## Gerd Faltings in den Orden pour le mérite aufgenommen

Gerd Faltings, Emeritus Direktor des Max-Planck-Instituts für Mathematik in Bonn, wurde zum Mitglied des Orden pour le mérite gewählt, wie am 11.9.2024 durch das Bundespresseamt bekannt gegeben wurde. Dem Orden gehören somit 34 deutsche und 37 ausländische Mitglieder, darunter 17 Nobelpreisträgerinnen und -träger, an. Zu Mitgliedern des Ordens zählten mit Friedrich Hirzebruch und Yuri Manin bereits zwei weitere Direktoren des Max-Planck-Instituts für Mathematik.

Die Zuwahl in den Orden Pour le mérite zählt zu den höchsten Ehrungen, die Wissenschaftlerinnen und Wissenschaftlern, Künstlerinnen und Künstlern in Deutschland zuteilwerden kann. Die Künstler- und Gelehrtenvereinigung wurde 1842 von Preußenkönig Friedrich Wilhelm IV. gegründet und 1952 von Bundespräsident Theodor Heuss wiederbelebt. Erster Kanzler des Ordens war der Naturforscher Alexander von Humboldt.

Der Orden Pour le mérite steht unter dem Protektorat des Bundespräsidenten. Finanziert und organisatorisch betreut wird er von der Staatsministerin für Kultur und Medien.

**Gerd Faltings** wurde in Gelsenkirchen Buer als Sohn eines Diplomphysikers und einer Diplomchemikerin geboren. In seiner Schulzeit nahm er zweimal am Bundeswettbewerb Mathematik des Stifterverbandes teil und wurde als Bundessieger in die Studienstiftung des deutschen Volkes aufgenommen. Nach dem Abitur studierte er Mathematik und Physik an der Universität Münster. 1978/79 war er zu Gast an der Harvard Universität in Cambridge, Massachusetts. Wieder zurück in Münster wurde er 1979 Assistent von Professor Nastold und habilitierte sich 1981. Als Professor in Wuppertal hatte er große Erfolge und wechselte Anfang 1985 als full professor an die Princeton University in New Jersey, USA.

Zu seinen ersten Auszeichnungen zählten der Danny Heinemann Preis der Akademie in Göttingen 1984 und 1986 in Berkeley die Fields Medaille, eine Auszeichnung, welche die International Mathematical Union nur alle vier Jahre auf ihrem Kongress an junge Mathematiker*innen unter 40 Jahren verleiht. Als seine Töchter älter wurden, kehrte er nach Deutschland zurück und war von 1994 bis zu seiner Emeritierung 2023 wissenschaftliches Mitglied der Max-Planck-Gesellschaft am Max-Planck-Institut für Mathematik in Bonn.

Mathematisch begann er seine Forschung auf dem Gebiet der kommutativen Algebra, der Spezialität seines Lehrers Nastold. Auch vermittelte Nastold den Kontakt zu Professor L. Szpiro in Paris, welcher Ideen zur Mordell Vermutung hatte. Faltings fand dies sehr interessant und arbeitete darüber in der Hoffnung, irgendein nützliches Teilresultat zu erzielen. Zu seiner Überraschung konnte er 1983 die Vermutung in seinem Artikel Endlichkeitssätze für abelsche Varietäten über Zahlkörpern (Faltings‘ Satz) beweisen und wurde über Nacht zum Star. In der Folge bearbeitete er Kompaktifizierungen von Modulräumen und p-adische Hodge-Theorie. Beide Gebiete spielten bei der Mordell-Vermutung eine wichtige Rolle und wurden zunächst mit adhoc-Konstruktionen behandelt, welche er dann durch eine systematischere Theorie ersetzte. Als nächstes spülte ihm das Schicksal eine Arbeit von P. Vojta über diophantische Approximation vor die Füße, welche er stark verallgemeinern konnte. Schließlich hörte er am IAS eine Vorlesung von E. Witten. Die Vorlesung enthielt interessante Aussagen zu Modulräumen von Bündeln, und auf diesem Gebiet konnte er eine ganze Reihe von mathematischen Resultaten erzielen.

Gerd Faltings ist Mitglied der Akademien in Düsseldorf, Göttingen, Berlin und Halle, in der European Academy, in der Royal Society (London) und in der National Academy of Science (Washington). In Deutschland erhielt er 1996 den Leibniz-Preis, 2008 den von Staudt-Preis, 2010 den Heinz Gumin Preis und 2017 die Georg-Cantor-Medaille. Internationale Preise waren 2014 der King Faisal International Preis und 2015 der Shaw Prize.

## Geordie Williamson receives the Max Planck-Humboldt Research Award 2024

Artificial intelligence and computer science are driving developments in many areas of society – including in scientific research. This has prompted the Max Planck Society and the Alexander von Humboldt Foundation to honour outstanding achievements in the use of algorithms in mathematics, microscopy and climate research in 2024: The Max Planck-Humboldt Research Award, endowed with 1.5 million euros, goes to Geordie Williamson, who was Advanced Researcher at the Max Planck Institute for Mathematics from 2011-2016, and is now Professor at the University of Sydney. Williamson uses artificial intelligence (AI) for his fundamental work in mathematics.

Scientists today use artificial intelligence in many areas, especially in the natural sciences, for tasks such as analysing data or images. In theoretical mathematics, on the other hand, AI has barely been used thus far. Now Geordie Williamson is aiming to change that. In his previous work he has already used artificial neural networks, which can guide mathematical intuition by drawing attention to previously unrecognised relationships in a large number of mathematical objects. Artificial intelligence can also help to generate examples or counterexamples that prove or disprove mathematical assumptions. Although artificial neural networks can recognise patterns in large data sets very efficiently and effectively, they know nothing about mathematics. It therefore remains the task of mathematicians to filter out the sensible proposals from AI, to interpret them and, in the case of new assumptions about mathematical relationships, to prove or disprove them. Geordie Williamson wants to optimise the possibilities of using AI in theoretical mathematics in the collaboration made possible by the Max Planck-Humboldt Research Award. To this end, he will work closely with researchers from the University of Bonn and the Max Planck Institute for Mathematics in Bonn, where he will also spend two periods of several months each.

