Université de Strasbourg

Lie Fu

Biographiy - Lie Fu

USIAS Fellow, Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS, France

Lie Fu, USIAS Fellow 2022Lie Fu obtained his PhD degree in mathematics in 2013 at Sorbonne University (France) under the supervision of Professor Claire Voisin. After spending one semester as member of the Institute for Advanced Study (Princeton, USA) in 2014, he returned to France to take up the position of associate professor (maître de conferences) at the Claude Bernard Lyon 1 University (2014-2019). From 2019-2021, he was a Radboud Excellence Fellow and remained at Radboud University (Netherlands), where he was assistant professor until 2022.

The research field of Lie Fu is algebraic geometry. Central objects of his research are Calabi-Yau manifolds and hyper-Kähler manifolds. Highlighting the use of the theory of motives, he studies the algebraic cycles on those varieties, as well as their other geometric and arithmetic properties.

During his Fellowship, Lie Fu will be welcomed by Professor Carlo Gasbarri at the Institute for Advanced Mathematical Research (IRMA).

Project - K-trivial varieties and K-equivalence: a motivic perspective

01/09/2022 – 31/08/2024

A fundamental invariant associated with a smooth algebraic variety is its canonical bundle. In broad terms, the aim of the project is to study how the canonical bundle affects various geometric, topological and arithmetic properties of the variety, and to investigate a series of deep conjectures around the idea that birationally isomorphic varieties with “equivalent” canonical bundles share many common features.

Within this context, naturally, the varieties with trivial/zero canonical bundle play a special role. These are the so-called Calabi-Yau manifolds, which form a class of geometric objects that are of central importance in mathematics and theoretical physics (string theory).

The intended approach via this project is to take the point of view of certain universal invariants in algebraic geometry, called motives, which govern concrete invariants related to algebraic cycles, such as cohomology, Hodge structures, K-theory, Chow groups, etc.

In technical terms, we are concerned with the so-called K-equivalence relation in the title of the project: two varieties are K-equivalent if there is a common birational model with regular morphisms to them such that the relative canonical divisors coincide. Our major goal is to relate the motive of K-equivalent varieties, especially the motive of birationally equivalent Calabi-Yau varieties.

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