This year marks the 60th birthday of mathematician Maxim Kontsevich, permanent professor at IHES since 1995. In his honor, Denis Auroux (Harvard University), Ludmil Katzarkov (University of Miami), Tony Pantev (University of Pennsylvania) and Yan Soibelman (Kansas State Universtiy & IHES), Yuri Tschinkel, SCGP & New York University organize a week-long conference at IHES from September 16-20, “Mathematics on the Crossroad of Centuries”.

The work of Maxim Kontsevich has been a unique combination of spectacular ideas in algebra, combinatorics, topology, algebraic geometry, and theoretical physics.

No other mathematician has played such a pivotal role in enhancing the interaction of mathematics and physics on the crossroad of 20th and 21st centuries.

In this week-long meeting we will be celebrating the 60th birthday of Maxim Kontsevich and his profound influence on mathematics.

Please register before September 5, 2024 on the dedicated web page.

Find out more about the guest speakers:

• Mohammed Abouzaid, Stanford University
• Mina Aganagić, UC Berkeley
• Jørgen Andersen, Odense University
• Denis Auroux, Harvard University
• Tom Bridgeland, University of Sheffield
• Vladimir Drinfeld, University of Chicago
• Pavel Etingof, MIT
• Kenji Fukaya, SCGP
• Davide Gaiotto, Perimeter Institute
• Alexander Goncharov, Yale University
• Fabian Haiden, Syddansk Odense University
• Mikhail Kapranov, IPMU
• Curtis McMullen, Harvard University
• Takuro Mochizuki, RIMS, Kyoto University
• Alexander Odesskii, Brock University
• Tony Pantev, University of Pennsylvania
• John Pardon, SCGP
• Yan Soibelman, Kansas State Univ. & IHES
• Yuri Tschinkel, SCGP & New York University
• Lauren Williams, Harvard University
• Don Zagier, MPI Bonn & ICTP

Several mathematicians affiliated to IHES are among the researchers who were distinguished with the Frontiers of Science Award during the International Congress of Basic Science whose inaugural edition took place in Beijing on July 16-28.

The award celebrates both basic and applied research results, published during the past five years in the fields of mathematics, theoretical physics and computer science. They must be of highest scientific value and originality and must have made an important impact in one of the three areas of interest. They must also have been published in a peer-reviewed journal.

Among the 134 publications selected overall, two were co-authored by Hugo Duminil-Copin, permanent professor at IHES, professor at the University of Geneva and laureate of the 2022 Fields Medal:

• Sharp phase transition for the random-cluster and Potts models via decision trees, published in the Annals of Mathematics in 2019. This paper was co-written by Hugo Duminil-Copin, Vincent Tassion (ETH Zürich), and Aran Raoufi, who spent three years at IHES between 2016 and 2018 as a PhD student, under the supervision of Prof. Duminil-Copin.
• Marginal triviality of the scaling limits of critical 4D Ising and $\phi_4^4$ models, published in the Annals of Mathematics in 2021and co-authored by Michael Aizenman (Princeton) and Hugo Duminil-Copin.

Three of the research articles selected for the award were co-authored by Maxim Kontsevich, permanent professor at the Institute:

• Canonical bases for cluster algebras, published in the Journal of the American Mathematical Society in 2018, and co-written by Mark Gross (University of Cambridge), Paul Hacking (University of Massachusetts Amherst), Sean Keel (University of Texas), and Maxim Kontsevich.
• Specialization of birational types, published in Inventiones mathematicae in 2019, and co-authored by Maxim Kontsevich and Yuri Tschinkel (New York University).
• Wick rotation and the positivity of energy in quantum field theory, published in the Quarterly Journal of Mathematics in 2021 and written by Maxim Kontsevich and Graeme Segal (University of Oxford).