**Connecting the countable with geometry**

Geordie Williamson's previous research work was characterised, among other things, by the fact that he brought together different fields such as combinatorics and geometry. In simple terms, combinatorics can be understood as the branch of mathematics that is dedicated to everything that can be counted; it includes subjects such as graph theory and discrete mathematics. Geometry is about objects in spaces, i.e. straight lines, surfaces, and solids, just like in school maths. Both sub-areas come together in a simple example when the intersection points of a curve and a surface are to be counted. Geordie Williamson has now opened up ways of solving combinatorics problems with geometric tools, for which purpose he first had to develop a kind of common mathematical language for the two fields so that combinatorial problems could be worked on in geometry, but geometry could also be translated into combinatorics. With this approach, Geordie Williamson has proved or disproved various assumptions that mathematicians have been working on intensively, but to no avail, for a long time.

For example, Williamson in collaboration with Ben Elias from the University of Oregon provided a general proof of an important conjecture in mathematics relating to Kazhdan-Lusztig polynomials. The work of David Kazhdan and George Lusztig provided precise recipes for building up certain mathematical objects out of constituent pieces. Imagine a recipe that contains a list of ingredients and instructions on what to do with them, but the recipe does not specify the quantities. Kazhdan and Lusztig hypothesised that there are polynomials in mathematics for such cases, from which the quantities for the recipe can be determined. Polynomials are formulae that are familiar to us in their simple form from the binomial formulae we study in school. Geordie Williamson has proven this assumption, for which evidence had previously been sought in vain for a long time. His methods, borrowed from geometry, also make it much easier to solve the polynomials that provide the unknown data and to analyse them in greater depth.

**Solving knot theory problems with the help of AI**

As part of the collaboration with researchers from the University of Bonn and the Max Planck Institute for Mathematics, all possible as a result of the award, Williamson will tackle various mathematical problems with the help of artificial intelligence. Amongst the problems that they will tackle is a problem in knot theory. In simple terms, this can be explained by the fact that it is often impossible to recognise whether knotted structures, such as in a string, are actually knotted. What this means is: does the knot remain intact when you pull on the ends of the cord or does it unravel? One aim of the project is to identify these cases in a simple way so that these uninteresting cases can be quickly filtered out and the researchers can focus on the real knots. AI is set to provide support here and assistance in gaining new mathematical insights. Geordie Williamson studied at the University of Sydney and received his doctorate from the University of Freiburg in 2008. He then conducted research at Oxford University until 2011 and headed a research group at the Max Planck Institute for Mathematics until 2016. After other shorter stints at the Hausdorff Centre for Mathematics in Bonn and at the Institute for Advanced Study, Princeton he was appointed Professor at the University of Sydney in 2017. He serves as the founding Director of the Sydney Mathematical Research Institute. Geordie Williamson is a Fellow of the British Royal Society and the Australian Academy of Science.

**About the award**

The Max Planck Society and the Alexander von Humboldt Foundation present the Max Planck-Humboldt Research Award, along with 1.5 million euros in prize money, to a researcher from abroad. 80,000 euros in personal prize money is also awarded. The focus here is on personalities whose work is characterised by outstanding potential for the future. The prize is intended to attract particularly innovative scientists working abroad to spend a fixed period of time at a German higher education institution or research facility. The Federal Ministry of Education and Research provides the funding for the award. The focus of the award alternates each year between natural and engineering sciences, life sciences, humanities and social sciences.

## Maryna Viazovska External Member of the Max Planck Institute for Mathematics

Maryna Viazovska, full professor and Chair of Number Theory at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne, has joined the Max Planck Institute for Mathematics as external scientific member. She was PhD student of Don Zagier from 2008-2012 and obtained her doctoral degree from the University of Bonn. Since then, she has returned to the institute regularly as a visitor and speaker. We are happy that Maryna will now play an even more active role in the research community and the development of the Max Planck Institute for Mathematics.

**Maryna Viazovska** was born in Kiev in Ukraine in 1984. She obtained her Bachelor degree in Mathematics in 2005 from Kiev National University and a Master's degree in 2007 from the University of Kaiserslautern. She was a doctoral student of Don Zagier in the MPIM graduate school from 2008-2012, working on modular forms. In 2013 she received her PhD from the University of Bonn. After a postdoctoral position at the Humboldt University in Berlin she joined the faculty of the École Polytechnique Fédérale Lausanne, where she became full professor in 2018. Maryna Viazovska has received a number of distinctions for her work: In 2016 the Salem Prize, in 2017 the Clay Research Award and the SASTRA Ramanujan Prize. She was awarded a 2018 New Horizons Prize in Mathematics and was an invited speaker at the 2018 International Congress of Mathematicians. In 2019 she received the Ruth Lyttle Satter Prize in Mathematics and the Fermat Prize, in 2020 the EMS Prize and the National Latsis Prize awarded by the Latsis Foundation. She was elected to the Academia Europaea in 2021 and appointed Senior Scholar at the Clay Mathematics Institute in July 2022. In 2022, she was awarded the Fields Medal.

