Nag Lecture 2025
Prof. Nikita Nekrasov
Stony Brook University
Public Lecture
17/11/2025, Monday at 17:00
Venue: Institute of Mathematical Sciences,Ramanujan Auditorium
Emergent space: from counting boxes to spacetime foam and beyond
We perceive our world (spacetime) as a differentiable manifold with Lorentzian metric, yet, at small scales, quantum mechanics tells us we should expect deviations from the classical intuition. I will present a few examples of enumerative problems going back to XIX century combinatorics, studied by S.Ramanujan and P.MacMahon, among others, which in the late XX century became problems of probability theory and representation theory and in the early XXI century have been given new mathematical life in differential, algebraic and noncommutative geometry, and then in high energy physics via string theory. The asymptotics of these counting problems reveal deep geometric structures suggesting interesting ideas on the pre-Big Bang universe.
About the Speaker
Nikita Nekrasov is a founding faculty member of the Simons Center for Geometry and Physics and Professor at the Yang Institute for Theoretical Physics at Stony Brook University. He earned his PhD from Princeton university under Nobel laureate David Gross in 1996. Formerly a permanent professor at IHES, he joined Stony Brook in 2013. His research focuses on quantum field and string theory, particularly the connections between two-dimensional conformal field theories and four-dimensional supersymmetric gauge theories. Prof. Nekrasov has received numerous honors, including the Hermann Weyl Prize (2004), the Compositio Prize (2009), and the Dannie Heineman Prize in Mathematical Physics (2023).
Technical Talks
Nag Lecture - I
Date and Time: Tuesday, November 18 2025, at 15:30
Venue: Alladi Ramakrishnan Hall, IMSc
Title: BPS/CFT correspondence
Abstract: Physics aims to find simplified models of complicated reality. Some of these models use the language of supergeometry and supersymmetry. In the last 50 years a lot of knowledge about the dynamics of quantum field theory has been gained by studying supersymmetric gauge theories. One of the surprising connections discovered along the way in 2002-2004 is the BPS/CFT correspondence: a connection between correlation functions of four, five and six dimensional gauge theories (BPS correlators, for Bogomol'nyi-Prasad-Sommerfield) and conformal blocks, their q-analogues and more generally representation theory of infinite dimensional Lie algebras found in two dimensional conformal field theory (CFT).
Nag Lecture - II
Date and Time: Friday, November 21 2025, at 15:30
Venue: Alladi Ramakrishnan Hall, IMSc
Title: Three dimensional gravity, Yang-Mills theory on origami worldsheet, and polymers
Abstract: This is a cute geometric story which came out of BPS/CFT correspondence. Integrable quantum many-body systems have an intricate connection to gauge theory. In particular, two dimensional Yang-Mills theory is related to the Calogero-Moser-Sutherland many body system. We generalize 2d Yang-Mills theory to allow for singular spacetimes which look like origami sheets. We find the associated integrable systems be the degenerations of Hitchin systems defined for Riemann surfaces of arbitrary genus. For rank one gauge group we identify the phase space of such a system with the configuration space of polymers (closed polygons) in Euclidean space with conical singularities (cosmic strings). Three dimensional Chern Simons theory and three dimensional gravity, a close relative of gauge theory under consideration, leads to the spherical and hyperbolic versions of such geometry.