HSE and Steklov Mathematical Institute Mathematician Alexander Efimov Awarded EMS Prize

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Alexander Efimov, a research fellow at the International Laboratory for Mirror Symmetry and Automorphic Forms of HSE University, has been awarded the European Mathematical Society’s prestigious Prize.

The Prize is awarded once every four years to ten outstanding European mathematicians under the age of 35 and presented to the recipients at the European Mathematical Congress two years before the International Congress of Mathematicians (ICM).

It is the ICM that awards Fields Medals, which are the equivalent to the Nobel Prize in the field of mathematics. The EMS Prize is considered the forerunner of the Fields medal. Twelve Fields laureates (including Grigori Perelman, Stanislav Smirnov, Andrei Okounkov, Maxim Kontsevich) were recipients of the EMS Prize in the early years of their careers.

Alexander Efimov is one of Russia’s most talented young algebraic geometers. He defended his thesis in 2011 at the Steklov Mathematical Institute of the Russian Academy of Sciences. His thesis advisor was RAS mathematician Dmitry Orlov.

Over the past ten years, Alexander Efimov has conducted breakthrough research in algebraic and categorical geometry, and the theory of homological mirror symmetry in particular. Mirror symmetry was discovered by physicists in the 1990s in the form of duality between superconformal field theories when constructing the theory of elementary particle models. The famous Russian-French mathematician, Fields Prize laureate Maxim Kontsevich, rethought this concept of theoretical physics as an incredibly deep mathematical duality, now known as homological mirror symmetry.

In 2009, Alexander Efimov proved the hypothesis of homological mirror symmetry for Riemann surfaces. Then, in 2011, together with Mohammed Abouzaid, Denis Auroux, Ludmil Katzarkov, and Dmitry Orlov, he proved a variant of this hypothesis for open Riemann surfaces.

In 2017, Alexander Efimov was awarded the Gold Medal of the Russian Academy of Sciences with a prize for young scientists of Russia for his series of works, ‘Derived Categories and Cyclic Homology’. Ludmil Katzarkov, Academic Supervisor of HSE’s International Laboratory for Mirror Symmetry and Automorphic Forms, called the scientist ‘a brilliant superstar in modern algebraic geometry’, comparing his achievements to those of Mohammed Abouzaid in symplectic geometry (for which Abouzaid received the New Horizons in Mathematics Prize).

Ludmil Katzarkov, Professor of mathematics at the University of Miami (USA) and Academic Supervisor of the International Laboratory for Mirror Symmetry and Automorphic Forms at HSE University

Alexander found a counterexample to King's hypothesis on toric Fano varieties in toric geometry. This is an amazing achievement. Many researchers, including Borisov and Hua, expected the opposite. Alexander also proved Kontsevich’s hypothesis on the homotopy finiteness of derived categories of coherent sheaves on finite type schemes. This result was actively used in the works of Toen, Vezzosi, Pantev and Vaquie. Alexander plays an important role in our laboratory. We are all ready to learn from him, to collaborate with him, and to promote the take-off of a new leader in modern Russian mathematics.

Alexander Efimov, Research Fellow, International Laboratory for Mirror Symmetry and Automorphic Forms, HSE University

I was pleasantly surprised when I learned that I received the award. The president of the European Mathematical Society informed me about it two months before the laureates were officially announced. The award ceremony will be held next year during the European Mathematical Congress, which is scheduled for June 20-26, 2021.

HSE University congratulates Alexander Efimov on receiving the prestigious EMS Prize and looks forward to future complex mathematical solutions from him!