Video portrait of Maryna Viazovska

**Photo credit: **EPFL/Fred Merz

## Max Planck Institute for Mathematics in Bonn Mourns Death of Yuri Manin

**Emeritus director of institute passed away at age 85**

*Bonn, January 8, 2023.* The Max Planck Institute for Mathematics in Bonn mourns the death of Professor Yuri Ivanovich Manin. The eminent mathematician passed away on Saturday, January 7, at the age of 85. Yuri Manin was a scientific member and director of the Max Planck Institute for Mathematics from 1992 to 2005, after which he remained an extremely active emeritus director. His work largely influenced the development of modern mathematics. With Yuri Manin, mathematics has lost one of his truly great personalities. He was a wonderful human being and a renowned researcher whose contributions have shaped the entire field. Our institute will always remain his institute, too.

**Yuri Ivanovich Manin** was born on February 16, 1937 in Simferopol, Crimea, in the Soviet Union. He studied physics and mathematics at Lomonosov Moscow State University where he graduated in 1958. In 1960 he received his doctorate and in 1963 his habilitation from the Steklov Institute of Mathematics in Moscow, where he was Principal Researcher until 1992. After a year on the faculty of MIT in 1992-1993, he became a director at the Max Planck Institute for Mathematics in 1993.

Yuri Manin's many important contributions to mathematics cover a wide spectrum of topics in algebraic geometry, number theory, and mathematical physics. He is an author of over 300 research papers and 11 books. For his manifold achievements he received a number of awards and prizes, among others, the Lenin Prize 1967, the Brouwer Medal 1987, the Frederic Esser Nemmers Prize 1994, the Rolf Schock Prize in Mathematics 1999, the King Faisal International Prize in Mathematics 2002, the Georg Cantor Medal 2002, the Order pour le Mérite for Science and Art, Germany, 2007, the Great Cross of Merit with Star, Germany, 2008, the János Bolyai International Mathematical Prize 2010. He was a member of nine Academies of Sciences and an Honorary Member of the London Mathematical Society. He held honorary degrees at the Sorbonne, and the Universities in Oslo and Warwick.

## Pius XI Medal Awarded to Peter Scholze

Peter Scholze, director at the Max Planck Institute for Mathematics and professor at the University of Bonn, was awarded the Pius XI Gold Medal 2020 by the Pontifical Academy of Sciences. The medal is awarded every two years to a young scientist under the age of 45, chosen for his or her exceptional promise. After Luis A. Caffarelli (1988), Laure Saint-Raymond (2004), and Cédric Villani (2014), Peter Scholze is only the fourth mathematician to receive this honor.

**Peter Scholze** was born in 1987. Studies of Mathematics at the University of Bonn, Master 2010, PhD 2012. Clay Research Fellow 2011-2016. Chancellor's Professor, UC Berkeley, Fall 2014. Hausdorff Chair, University of Bonn, since October 2012. Scientific Member and Director, MPI for Mathematics, since July 2018. Awards (selection): 2014 Clay Research Award, 2015 Ostrowski Prize, 2016 Leibniz Prize of the DFG, 2018 Fields Medal, 2019 Great Cross of Merit of Germany, 2022 Foreign Member of the Royal Society.

**The Pontifical Academy of Sciences** is the only supranational academy of sciences in the world. Founded in Rome in 1603 as the first exclusively scientific academy in the world with the name Linceorum Academia, to which Galileo Galilei was appointed member in 1610, it was reestablished in 1847 by Pius IX with the name Pontificia Accademia dei Nuovi Lincei. It was moved to its current headquarters in the Vatican Gardens in 1922, and given its current name and statutes by Pius XI in 1936. Its mission is to honor pure science wherever it may be found, ensure its freedom, and encourage research for the progress of science. Its 80 Pontifical Academicians are appointed for life by the Holy Father following proposals by the academic body and chosen without any form of ethnic or religious discrimination from the most eminent scientists and scholars of the mathematical and experimental sciences of every country of the world.

(Source: The Pontifical Academy of Sciences, Photo credit: Barbara Frommann)

## Fields Medal awarded to Maryna Viazovska. Former doctoral student of the Max Planck Institute for Mathematics receives highest distinction in mathematics

**The Fields Medal is considered the Nobel Prize of mathematics. This year the International Mathematical Union chose to award it to Maryna Viazovska, who wrote her doctoral thesis at the Max Planck Institute for Mathematics with Don Zagier and received her PhD from the University of Bonn in 2013. The Ukranian mathematician is second woman to ever receive this prize.**

Maryna Viazovska is awarded the Fields Medal 2022 "for the proof that the E8 lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis." In doing so, she resolved a question that had stumped mathematicians for more than four centuries: how to pack spheres – such as oranges stacked in a pyramid – as close together as possible. It was in 1611 that Johannes Kepler posited, without proof, that the best solution for packing spheres in a three-dimensional space was in the shape of a pyramid. That hypothesis was finally proved in 1998. With the third dimension resolved, it was time for mathematicians to move on to other dimensions. “Formulating the problem in the same way complicates matters because each dimension is different, and the optimal solution depends very much on the dimension,” says Viazovska. Why did she focus on 8 and 24 dimensions? “Because these are special dimensions, and the solutions are particularly elegant.” The way spheres are packed in these particular dimensions is remarkably symmetrical, and uses the E8 and Leech lattices, respectively. More than a decade ago Henry Cohn and Noam Elkies found that these lattice patterns were close to perfection – to one billionth of a percent – but were unable develop a proof. Viazovska’s brilliant work provided the missing ingredient, demonstrating that these lattices are the densest possible packing patterns in their respective dimensions.

But Viazovska wanted to prove it, suspecting that an auxiliary function existed that could provide the right answer and match the density of the E8 and Leech lattices. In her quest for the right function, she drew on other areas of mathematics – a fact that, according to experts, makes her proof particularly elegant and original. Fueled by creativity and intuition, Viazovska turned to the focus of her dissertation: modular forms, a type of mathematical function with a high level of symmetry. After two years of work, she came up with the right function for 8 dimensions.

