Yan Soibelman

Yan Soibelman
Name	Yan Soibelman
Birth date	1970s
Birth place	Kyiv, Ukrainian SSR
Fields	Mathematics
Workplaces	Harvard University; Columbia University; Massachusetts Institute of Technology; University of Pennsylvania; Institute for Advanced Study
Alma mater	Moscow State University; University of Tel Aviv
Doctoral advisor	Maxim Kontsevich
Known for	Noncommutative geometry; Donaldson–Thomas theory; wall-crossing formulas; cluster algebras
Awards	EMS Prize; Sloan Fellowship; Packard Fellowship

Yan Soibelman is a mathematician known for contributions to noncommutative geometry, symplectic geometry, and the theory of Donaldson–Thomas invariants. He has worked on wall-crossing phenomena linking algebraic geometry, mathematical physics, and representation theory, collaborating with figures from Maxim Kontsevich to researchers at the Institute for Advanced Study. His work connects topics ranging from Calabi–Yau manifolds to cluster algebras, influencing research in string theory, mirror symmetry, and enumerative geometry.

Early life and education

Soibelman was born in Kyiv in the late 1970s and received early mathematical training influenced by the tradition of the Moscow School of Mathematics and the mathematical communities of Kyiv and Moscow. He studied at Moscow State University where he was exposed to the work of scholars associated with Israel Gelfand and the analytic traditions of Andrei Kolmogorov and Israel Moiseevich Gelfand. He pursued doctoral studies under Maxim Kontsevich, obtaining a Ph.D. that situated him at the intersection of algebraic geometry and mathematical physics while engaging with the intellectual milieus of Paris and Jerusalem research centers.

Mathematical career and positions

Soibelman has held positions in leading centers including postdoctoral and faculty roles at Harvard University, Columbia University, the Massachusetts Institute of Technology, and the University of Pennsylvania. He has spent time at the Institute for Advanced Study and maintained collaborations with researchers at the Perimeter Institute, IHES, and the Simons Center for Geometry and Physics. His appointments bridged faculties in departments anchored in connections to Stanford University, Princeton University, and international institutions such as Tel Aviv University and ETH Zurich.

Major contributions and research

Soibelman is best known for foundational work on wall-crossing formulas for BPS state counts and Donaldson–Thomas theory, often in collaboration with Maxim Kontsevich. Their joint formulation clarified the behavior of enumerative invariants across stability conditions and linked to structures in cluster algebras and Hall algebras. He contributed to the formalism relating Calabi–Yau categories, Fukaya category constructions, and categories appearing in mirror symmetry conjectures of Strominger–Yau–Zaslow type.

His research on noncommutative algebraic geometry explored deformation quantization and categories of representations, connecting to work of Alexander Beilinson, Joseph Bernstein, and Bertram Kostant. He investigated motivic Donaldson–Thomas invariants and their relation to Gromov–Witten theory, expanding the bridge between enumerative theories initiated by Richard Thomas and developments in Seiberg–Witten theory and topological string theory. Soibelman also studied cluster transformations and their categorical incarnations, interfacing with developments by Fomin–Zelevinsky and applications to the theory of quantum groups related to Lusztig and Drinfeld.

His papers elucidated structures in stability conditions on triangulated categories as developed by Tom Bridgeland and explored connections to representation theory of quivers initiated by Pierre Gabriel and extended by Hugh Thomas and others. He contributed to understanding categorical wall-crossing in contexts influenced by Edward Witten and Seiberg dualities, and he produced work on noncommutative Donaldson–Thomas invariants that influenced later research by scholars at Caltech, Yale University, and University of Cambridge.

Awards and honors

Soibelman received an EMS Prize and was awarded fellowships such as the Sloan Research Fellowship and a Packard Fellowship for his early career achievements. He has been invited to speak at major gatherings including the International Congress of Mathematicians and the European Congress of Mathematics, and he held visiting positions at the Institute for Advanced Study and IHES. His research has been recognized by professional societies including the American Mathematical Society and European mathematical institutes.

Selected publications and students

Selected publications include influential papers on wall-crossing and motivic Donaldson–Thomas invariants coauthored with Maxim Kontsevich, foundational works on cluster structures and noncommutative geometry, and expository contributions to the mathematics of stability conditions and enumerative invariants. His writing appears alongside contributions in proceedings of conferences organized by Clay Mathematics Institute, MSRI, and the Simons Foundation.

Soibelman has supervised doctoral students who have taken faculty and research positions at institutions such as University of Michigan, University of Oxford, École Normale Supérieure, University of Chicago, and Tel Aviv University. His trainees have continued work on topics including derived categories, mirror symmetry, motivic invariants, and cluster categories.

Personal life and legacy

Soibelman maintains collaborations across the international mathematical community, contributing to networks linking research centers such as Perimeter Institute, Bonn Mathematical Institute, Princeton, and Cambridge. His legacy includes the propagation of techniques that connect enumerative geometry, representation theory, and mathematical physics, influencing research programs at institutions like IHES, MPI Bonn, University of Tokyo, and Seoul National University. His work continues to inform developments in the study of Calabi–Yau categories, quantum invariants, and categorical approaches to mirror symmetry.

Category:Living people Category:Mathematicians Category:People from Kyiv