Tomer Moshe Schlank (; born 1982) is an Israeli

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and a professor at

The University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park neighborhood on Chicago's South Side, near the shore of Lake Michigan about fr ...

. Previously, he was a professor at

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...

. He primarily works in

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which Map (mathematics), maps can come with homotopy, homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipli ...

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. In 2022 he won the

Erdős prize The Anna and Lajos Erdős Prize in Mathematics is a prize given by the Israel Mathematical Union to an Israeli mathematician (in any field of mathematics and computer science), "with preference to candidates up to the age of 40." The prize was e ...

in mathematics and in 2023 he was awarded a

European Research Council The European Research Council (ERC) is a public body for funding of scientific and technological research conducted within the European Union (EU). Established by the European Commission in 2007, the ERC is composed of an independent Scientific ...

consolidator grant. He is an editor for the

Israel Journal of Mathematics '' Israel Journal of Mathematics'' is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem ( Magnes Press). History Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section ...

Biography

Schlank was born on July 29, 1982, in

Jerusalem, Israel Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ...

. He graduated with a bachelor's degree from

Tel Aviv University Tel Aviv University (TAU) is a Public university, public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv, the university is the center of teaching and ...

in 2001 and a master's degree from Tel Aviv University in 2008. He received his PhD from

in January, 2013, working under the supervision of

Ehud de Shalit Ehud de Shalit (; born 16 March 1955) is an Israeli number theorist and professor at the Hebrew University of Jerusalem. Biography Ehud de Shalit was born in Rehovot. His father was Amos de-Shalit. He completed his B.Sc. at the Hebrew Univers ...

. His education was also influenced by the close proximity of

David Kazhdan David Kazhdan (), born Dmitry Aleksandrovich Kazhdan (), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 MacArthur Fellow. Biography Kazhdan was born on 20 June 1946 in Moscow, USSR. His father ...

and Emmanuel Dror Farjoun. After completing his PhD, Schlank was hired as a Simons postdoctoral fellow at

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

. Afterwards he moved back to the Hebrew University in Jerusalem. Schlank is the great-grandson of the scientist Maria Pogonowska.

Research

Schlank is primarily known for his work on

chromatic homotopy theory In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theory, complex-oriented cohomology theories from the "chromatic" point of view, which is based on Daniel Quillen, Quillen's ...

. Together with Robert Burklund, Jeremy Hahn, and Ishan Levy, he disproved the telescope conjecture for all heights greater than 1 and for all primes. This was the last outstanding conjecture among

Ravenel's conjectures In mathematics, the Ravenel conjectures are a set of mathematical conjectures in the field of stable homotopy theory posed by Douglas Ravenel at the end of a paper published in 1984. It was earlier circulated in preprint. The problems involved have ...

. The disproof made use of his work on ambidexterity of the T(n)-local category and cyclotomic extensions of the T(n)-local sphere with Ben-Moshe, Carmeli, and Yanovski. With Barthel, Stapleton, and Weinstein, he calculated the homotopy groups of the rationalization of the K(n)-local sphere. With Burklund and Yuan, Schlank proved the "chromatic nullstellensatz", a version of

Hilbert's nullstellensatz In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental relationship between geometry and algebra. This relationship is the basis of algebraic ge ...

for the T(n)-local category in which Morava E-theories play the role of algebraically closed fields. This work resolved the Ausoni—Rognes

redshift conjecture In mathematics, more specifically in chromatic homotopy theory, the redshift conjecture states, roughly, that algebraic K-theory K(R) has chromatic level one higher than that of a complex-oriented ring spectrum ''R''. It was formulated by John Rogne ...

for

E_\infty

-ring spectra and also produced

E_\infty

-orientations of Morava E-theory. Schlank's early work was a synthesis of homotopy theory and number theory. With Harpaz, he developed homotopy obstructions to the existence of rational points on smooth varieties over number fields and related these homotopy obstructions to the

Manin obstruction In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety ''X'' over a global field, which measures the failure of the Hasse principle for ''X''. If the value of the obstru ...

. He wrote his thesis, titled "Applications of homotopy theory to the study of obstructions to existence of rational points", on this topic. Schlank is known for the breadth of his work and for bringing together seemingly unrelated concepts from different fields to solve problems. In mathematics, he has published papers in algebraic geometry, algebraic topology, category theory, combinatorics, dynamical systems, geometric topology, number theory, and representation theory.

References

{{reflist Living people 1982 births Academics from Jerusalem Israeli mathematicians Hebrew University of Jerusalem alumni