**Maryna Viazovska** was born in Kiev in Ukraine in 1984. She obtained her Bachelor degree in Mathematics in 2005 from Kiev National University and a Master's degree in 2007 from the University of Kaiserslautern. She was a doctoral student of Don Zagier in the MPIM graduate school from 2008-2012, working on modular forms. In 2013 she received her PhD from the University of Bonn. After a postdoctoral position at the Humboldt University in Berlin she joined the faculty of the École Polytechnique Fédérale Lausanne, where she became full professor in 2018.

Video portrait of Maryna Viazovska

Official announcement of the Fields Medals 2022 by the International Mathematical Union

**Photo credit:**

Matteo Fieni

## Fields Medal awarded to Peter Scholze. New director at the Max Planck Institute for Mathematics receives highest distinction in Mathematics

**The Fields Medal is considered the Nobel Prize of mathematics, and this year the International Mathematical Union chose to award it to Peter Scholze. The professor at the University of Bonn’s Hausdorff Center for Mathematics and Director at the Max Planck Institute for Mathematics was presented with the award during the International Congress of Mathematicians in Rio de Janeiro. The 30-year-old is only the second German to ever receive this prize.**

“I am grateful for the extraordinary honour, bestowed upon me with the Fields Medal,” says Peter Scholze. The first German mathematician to be awarded the prize was Gerd Faltings in 1986, who is also a Director at the Max Planck Institute for Mathematics and a professor at the Hausdorff Centre for Mathematics. The Fields Medal is awarded every four years to recognize ‘outstanding mathematical achievement for existing work and for the promise of future achievement’. Recipients must be no more than 40 years of age. The other three fields medals of 2018 went to Caucher Birkar (Cambridge University), Alessio Figalli (ETH Zurich), and Akshay Venkatesh (Stanford University and IAS Princeton).

These type of age limits have never been an issue for Peter Scholze: Right after his doctorate in 2012 at the age of 24 he became the youngest full professor at a German university, taking over one of the prestigious Hausdorff Chairs of the Hausdorff Centre at the University of Bonn. Even at this young age, he was considered one of the most brilliant mathematicians in his field. Now, at 30 years of age, Peter Scholze can already look back on an outstanding career and numerous awards, including the Leibniz Prize from the German Research Foundation. “I am delighted that we were able to attract Peter Scholze to the Max Planck Institute for Mathematics, and that together with the University of Bonn we have been able to keep him in Germany,” says Martin Stratmann, President of the Max Planck Society.

**Groundbreaking methods at the intersection between number theory and geometry**

With the Fields Medal, the International Mathematical Union acknowledges Peter Scholze’s groundbreaking contributions to arithmetic geometry. Number theory and geometry come together in this field of mathematics, which means that the properties of integral numbers are explored using geometric methods. In the past, this approach has allowed for century old problems – such as Fermat’s Last Theorem – to be proven, which could not be solved with purely number theoretic methods. The field also provides for the basic principles of many modern encryption methods.

The objective of number theory is to answer questions about integral numbers, for example whether there is an infinite number of twin primes such as 3 and 5, 5 and 7, 11 and 13, etc. Or the question, how prime numbers are distributed along the number line. Geometry is dedicated to studying such objects as knots, planes, or higher-dimensional spaces. One important issue is the question, when two geometrical shapes are equivalent, that is when their essential geometric properties are the same. Mathematicians develop procedures for finding out, for example, whether two knots that initially appear to be different may still have been formed based on the same knotting rule. In arithmetic geometry, numbers are themselves understood as points in larger geometric spaces.

**Entirely new possibilities for number theorists**

Peter Scholze has discovered a new class of geometric structures, known as perfectoid spaces. These spaces are very large and complex, but they possess geometric properties that are useful for many problems. Several old and difficult problems of number theory could now be solved, with the help of perfectoid spaces.

“The award and Peter Scholze’s personal success are of great importance, also for the University of Bonn,” says Michael Hoch, Rector of the University of Bonn. “He will, without a doubt, continue to contribute greatly to shaping mathematical research in the future.” Peter Scholze is going to continue his research in Bonn: “The working conditions here in Bonn are excellent, and the international atmosphere is very inspiring,” says the researcher. In addition to his chair at the University’s Hausdorff Centre for Mathematics, he has only recently become Director of the Max Planck Institute for Mathematics. “The Max-Planck-Gesellschaft strives to provide the best resources available to support his research,” says Martin Stratmann. This means that Peter Scholze is able to fully devote himself to his next breakthroughs in mathematics.

A **press conference** with Peter Scholze is held at the Hausdorff Centre for Mathematics on Endenicher Allee 60 in Bonn, at 10:00 a.m. on Tuesday, 7 August 2018.

The **Max Planck Institute for Mathematics** in Bonn is one of 82 research institutes of the Max Planck Society. The Institute was founded in 1980, and has soon become one of the world’s most prestigious research institutes for mathematics. It is managed by Directors Don Zagier, Gerd Faltings, Werner Ballmann, Peter Teichner and the newest addition to the Board of Directors, Peter Scholze. With only a small number of permanent research and administrative staff, the Institute’s guest program attracts over 400 research mathematicians from around the globe every year. The Institute is home to around 100 long-term guest researchers at all times. Research at the Institute covers most areas of pure mathematics. The Max Planck Institute for Mathematics is one of the six Institutes of the Hausdorff Center of Mathematics.