The list of publications that were celebrated during the International Congress for Basic Science also includes ‘On the implosion of a compressible fluid II: Singularity formation’, published in the Annals of Mathematics in 2022. This is one of three much celebrated papers co-written by Frank Merle, CY Cergy Paris Université-IHES Chair in Analysis, Pierre Raphaël, holder of the Schlumberger Chair for mathematical sciences at IHES and Professor at the University of Cambridge, Igor Rodnianski, Professor at Princeton University, and Jérémie Szeftel, CNRS Research Director at Sorbonne Université. In addition to the Frontiers of Science Award, their most recent contributions have already earned them the 2023 Bôcher Prize of the American Mathematical Society and the 2023 Clay Research Award, of the Clay Mathematics Institute.

Sébastien Boucksom, editor in chief of the Publications mathématiques de l’IHES, and a CNRS Research Director at Institut de Mathématiques de Jussieu – Paris Rive Gauche, is also among the researchers who were distinguished in Beijing for his paper entitled ‘A variational approach to the Yau-Tian-Donaldson conjecture’, published in the Journal of the American Mathematical Society in 2021 and co-written with Robert J. Berman (University of Gothenburg) and Mattias Jonsson (University of Michigan).

IHES is very proud of the important scientific contributions achieved by the IHES researchers honored with the Frontiers of Science Award and extends its sincere congratulations to all of them!

From February 10 to 14, 2020, the Institut des Hautes Études Scientifiques hosted the conference “Integrability, Anomalies and Quantum Field Theory“. Organised by Anton Alekseev (University of Geneva) and Maxim Kontsevich (IHES), this conference honoured Professor Samson Shatashvili on his 60^th birthday.

The interactions of Mathematics and Physics have greatly intensified during the last three decades, and it led to a number of very significant breakthroughs in Mathematics. Among other things, these breakthroughs include new invariants of 3 and 4-dimensional manifolds, the discovery of mirror symmetry in Algebraic Geometry, and the theory of deformation quantization.
This progress became possible due to close interactions between Mathematics and theoretical Physics and due to the dialogue between mathematicians and physicists working on similar problems but using very different methods.

The conference touched upon two important aspects of interaction between Mathematics and Quantum Field Theory.

Quantum Integrability is a very interesting theory which was first discovered on the Physics side. It was soon realized that it is related to Algebra through the theory of Vertex Operator Algebras (VOA) and to Complex Analysis (through the study of various Riemann-Hilbert problems). The problem of Bethe Ansatz completeness became an important mathematical problem and a driving force in Combinatorics and Representation Theory. Recently, relations between quantum integrability and Geometric Representation Theory (on the Mathematics side) and Quantum Gauge Theory (on the Physics side) attracted a lot of attention of the research community. These links will be one of the major topics of the conference.

Anomalies were discovered in Physics as the phenomenon when symmetry of a system changes under quantization. Famously, it occurs in gauge theories and in string theory, and it serves as one of the key criteria for choosing realistic models of field theory. Anomalies also became one of the important topics in Mathematics. They are related to the behaviour of determinant bundles of Dirac operators on manifolds, to the index theory and to K-theory. In many cases, anomalies represent the part of Quantum Field Theory which can be defined and computed mathematically. Anomalies will be one of the key topics of the meeting.

Professor Samson Shatashvili made deep contributions in the theory of anomalies and in quantum integrability. In particular, in collaboration with Ludwig Faddeev he discovered the interpretation of gauge theory anomalies in terms of abelian extensions of gauge groups on manifolds of odd dimension. In the theory of quantum integrability, together with a number of collaborators he discovered a deep link between Bethe equations and supersymmetric quantum gauge theory.
Professor at the Trinity College, Dublin and at the Simons Center for Geometry and Physics, Stony Brook, he served as a Louis Michel Chair and then as an Israel Gelfand Chair at IHES. He contributed in a significant way in the development of ideas and in the unique research atmosphere of IHES.

