the periods of differential forms on the variety. While Hodge theory simplifies the objects it studies, it involves transcendental operations. Two major conjectures—the Hodge conjecture and the Grothendieck period conjecture—suggest that this transcendence is limited. The work by Klingler and his collaborators has shown a significant connection between Hodge theory and tame geometry. Tame geometry, proposed by Grothendieck in the 1980s and developed by logicians as o-minimal geometry, studies structures with finite geometric complexity. The TameHodge project aims to establish that tame geometry is the natural framework for Hodge theory, with significant applications to the transcendence of periods, atypical intersections, and non-abelian Hodge theory.

In an interview with MATH+, Bruno Klinger elaborates on his recent work: “This tame geometry had a lot of success in the last 20 years, and my best results are in this area nowadays. In the coming years, I’m trying to develop various aspects—one which is related to arithmetic and another to theoretical physics.” Collaborating with physicists, he wants to explore how tame geometry could provide insights into complex, non-algebraic functions encountered in these fields. This interdisciplinary approach indicates the broader applicability of tame geometry beyond fundamental mathematics.

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For more information about his research, please visit Bruno Klingler’s ** personal homepage**.

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**MATH+ Distinguished Fellowship Program**

The *MATH+ Distinguished Fellowship* is bestowed upon individuals in recognition of outstanding contributions to the mathematical sciences in general. The program’s goal is to support the work of world-leading mathematicians who hold permanent professorships at one of the MATH+ partner institutions, i.e., FU, HU, TU Berlin, WIAS, or ZIB. MATH+ provides *Distinguished Fellows* with a fellowship allowance for fostering innovative ideas and research activities, initiating exciting and vibrant research collaborations, and expanding the international research network and activities of the *Fellows*. There are currently __five MATH+ Distinguished Fellows__: __Gavril Farkas__, __Peter K. Friz__, __Michael Joswig__, __Bruno Klingler__, and __Alexander Mielke__.

For international colleagues, MATH+ offers funding as__ (Distinguished) Visiting Scholars____.__

**LINKS**

- Bruno Klingler at Humboldt-Universität zu Berlin
- The MATH+ Distinguished Fellowship Program
- Bruno Klingler at Einstein Foundation Berlin