**For further information about Peter Scholze, please visit:**

http://www.hcm.uni-bonn.de/scholze-background

**Media contact person:**

Christian Blohmann

Max Planck Institute for Mathematics, Bonn

Phone: +49-228-402302

Email: blohmann@mpim-bonn.mpg.de

**Photo credit:**

Volker Lannert / University of Bonn

## International Congress of Mathematicians 2018: Many Invited Speakers with Ties to MPIM

A number of mathematicians who have held positions, were long-term visitors, or PhD students at the Max Planck Institute for Mathematics are invited to present their work at the next International Congress of Mathematicians (ICM), which will take place on August 1-9, 2018 in Rio de Janeiro. Most notably, the newly appointed MPIM director **Peter Scholze** and **Geordie Williamson**, who has been Advanced Researcher at MPIM from 2011-2016, are both invited plenary speakers. Further invited speakers with ties to MPIM include:

- Yves André (09/1985-01/1986: 11/1986-07/1987; 09/1989-12/1990)
- Arthur Bartels (PhD 1999 with Peter Teichner)

- Alexander Belavin (02-03/2012; 02-03/2014)
- Men Chen (academic year 2011/12)
- Vyacheslav Futorny (academic year 2011/12)
- Christof Geiss (academic years 2010/11, 2017/18)
- June Huh (08-11/2013)
- Adrian Iovita (06/2015)
- Jochen Koenigsmann (02-06/2007; 11/2007-02/2008)
- Ulrich Kohlenbach (03-06/2007)
- Wojciech Kucharz (fall 2015/16)
- Martin Möller (Advanced Researcher 2007-2009, recurring visitor since 2010)
- Andrei Okounkov (07/2002)
- Rahul Pandharipande (07/2002)
- Georgios Pappas (07-08/1999; 06/2007)
- Dipendra Prasad (09-10/2007)
- Feliks Przytycki (07-08/1996)
- Sujatha Ramdorai (2003)
- Alan Reid (06/2010, 06/2015)
- Tadashi Tokieda (Hirzebruch lecture 2018)
- Bernardo Uribe (multiple visits 2003, 2004, 2006, 2008, 2015, 2016, 2018)
- Maryna Viazovska (PhD 2009-2012 with Don Zagier, 08-09/2016)
- Anna Wienhard (PhD 2004 with Werner Ballmann)

The **International Congress of Mathematicians** is the largest and the most important conference in mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize, the Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Being invited to talk at the ICM is considered to be one of the highest honors for a mathematician.

## New Horizons in Mathematics Prize awarded to Geordie Williamson

**Geordie Williamson**has received a New Horizons in Mathematics Prize jointly with Benjamin Elias for pioneering work in geometric representation theory, including the development of Hodge theory for Soergel bimodules and the proof of the Kazhdan-Lusztig conjectures for general Coxeter groups. Geordie had been advanced reseracher at the Max Planck Institute for Mathematics from 2011 until August 2016, when he moved to a position at the University of Sydney in his native country Australia.

## Pavel Mnev awarded 2016 André Lichnerowicz Prize in Poisson Geometry

Pavel Mnev, an Advanced Researcher at the Max Planck Institute for Mathematics from 2014-2016, has been awarded the 2016 André Lichnerowicz Prize in Poisson Geometry. The biennial award is given for outstanding work by young mathematicians in Poisson Geometry.

**Pavel Mnev** received his Ph.D. in 2008 from the Steklov Mathematical Institute of the Russian Academy of Sciences in St. Petersburg under the direction of the mathematical physicist Ludwig Faddeev. Mnev held a postdoctoral position at the University of Zurich, before coming to the Max Planck Institute for Mathematics in Bonn in 2014. This fall, he has moved to a faculty position at the University of Notre Dame. His research interests are in mathematical physics, in particular in the interactions of quantum field theory with topology, homological/homotopical algebra, and supergeometry.

**The André Lichnerowicz Prize in Poisson Geometry** was established in 2008. It is awarded for notable contributions to Poisson geometry, every two years at the "International Conference on Poisson Geometry in Mathematics and Physics", to researchers who completed their doctorates at most eight years before the year of the Conference. The prize is named in memory of André Lichnerowicz (1915-1998) whose work was fundamental in establishing Poisson Geometry as a branch of mathematics.

## Interview with PhD student Danylo Radchenko on solving the sphere packing problem in dimension 24

Danylo Radchenko, PhD student at the Max Planck Institute for Mathematics and the Bonn International Graduate School for Mathematics, on the famous sphere packing problem, his contribution to the proof in dimension 24, and on being a PhD student in Bonn.

**You are co-author of a paper about the sphere packaging problem in dimension 24. Let’s start from the scratch: What’s the sphere packing problem about?**

This problem goes way back to 1611 when Johannes Kepler discussed the question how to stack cannon balls most efficiently. He found the answer, but he couldn’t prove it. This is why it’s called the “Kepler conjecture”. Since then, physicists have been working with his solution. But for mathematicians it’s not enough to know the answer, we also have to find a way to deduce logically why it is indeed correct. The solution is actually pretty simple. Almost everyone will find it intuitively if you give them a bunch of balls and some time. But the mathematical proof of this is highly complex. Even for a normal three dimensional room, the proof was found only in 1998 by Thomas Hales.

**And how did you get from there to dimension 24?**

We did not start working on this problem with any particular dimension in mind. However, it was known for some time, from the work of Cohn and Elkies that the sphere packing problem in dimensions 8 and 24 is rather special, and the solution could follow in these dimensions from the existence of certain mysterious functions. Therefore, we were always focused on these special dimensions and the properties of those mysterious functions.

**How did you solve this problem?**

We have been working on it for several years already. There were phases when we were more focused on it and phases when we were less involved, but we never stopped. It was a group of three people: Maryna Viazovska (a former MPIM student), Andrii Bondarenko,and myself. We did a lot of computations over the time, but somehow didn’t make the progress we wanted. Then, last year, Maryna had the brilliant idea of not constructing the functions we actually needed, but slightly different ones using the theory of modular forms. She discovered that there is a direct relation between these two different fields. She made the real breakthrough. At first, I was skeptic and thought this couldn’t be true. But then I realized quickly that this was going to be the answer. Still, it took us more than a year of hard work until the solution was complete in dimension eight. I helped Maryna on some minor details and with some of the computer calculations, but the solution in this case is rightfully hers.