Invited speakers were:
Costas Bachas (ENS-Paris), Jean-Michel Bismut (Université Paris-Sud Orsay), Gregory Gabadadze (New York University), Sergei Gukov (Caltech), Simeon Hellerman (IPMU), Chris Hull (Imperial College London), Vladimir Kazakov (ENS-Paris), Zohar Komargodski (SCGP), Vladimir Korepin (Stony Brook University), Manuela Kulaxizi (Trinity College Dublin), Sergei Lukyanov (Rutgers University), Ruben Minasian (IPhT & CEA Saclay), Vasily Pestun (IHES), Alexey Rosly (ITEP, Skoltech, HSE, IITP, Moscow), Sinead Ryan (Trinity College Dublin), Ivo Sachs (LMU Munich), Nana Shatashvili (Tbilisi State University, Georgia), Fedor Smirnov (LPTHE Sorbonne-Université), Leon Takhtajan (Stony Brook University), Anne Taormina (Durham University), Cumrun Vafa (Harvard University), Pierre Vanhove (IPhT & CEA Saclay), Erik Verlinde (Universiteit van Amsterdam), Alexander Zamolodchikov (Stony Brook University).

Programme and registration on the conference web page.

Video playlist of the conference:

On 25-27 February 2019, a conference on “Space Time Matrices” will be organised by Thibault Damour, Jens Hoppe and Maxim Kontsevich at IHES.

Large-N limits of matrix models have been proposed as a way of describing the structure of Space and Time.

The conference will review these models that may bring a new light on trying to reconcile Gravity and the Quantum.

Invited speakers are : Joakim Arnlind (Linköping University), Niklas Beisert (ETH Zürich), Martin Bordemann (UHA), Alain Connes (Collège de France – IHES),  Jürg Fröhlich (ETH Zürich), Antal Jevicki (Brown University), Hikaru Kawai (Kyoto University), Douglas Lundholm (KTH), Maxim Kontsevich (IHES), Denjoe O’Connor (DIAS), Harold Steinacker (University of Vienna), Asato Tsuchiya (Shizuoka University), Teoman Turgut (Boğaziçi University) et Piljin YI (KIAS).

For information and registration, please visit the conference webpage.

In the era of global communication, mathematical concepts that help controlling information flow become increasingly important. In particular, Markov chains, first introduced in 1906, are currently applied in information search processes and in the analysis of information flow, which are at the very heart of search engines and the internet industry.

In 1998 the algorithm used by the Google search engine was described in detail by Sergey Brin and Larry Page in their seminal paper.

Twenty years later, with the GOMAX conference held from 15 to 18 October 2018, IHES wanted to create new contact points between mathematics, physics, computer science and the high-tech industry by hosting a conference which will review key milestones, as well as the future research directions on the efficiency and control of information flow on directed networks.

The workshop has been organised by Andras Benczur (MTA SZTAKI Budapest), Dima Shepelyansky (CNRS-Univ. Paul Sabatier, Toulouse) and Emmanuel Ullmo (IHES).

The list of speakers included: Paolo Boldi (Università di Milano), Jean-Philippe Bouchaud (CFM, Paris), Sergey Dorogovtsev (University of Aveiro), Leonardo Ermann (Comisión Nacional de Energía Atómica, Argentina), Klaus Frahm (Université de Toulouse), Katia Jaffres-Runser (IRIT, INPT-ENSEEIHT, Toulouse), Ravi Kumar (Google CA), Jose Lages (Institut UTINAM, Besançon), Yann LeCun (Facebook AI Research), Matteo Marsili (ICTP Trieste), Stéphane Nonnenmacher (Université Paris-Sud, Orsay), Robert Palovics (Hungarian Academy of Sciences), Lior Rokach (Ben-Gurion University of the Negev), Jean-Jacques Slotine (MIT), Andrew Tomkins (Google CA), Piet Van Mieghem (Delft University of Technology), Andrey Zinovyev (Institut Curie).

The scientific advisory board consisted of Andras Benczur, Misha Gromov (IHES), Maxim Kontsevich (IHES), and Dima Shepelyansky.

Conference webpage