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Thomas H. Willwacher | |
---|---|

Born | |

Nationality | German |

Alma mater | ETH Zurich |

Awards | EMS Prize (2016) |

Scientific career | |

Fields | Mathematical physics |

Institutions | ETH Zurich |

Doctoral advisor | Giovanni Felder |

**Thomas Hans Willwacher** (born 12 April 1983) is a German mathematician and mathematical physicist working as a Professor at the Institute of Mathematics, ETH Zurich.^{ [1] }

**Germans** are a Germanic ethnic group native to Central Europe, who share a common German ancestry, culture and history. German is the shared mother tongue of a substantial majority of ethnic Germans.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

**ETH Zurich** is a science, technology, engineering and mathematics university in the city of Zürich, Switzerland. Like its sister institution EPFL, it is an integral part of the Swiss Federal Institutes of Technology Domain that is directly subordinate to Switzerland's Federal Department of Economic Affairs, Education and Research. The school was founded by the Swiss Federal Government in 1854 with the stated mission to educate engineers and scientists, serve as a national center of excellence in science and technology and provide a hub for interaction between the scientific community and industry.

Willwacher completed his PhD at ETH Zurich in 2009 with a thesis on "Cyclic Formality", under the supervision of Giovanni Felder , Alberto Cattaneo , and Anton Alekseev.^{ [2] } He was later a Junior member of the Harvard Society of Fellows. In July 2016 Willwacher was awarded a prize from the European Mathematical Society for "his striking and important research in a variety of mathematical fields: homotopical algebra, geometry, topology and mathematical physics, including deep results related to Kontsevich's formality theorem and the relation between Kontsevich's graph complex and the Grothendieck-Teichmüller Lie algebra".^{ [3] }^{ [4] }

**Anton Yurevich Alekseev** is a Russian mathematician.

The **Society of Fellows** is a group of scholars selected at the beginning of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intellectual growth. Junior Fellows are appointed by Senior Fellows based upon previous academic accomplishments and receive generous financial support for three years while they conduct independent research at Harvard University in any discipline, without being required to meet formal degree requirements or to be graded in any way. The only stipulation is that they remain in residence in Cambridge, Massachusetts, for the duration of their fellowship. Membership in the society is for life.

The **European Mathematical Society** (**EMS**) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current president is Pavel Exner, Scientific Director of the Doppler Institute for Mathematical Physics and Applied Mathematics in Prague.

Notable results of Willwacher include the proof of Maxim Kontsevich's cyclic formality conjecture and the proof that the Grothendieck–Teichmüller Lie algebra is isomorphic to the degree zero cohomology of Kontsevich's graph complex.

**Maxim Lvovich Kontsevich** is a Russian and French mathematician. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014.

In mathematics, the **Grothendieck–Teichmüller group***GT* is a group closely related to the absolute Galois group of the rational numbers. It was introduced by Vladimir Drinfeld (1990) and named after Alexander Grothendieck and Oswald Teichmüller, based on Grothendieck's suggestion in his Esquisse d'un Programme to study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of Teichmüller groupoids *T*_{g,n}, the fundamental groupoids of moduli stacks of genus *g* curves with *n* points removed. There are several minor variations of the group: a discrete version, a pro-*l* version, a *k*-pro-unipotent version, and a profinite version; the first three versions were defined by Drinfeld, and the version most often used is the profinite version.

In mathematics, a **Lie algebra** is a vector space together with a non-associative operation called the **Lie bracket**, an alternating bilinear map , satisfying the Jacobi identity.

**Alexander Grothendieck** was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century.

**Paul Julius Oswald Teichmüller** was a German mathematician who made contributions to complex analysis. He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfaces. Teichmüller spaces are named after him.

**Jean-Pierre Serre** is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954 and the inaugural Abel Prize in 2003.

**Richard Ewen Borcherds** is a British-American mathematician currently working in quantum field theory. He is known for his work in lattices, number theory, group theory, and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998.

**Pierre René, Viscount Deligne** is a Belgian mathematician. He is known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.

**Bass–Serre theory** is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated applications of the operations of free product with amalgamation and HNN extension, via the notion of the **fundamental group of a graph of groups.** Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory.

In the mathematical theory of knots, the **Kontsevich invariant**, also known as the **Kontsevich integral** of an oriented framed link, is a universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients. It was defined by Maxim Kontsevich.

**"Esquisse d'un Programme"** is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be of major interest in several branches of advanced mathematics. Grothendieck's vision provides inspiration today for several developments in mathematics such as the extension and generalization of Galois theory, which is currently being extended based on his original proposal.

**Karen Vogtmann** is an American mathematician working primarily in the area of geometric group theory. She is known for having introduced, in a 1986 paper with Marc Culler, an object now known as the Culler–Vogtmann Outer space. The Outer space is a free group analog of the Teichmüller space of a Riemann surface and is particularly useful in the study of the group of outer automorphisms of the free group on *n* generators, Out(*F*_{n}). Vogtmann is a Professor of Mathematics at Cornell University and The University of Warwick.

**Artur Avila Cordeiro de Melo** is a Brazilian mathematician working primarily on dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, being the first Latin American to win such an award. He has been a researcher at both the IMPA and the CNRS. Since September 2018 he is a professor at the University of Zurich.

**Luc Illusie** is a French mathematician, specializing in algebraic geometry. His most important work concerns the theory of the cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic geometry. In 2012, he was awarded the Émile Picard Medal of the French Academy of Sciences.

In mathematics, the **Duflo isomorphism** is an isomorphism between the center of the universal enveloping algebra of a finite-dimensional Lie algebra and the invariants of its symmetric algebra. It was introduced by Michel Duflo (1977).

**Leila Schneps** is an American mathematician, living in France, employed by Centre national de la recherche scientifique, and based at the *Institut de Mathématiques de Jussieu* of Pierre and Marie Curie University, France, where she specializes in number theory. In addition to academic publication, she has edited several text books on aspects of mathematics, written a popular book and articles on the use and abuse of mathematics in criminal proceedings, and, under the pseudonym Catherine Shaw, written a series of mathematically themed murder mysteries.

**Dmitry Feichtner-Kozlov** is a Russian-German mathematician.

**Ralph Martin Kaufmann** is a German mathematician working in the United States.

- ↑ "Prof. Dr. Thomas Willwacher".
*ETH Zurich*. ETH Zurich . Retrieved 25 July 2016. - ↑ Thomas Willwacher at the Mathematics Genealogy Project
- ↑ "7 ECM Berlin: Twelve prizes awarded". European Mathematical Society. 18 July 2016. Retrieved 31 August 2016.
- ↑ "7ECM — Laureates".
*7th European Congress of Mathematics*. European Mathematical Society. July 2016. Retrieved 31 August 2016.

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