**What was the next step?**

Several days after Maryna had submitted her paper on the sphere packing problem in dimension eight, she called me and asked if we could now join forces with Henry Cohn, Abhinav Kumar, and Stephen D. Miller, who were also working on this problem, to solve the problem in dimension 24, which is more challenging for technical reasons. Of course I was happy to do so. We then completed the paper in one week of very intense work. At peak moments our team exchanged about ten emails every hour. We were in quite a hurry, because now that the solution in dimension eight was out there, others could have done it for dimension 24 as well.

**Is this only of theoretical interest or are there some aspects of the sphere packaging problem that are related to practical issues?**

It is for example related to coding theory and combinatorics. Improvements made for the sphere packing problem also stimulate new developments in those fields. An object closely related to the solution in the 24-dimensional case, the so-called binary Golay code, was used by the NASA in the Voyager program to check if messages sent through long distances arrive correctly despite the high background noise in space.

In the end, I think that the most important result of our work is different: it is not the solution of the sphere packing problem itself, but the newly discovered connection to modular forms. This could lead to completely new developments. That’s very exciting, and we are currently trying to better understand this connection.

**Is the sphere packaging problem part of your PhD project, too?**

No. In my PhD, I’m working on the topic of functional equations for polylogarithms. That was a bit stressful because when the intense phase of working on the sphere packaging problem started, I was about to submit my PhD thesis. Of course, then I thought, the PhD could wait. But now I’ve submitted it, finally, and I will defend it soon.

**You’re originally from the Ukraine. How did you come to Bonn?**

Maryna invited me as a guest to the Max Planck Institute when she was a PhD student here herself and I was still a bachelor student. Back then I also met Don Zagier for the first time, who’s now my advisor. I was really impressed by the atmosphere here and wanted to return. It’s actually hard to find words for how nice it is. There just happens so much in mathematics in Bonn. You have really great colleagues to talk to, there are a lot of talks and events, and researchers from all over the world come to the Hausdorff Center for guest programs. That’s very inspiring. The mood here in Bonn definitely contributed significantly to my work.

*The interview was conducted by Astrid Slizewski.*

## Shaw Prize in Mathematical Sciences Awarded to Gerd Faltings

At a press conference on June 1, 2015 in Hong Kong, the Shaw Prize Foundation announced that this year's Shaw Prize in Mathematical Sciences is awarded in equal shares to Gerd Faltings and Henryk Iwaniec for their introduction and development of fundamental tools in number theory, allowing them as well as others to resolve some longstanding classical problems. The prize consists of a monetary award of one million US dollars.

**From the prize justification of the Shaw Foundation:** A polynomial equation of degree n in one variable with coefficients which are rational numbers has just n complex numbers as solutions. Such an equation has a symmetry group, its Galois group, that describes how these complex solutions are related to each other.

A polynomial equation in two variables with rational coefficients has infinitely many complex solutions, forming an algebraic curve. In most cases (that is, when the curve has genus 2 or more) only finitely many of these solutions are pairs of rational numbers. This well-known conjecture of Mordell had defied resolution for sixty years before Faltings proved it. His unexpected proof provided fundamental new tools in Arakelov and arithmetic geometry, as well as a proof of another fundamental finiteness theorem — the Shaferavich and Tate Conjecture — concerning polynomial equations in many variables. Later, developing a quite different method of Vojta, Faltings established a far-reaching higher dimensional finiteness theorem for rational solutions to systems of equations on Abelian Varieties (the Lang Conjectures). In order to study rational solutions of polynomial equations by geometry, one needs arithmetic versions of the tools of complex geometry. One such tool is Hodge theory. Faltings’ foundational contributions to Hodge theory over the p-adic numbers, as well as his introduction of other related novel and powerful techniques, are at the core of some of the recent advances connecting Galois groups (from polynomial equations in one or more variables) and the modern theory of automorphic forms (a vast generalization of the theory of periodic functions). The recent striking work of Peter Scholze concerning Galois representations is a good example of the power of these techniques.

**Prof. Dr. Gerd Faltings**, born in 1954, studied mathematics and physics at the University of Münster where he received his Diploma and Ph.D. in 1978. After visiting Harvard University from 1978-1979, he was Assistant at the University of Münster from 1979-1982, completing his Habilitation in 1981. Following Professorships at the University of Wuppertal from 1982-1984 and Princeton University from 1985-1994, he became director of the Max Planck Institute for Mathematics in Bonn in 1995. He has already received numerous awards for his work: the Fields Medal in 1986, a Guggenheim Fellowship in 1988, the Gottfried Wilhelm Leibniz Prize in 1996, the Karl Georg Christian von Staudt Prize in 2008, the Heinz Gumin Prize in 2010, and the King Faisal International Prize for Science in 2014.

**The Shaw Prize** honors individuals who have achieved significant breakthroughs in academic and scientific research or applications and whose work has resulted in a positive and profound impact on mankind. The prize is awarded annually in the three fields: Astronomy, Life Science and Medicine, and Mathematical Sciences,. This is the twelfth year that the Prize has been awarded and the presentation ceremony is scheduled for Thursday, 24 September 2015.

(Photo credit: MFO / Gert-Martin Greuel)

## Humboldt research award winner Kari Vilonen coming to MPIM

Prof. Kari Vilonen has received one of the prestigeous Humboldt Research Awards of 2014 for his important contributions to geometric representation theory. He will use the award for a research stay at the Max Planck Institute for Mathematics in Bonn. His host is MPIM researcher Geordie Williamson.

