Samson Shatashvili MRIA, theoretical and mathematical physicist

Professor Shatashvili’s research has recently established the deep connection between two major aspects of mathematics and theoretical physics: supersymmetric quantum field theories and quantum integrable systems. This discovery has multiple applications—both in pure mathematics and mathematical physics—and at present is a highly active area of research worldwide.

2025 marks twenty years since the RIA and the Higher Education Authority established the Gold Medals to acclaim Ireland’s foremost thinkers in the humanities, social sciences, and across the fields of science. The Gold Medals have become the ultimate accolade in scholarly achievement in Ireland. Since 2005, 34 medals have been awarded. In recognition of this important milestone, past RIA Gold Medals recipients have contributed blogs focusing on their research to our Members’ Research Series.

Samson Shatashvili MRIA is University Chair of Natural Philosophy (1847) at Trinity College Dublin (TCD) and director of the Hamilton Mathematics Institute TCD. From 1994, he was Professor at Yale University (USA) before coming to Ireland (TCD) in 2002. He was awarded the RIA Gold Medal in Physical–Mathematical Sciences in 2010, has held the Louis Michel Chair (2003–14) and Gelfand Chair (2014–19) at the Institut des Hautes Études Scientifiques near Paris, and was visiting professor (2014–24) at the Simons Center for Geometry and Physics at the State University of New York, Stony Brook.

Isaac Newton’s Philosophiae Naturalis Principia Mathematica (1687) reflects on the use of the term ‘Natural Philosophy’ at a time when no boundary between mathematics and physics existed. This is in fact my research discipline—theoretical and mathematical physics, which at Trinity College Dublin is still called Natural Philosophy.

Samson Shatashvili MRIA

Newton invented calculus and discovered the law of gravitation, but later the two disciplines started to split. It took over two centuries to improve our understanding of gravitation. In 1915 Einstein introduced his Theory of General Relativity. Ten years earlier, he had introduced the Special Theory of Relativity and contributed to the foundation of quantum mechanics. Unification of quantum mechanics with the Special Theory of Relativity was achieved in the mid twentieth century, and a powerful Quantum Field Theory was developed. It has been well-established experimentally that Quantum Field Theory describes three of the four known forces of nature: electromagnetic, weak and strong forces. Unifying quantum mechanics with General Relativity, usually called ‘Quantum gravity’, turned out to be an exceedingly challenging task, and the most promising approach at present is through the framework of String Theory. An important spinoff of string theory framework is that it brings back together the powerful methods of modern mathematics and the ideas and intuition of physics.

My research interests over the last four decades can be broken down into six main topics:

• quantum anomalies,
• coadjoint orbits of infinite-dimensional groups and representation theory,
• open string field theory,
• manifolds with exceptional holonomy,
• supersymmetric quantum field theory and
• quantum integrable systems.

Interestingly, these topics involve many ideas and methods developed in Ireland, at Trinity College Dublin, by William Rowan Hamilton and James MacCullagh. These are also the subjects in the mathematical foundations of Quantum Field Theory. For example, the standard model of particle physics, spectacularly confirmed by experiments, incorporates as a key element the principle of cancellations of anomalies.

In my work at the St Petersburg Steklov Mathematical Institute in early 1980s I was able to show that the best mathematical language describing quantum anomalies is group cohomolgy. While there, I also developed geometric methods for conformal field theories. Understanding quantum anomalies as a mathematical aspect of group cohomolgy led to progress both in mathematics and physics. At the Princeton Institute for Advanced Study (IAS) in the early 1990s, I studied exceptional holonomy manifolds, with the aim of uncovering their role in Quantum Field Theory (and String Theory), and discovered infinite-dimensional quantum algebra, which is unique and underlies most of the properties of the corresponding quantum field theory. In addition, I developed background independent open string field theory, which I used later at Yale University, to prove conjectures about open string tachyon condensation.

I studied supersymmetric quantum field theories in four space–time dimensions by developing intersection theory on the moduli space of instantons (and related moduli spaces—which define the non-perturbative part of partition function in these theories), and the connection with the theory of four-dimensional manifolds invariants. I was able to show exactly how Quantum Field Theory helps with learning the properties of these invariants. From 2002, when I came to Trinity College Dublin, I have mostly focused on spin-offs of these. Recently, when studying the detailed structure of supersymmetric vacua of various Quantum Field theories, my collaborators and I uncovered the precise connection between quantum integrable systems and supersymmetric vacua.

Supersymmetry is a symmetry between bosons (related to particles with integer spins) and fermions (half-integer spins). Experimental discovery of supersymmetry (search is ongoing, at institutes such as CERN) certainly will be revolutionary in our understanding of the universe. At present, supersymmetric theories form a sub-class of Quantum Field theories, through which one hopes to get exact answers to the most interesting physics questions.

Quantum integrable systems are quantum-mechanical systems for which one can find the exact solutions to Schrödinger equations; they are exactly solvable. Various interesting quantum many-body systems appearing in condensed-matter physics, statistical physics, particle physics, black-hole physics and certain problems of gravity have such properties. On the mathematics side, they appear in studies of partial differential equations, algebraic geometry, representation theory, quantum groups, etc., and have attracted the interest of mathematicians for many decades.

My discovery, with collaborators, of the deep connection between supersymmetric quantum field theories and quantum integrable systems turned out to be a powerful tool, which is now used in the study of black holes, string theory, enumerative geometry, and in many other areas of pure mathematics and theoretical physics.