News

Carlo Pagano of Concordia University, currently a visitor at Max Planck Institute for Mathematics in Bonn, has received the 2025 André Aisenstadt Prize. This celebrates the achievements of young Canadians in both pure and applied mathematics. 

In joint work with Peter Koymans, he settled Stevenhagen's conjecture on the negative Pell equation, which is a very strong result in arithmetic statistics. Their breakthrough was covered extensively in the Quanta magazine and can be found here.

But Peter and Carlo have not stopped there. They switched gears and are now tackling problems concerning decidability, in particular related to the (non-)existence of an algorithm that determines, under certain assumptions, whether a Diophantine equation has a solution. You can read more about this in another Quanta magazine article about their work.

Carlo’s strong ties to MPIM include his two year postdoctoral stay, followed by multiple subsequent visits.  

Doug Ulmer, currently a visitor at the Max Planck Institute for Mathematics in Bonn, was selected as member of the new class of 2025 fellows of the American Mathematical Society. The new group of fellows includes also the former MPIM guests Wiesława Nizioł and Florian Herzig. The prestigious Fellows of the AMS program recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.

SCAM E-MAILS GOING AROUND FROM VARIOUS E-MAIL ADDRESSES

It has come to our attention that some people have been contacted by various e-mail addresses about their stay during MPIM conferences (even if they are not planning to attend any conferences). Please be aware that this is a scam!

Here are some of the addresses we know have sent scam e-mails:
operations@gtravelservice.com
reservations@gtravelexpert.com
bookings@g-travelexperts.com
dse_NA4@docusign.net
support@g-travelexperts.com
rooms@g-travelexperts.com
booking@gtravelmanagement.com
housing@conferencesmanagement.org
Accommodations@conferencecare.org

Please DO NOT give out any personal information to these or other companies. Please ignore any emails and calls from them or any other travel agent.

MPIM is not affiliated in any way with this or any other travel agent. We will only ever contact you via official MPIM-e-mail-addresses that end in "@mpim-bonn.mpg.de".

We take data privacy and security with the utmost importance and your contact information is not forwarded to a third party. The agencies DO NOT have access to your information through us.
They are accessing public information and searching contact details through search engines like Google.

If you receive a phone call or an email from them or have been contacted by any other travel agent, please forward the information immediately to us. Your kind understanding and support is much appreciated.

What to do if you have been contacted by a scam company about booking hotels?

1. If you have given out your credit card information to an external company or anyone who called you about booking hotel rooms for the conference, call your credit card company immediately, alert them to the
scam, and deny the charge.

2. Change your online passwords and PINs to prevent fraudsters from doing any further damage.

3. Continue to monitor your credit card to look for fraudulent charges. Request further information from your credit card company regarding closing your account or issuing a new card.

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.

Proposed by Robert Langlands in the 1960s, the eponymous program is one of the largest projects in modern mathematic and it consists of different branches. Over the years, the MPIM has gained a reputation as one of the hubs for the Langlands program. We are proud that MPIM Director Dennis Gaitsgory led a nine-person team of mathematicians that settles the geometric Langlands conjecture. The proof is the culmination of a research program that spanned three decades. You can read the full story in a recent article in Quantamagazine.

Link to the Quantamagazine article

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

Ana Caraiani, who holds the Hausdorff Chair at the University of Bonn, is newly appointed Max Planck Fellow at the Max Planck Institute for Mathematics. The Max Planck Fellowship is a prestigeous honor bestowed on outstanding university professors by the Max Planck Society for a limited term of 5 years. The fellows receive funds to build up a small research group at the host institute. The goal is to promote cooperation between university faculty and Max Planck Society researchers.

Ana Caraiani works at the interface between the Langlands program and arithmetic geometry. In recent years, she has co-authored many of her papers with Peter Scholze who is very happy about his new colleague in Bonn: "With Ana Caraiani, a world-leading scientist in arithmetic geometry comes to Bonn. We have already worked together a lot in the past, on questions in the Langlands program and especially on the cohomology of Shimura varieties. I'm very much looking forward to continuing this work, and especially to organizing seminars and other events together," says Peter Scholze.

Ana Caraiani was born in Bucharest in 1985. She won a silver medal and two gold medals for the Rumanian Team in the International Math Olympiad. After graduating high school in 2003, she studied at Princeton University, where she graduated summa cum laude in 2007, with an undergraduate thesis on Galois representations supervised by Andrew Wiles. She did her graduate studies at Harvard University under the supervision of Wiles' student Richard Taylor, earning her Ph.D. in 2012 with a dissertation concerning local-global compatibility in the Langlands correspondence. After spending a year at the University of Chicago, she returned to Princeton and the Institute for Advanced Study as a postdoc. In 2016, she moved to the Hausdorff Center for Mathematics as a Bonn Junior Fellow. She moved to Imperial College London in 2017 as a Royal Society University Research Fellow and Senior Lecturer. In 2019, she became a Royal Society University Research Fellow and Reader at Imperial College London. In 2021, Caraiani became a full professor at Imperial College London before moving to her position as Hausdorff Chair in Bonn in the fall of 2022. In 2018, she was one of the winners of the Whitehead Prize of the London Mathematical Society. In 2020, she was elected as a Fellow of the American Mathematical Society and was one of the 2020 winners of the EMS Prize. Recently, she was awarded one of the New Horizon Prizes in Mathematics of 2023.

A recent interview with Ana Caraiani can be found in Quantamagazine.

Photo credit: Barbara Frommann/Uni Bonn; HCM

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

Peter Scholze, director at the Max Planck Institute for Mathematics and professor at the University of Bonn, was elected Foreign Member of the Royal Society.

Official announcement of the Royal Society

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.

The Royal Society, founded in 1660 by King Charles II, is the oldest scientific institution of its kind in the world. The Society’s fundamental purpose is to recognise, promote, and support excellence in science and to encourage the development and use of science for the benefit of humanity. The Society has played a part in some of the most fundamental, significant, and life-changing discoveries in scientific history and Royal Society scientists continue to make outstanding contributions to science in many research areas.

(Source: The Royal Society)