**Kari Vilonen** received his PhD in 1983 from Brown University. After postdoctoral positions at MIT and MSRI from 1983-1986, he was Assistant Professor at Harvard University from 1986-1989. From 1989-2000 he held a faculty position at Brandeis University and was visiting professor at MPIM in 1998 and Harvard University in 1999. Since 2000 he is on the faculty at Northwestern University and since 2010 at Helsinki University. Kari Vilonen was awarded a Guggenheim Fellowship in 1997 and an AMS Centennial Fellowship in 1991. He was editor of Annals of Mathematics from 2003-2009 and is member of the Finnish Academy of Science and Letters.

The **Humboldt research award** is granted "in recognition of a researcher's entire achievements to date to academics whose fundamental discoveries, new theories, or insights have had a significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future." Award winners are invited to spend a period of up to one year cooperating on a long-term research project with specialist colleagues at a research institution in Germany. The award is valued at 60,000 EUR.

## Azubipreis 2014 der Max-Planck-Gesellschaft für MPIM-Auszubildenden

Die Max-Planck-Gesellschaft hat Stefan Willems vom Bonner Max-Planck-Institut für Mathematik mit dem Azubipreis 2014 ausgezeichnet. Stefan Willems hat seine dreijährige Ausbildung zum Fachinformatiker Fachrichtung Systemintegration im Sommer 2013 abgeschlossen und ist derzeit weiter in der IT-Abteilung des MPIM beschäftigt.

Die seit 2007 existierende Auszeichnung, die mit 750 Euro dotiert ist, ist eine Anerkennung für herausragende berufliche und schulische Leistungen und besonderes soziales Engagement während der Ausbildung; es wird außerdem ein Augenmerk auf die persönliche Entwicklung gelegt. Bis zu 20 dieser Preise vergibt das Auswahlgremium, dem vier Ausbilderinnen und Ausbilder und je ein Mitglied des Gesamtbetriebsrats sowie der Gesamt-Jugend- und Auszubildendenvertretung angehören.

## Preis für Moritz Rodenhausen: jüngster Doktorand der Max-Planck-Gesellschaft

Im Alter von nur 25 Jahren und 3 Monaten hat Moritz Rodenhausen seine Dissertation „Centralisers of polynomially growing automorphisms of free groups“ abgeschlossen. Dafür wurde ihm auf der Jahreshauptversammlung der Max-Planck-Gesellschaft im Juni dieses Jahres der Dieter-Rampacher-Preis 2013 für den jüngsten Doktoranden der gesamten Max-Planck-Gesellschaft verliehen. Der Preis ist mit 2400 Euro dotiert und wurde vom Präsidenten der MPG, Prof. Dr. Martin Stratmann, überreicht. Die Doktorarbeit wurde von Prof. Dr. Carl-Friedrich Bödigheimer von der Universität Bonn betreut und abschließend mit „sehr gut“ bewertet.

**Der Dieter-Rampacher-Preis:** Um einen Anreiz für eine frühzeitige Promotion zu geben, zeichnet die Max-Planck-Gesellschaft alljährlich ihren jüngsten Doktoranden - meist im Alter zwischen 25 und 27 Jahren - für seinen hervorragenden Promotionsabschluss mit dem Dieter-Rampacher-Preis aus. Der Preis wurde 1985 von Hermann Rampacher, Förderndes Mitglied der Max-Planck-Gesellschaft, gestiftet; er dient dem Andenken an seinen 1945 im Alter von zwanzig Jahren gefallenen Bruder Dieter Rampacher, Student der Physik an der TH Stuttgart. Seit 2011 hat Carsten A. Rampacher, der Sohn des Stifters und ebenfalls Förderndes Mitglied der Max-Planck-Gesellschaft, die Finanzierung des Preises übernommen.

(Photo credit: Denise Vernillo/MPG)

## Gerd Faltings awarded King Faisal Prize

Gerd Faltings, Director at the Max Planck Institute for Mathematics in Bonn and Professor at the University of Bonn, was awarded the 2014 King Faisal International Prize for Science for his groundbreaking contributions to algebraic geometry and number theory. This was announced by the president of the King Faisal Foundation, Prince Khaled Al-Faisal, on 14 January 2014.

The King Faisal International Prize is awarded to “scientists and scholars whose research results in significant advances in specific areas that benefit humanity.” It consists of a certificate, hand-written in Arabic calligraphy summarizing the laureate’s work, a commemorative 24 carat gold medal, uniquely cast for each prize, and a cash award of 750,000 Saudi riyal (150,000 Euro).

Prof. Gerd Faltings is the second director of the Max Planck Institute for Mathematics to receive the prize, after Prof. Yuri Manin in 2002.

The prize committee stated that Prof. Faltings “work combines ingenuity, vision and technical power. He has introduced stunning new tools and techniques which are now constantly used in modern mathematics. His deep insights into the p-adic cohomology of algebraic varieties have been crucial to modern developments in number theory. His work on moduli spaces of abelian varieties has had great influence on arithmetic algebraic geometry. He has introduced new geometric ideas and techniques in the theory of Diophantine approximation, leading to his proof of Lang’s conjecture on rational points of abelian varieties and to a far-reaching generalization of the subspace theorem. Professor Faltings has also made important contributions to the theory of vector bundles on algebraic curves with his proof of the Verlinde formula.”

