"Alexander is a bright superstar in modern algebraic geometry"

Alexander Efimov awarded the European Mathematical Society (EMS-Prize). This prestigious international award is awarded once every four years of ten outstanding young European mathematicians (up to 35 years) and is awarded during the European Mathematical Congress two years before the international congress of mathematicians (ICM).

It is ICM that awards Fields medals - an analogue of the Nobel Prize in mathematics. The Prize of the European Mathematical Society is considered the harbinger of the Fields medal: at one time it was received by 12 Fields laureates (among them Grigory Perelman, Stanislav Smirnov, Andrey Okunkov and Maxim Kontsevich).

Alexander Efimov is one of the most talented young Russian algebraic geometers. He defended his thesis in 2011 at the Mathematical Institute. Steklov RAS. The supervisor of his dissertation is Academician of the Russian Academy of Sciences Dmitry Orlov.

For ten years, a scientist received a series of outstanding results in algebraic and categorical geometry, in particular in the theory of homological mirror symmetry. Mirror symmetry was discovered by physicists in the 1990s in the form of duality between the superformal theories of fields when constructing the theory of models of elementary particles. The most famous Moscow and French mathematician, laureate of the Fields Prize, Maxim Kontsevich rethought this concept of theoretical physics as an incredibly deep mathematical duality, now known as a homological mirror symmetry.

In 2009, Alexander Efimov proved the hypothesis of homological mirror symmetry for Riman surfaces. Then, in 2011, together with Abuzaid, Aru, Orlov and the author of this note, he proved the variant of this hypothesis for open riman surfaces.

In 2017, Alexander Efimov was awarded the Golden Medal of the Russian Academy of Sciences with a prize for young scientists in Russia for the work cycle “Derivatives of categories and cyclic homologies”.

In my opinion, Alexander is a bright superstar in modern algebraic geometry, the achievements of which are comparable to the results of Mohammed Abusida, the New Horizons in Mathematics Prize, sympyed geometry.

"Already in the first courses he became interested in algebraic geometry and homological algebra"

Alexander Efimov, cand. physical. Sciences, a researcher at the International Laboratory of Mirror Symmetry and Automorphic Forms of the NIU-SBE, told our newspaper about himself.

I have been fond of mathematics since childhood: I participated in the Olympiads, read books in different fields of science, including the brochures of the MCNMO Publishing House. He began to seriously engage in mathematics from about the eighth grade, when he entered the 57th school and made a choice between mathematics and chess in favor of mathematics (he stopped at the CCM level in chess). Studying at school, he won in various Olympiads, including all -Russian, all -Russian and all -Chinese.

He graduated from the school in 2005, entered the MHCAM of Moscow State University and at an independent Moscow University. In the first courses of the university, he became interested in algebraic geometry and homological algebra. Pretty quickly became interested in various interesting tasks associated with triangulated categories and equivalents between them, and tried to solve them. The first significant result was in the fourth year: he proved a homological mirror symmetry for the genus of the genus 3, using the ideas of proof of P. Zaidel for the Krivoy 2. Then he began to deal with different issues related to homological mirror symmetry, Donaldson’s invariants - Thomas Kolchanov with the potential, cluster algebras and various tasks related to Differential-graded categories and their invariants.

He proved several hypotheses of Klekvich and Soybelmann, including the structure of the claw algebra of the Hall, as well as about the homotopical limb of the derivatives of the derivatives of the coherent beams. He also recently refuted the two hypotheses of the end-led, associated with generalized versions of the degeneration of the spectral sequence from the Khoja claws to the Martials of de Ram for differential-degraded categories.

I work at the Mathematical Institute. V. A. Steklov RAS since 2010, as well as at the Faculty of Mathematical Faculty of Higher School, in the laboratory of algebraic geometry and its applications (2010–2016), laboratory of mirror symmetry and automatic forms (from 2017 to the present). Also in 2013-2014 he worked as Newton Research Flow at the University of Varvik (Great Britain).

At the moment, I am dealing with various issues related to the K-theori version invented by me for a certain class of “large” triangulated categories (the naive K-theory for them is zero). This new concept of K-theoria, in particular, turned out to be useful in the context unexpected for me: it was used by D. Clausen and P. Scholce to determine the K-theoriya of Aditic spaces.