(Photo credit: MFO / Gert-Martin Greuel)

## Werner Nahm erhält Max-Planck-Medaille 2013

Werner Nahm, externes wissenschafliches Mitglied des Max-Planck-Instituts für Mathematik, wird die **Max-Planck-Medaille 2013**, die höchste Auszeichnung für theoretische Physik der Deutschen Physikalischen Gesellschaft, verliehen. Werner Nahm hat auf dem Gebiet der Quantenfeldtheorie herausragende Leistungen vollbracht. Grundlegend waren seine Arbeiten zur Klassifikation der Super-Lie-Algebra, die Klassifikation der magnetischen Monopol-Lösungen in Yang-Mills-Theorien, und die in diesem Zusammenhang aufgestellten, nach ihm benannten „Nahm-Gleichungen“. Nahm hat Pionierarbeit bei der Entwicklung der so genannten „heterotischen Stringtheorie“ geleistet. Diese Theorie bildet heute die Basis für die Mehrzahl der gegenwärtig diskutierten phänomenologischen Anwendungen der Superstringtheorie. Die Auszeichnung besteht aus einer Goldmedaille, die im März 2013 während der DPG-Jahrestagung in Dresden überreicht wird.

**Werner Nahm** wurde 1972 in Bonn promoviert. Von dort wechselte er ans CERN, arbeitete am Max-Planck-Institut für Mathematik in Bonn und ging 1986 als Associate Professor an die University of California (UC Davis). 1989 wurde er auf einen Lehrstuhl nach Bonn berufen, folgte aber 2002 einem Ruf als „Senior Professor“ an das Dublin Institute for Advanced Studies. Nahm zeichnet sich durch ein breites wissenschaftliches Interesse aus, das von der Mitarbeit im Arbeitskreis Energie der DPG bis zur Linguistik und Altertumswissenschaft reicht.

## Max Planck Institute for Mathematics in Bonn Mourns Death of Friedrich Hirzebruch

**Founding director of institute passed away at age 84**

*Bonn, May 30, 2012.* The Max Planck Institute for Mathematics in Bonn mourns the death of Professor Dr. Friedrich Hirzebruch. As it became known on Tuesday, the eminent mathematician and citizen of Bonn passed away on Sunday, May 27 at the age of 84. Professor Hirzebuch is the founding director of the Max Planck Institute for Mathematics, which he headed from 1980 to 1995. His work largely influenced the development of modern mathematics. Through his personal efforts and achievements he contributed in an essential way to the reconstruction of mathematics research in Germany after World War II.

Friedrich Hirzebruch was born on October 17, 1927 in Hamm, Westphalia. From 1945 to 1950 he studied mathematics in Munster and Zurich. After two years in Princeton from 1952 to 1954 he was appointed as full Professor at the University of Bonn. His research interests were in the fields of topology and geometry.

For his manifold achievements Friedrich Hirzebruch received a number of awards and prizes. Among others, the Grand Merit Cross with Star of the Federal Republic of Germany, the Wolf Prize for Mathematics, the Seki Takakazu Prize, the Lomonossov Gold Medal, the Albert Einstein Medal, and the Georg Cantor Medal of the Deutsche Mathematikervereinigung. He held honorary doctorates from over 14 universities. He was member of a number of Academies of Science and of the Order pour le mérite.

"With Friedrich Hirzebruch, mathematics has lost one of his truly great personalites. He was a wonderful human being and an eminent researcher whose contributions have shaped the entire field", said Peter Teichner, managing director of the Max Planck Institut for Mathematics in Bonn. "Our institute, which he founded, will always remain his institute, too."

## Curtis McMullen with Humboldt Research Award at MPIM

The renowned mathematician Curtis McMullen from Harvard University is one of the recipients of the Humbold Research Award 2011. He will use the award to spend the Fall of 2011 as sabbatical at the Max Planck Institute for Mathematics in Bonn.

The award is given to researchers whose fundamental discoveries, new theories, or insights have had a significant impact on their own discipline and beyond and who are expected to continue producing cutting-edge academic achievements in future. It consitst of a cash prize of 60,000 euro. In addition, award winners are invited to conduct a research project of their own choosing in Germany in close collaboration with a specialist colleague.

Curtis McMullen is Professor for Mathematics at Harvard University. He works in the field of Riemann surfaces, complex dynamics, and hyperbolic geometry. His research has already earned him a number of prizes, among others the Fields Medal of 1998.

## Sieger im Bundeswettbewerb Mathematik ans MPIM eingeladen

Das Max-Planck-Institut für Mathematik lädt in diesem Jahr zum ersten Mal die Sieger im Bundeswettbewerb Mathematik zu einem Besuch nach Bonn ein. Direktor Gerd Faltings überreichte am 29.3.2011 die Einladungsurkunden im Rahmen der Siegerehrung in Berlin. Die Schülerinnen und Schüler wurden zuvor von Bundespräsident Wulff empfangen.

Mehr als 1.000 Jugendliche haben sich 2010 am Bundeswettbewerb Mathematik beteiligt. Nach zwei Hausaufgabenrunden und einer mündlichen Prüfung standen die Preisträger fest. Acht Schüler haben den Spitzenplatz zum ersten Mal erobert: Dominik Duda (Wiesbaden), Paul Görlach (Schleusingen), Fabian Henneke (Bremen), Kevin Höllring (Nürnberg), Achim Krause (Horb), Markus Penner (Berlin), Daniel Sanusi (Bremen) und Malte Leip (Varese, Italien). Sie wurden zu einem einmonatigen Aufenthalt am Max-Planck-Institut für Mathematik in Bonn eingeladen.

Etwa 500 Mathematikerinnen und Mathematiker kommen jedes Jahr aus der ganzen Welt zum Forschen an das MPIM nach Bonn. Wie alle Gäste, können die mathematischen Nachwuchstalente hier eigene Projekte verfolgen, die zahlreichen Vorträge besuchen, in Ruhe in der Institutsbibliothek lesen, mathematische Einfälle beim Institutstee diskutieren oder einfach nur ins Gespräch mit einer der vielen renommierten Forscherpersönlichkeiten kommen, die das MPIM jedes Jahr mit Leben füllen.

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