The 2nd Thematic Year

Mathematics of Quantum Field Theory

July 2015 – August 2016

  • Conference 1 Geometry and Physics (GAP) XIII; July 6 – 10, 2015.
  • Organizers: Calin Iuliu Lazaroiu (IBS-CGP), Jae-Suk Park (IBS-CGP & POSTECH), Mathieu Stienon (Pennsylvania State University), Yannick Voglaire (University of Luxembourg), Ping Xu (Pennsylvania State University)

GAP (Geometry and Physics — Séminaire itinérant) is a series of conferences and summer schools held annually since 2003 in various countries around the world. This year will see the thirteenth edition of the annual GAP conference and summer school, to be held at the IBS Center for Geometry and Physics from July 6 to July 10, 2015. The focus of this edition is Derived Geometry. The list of previous GAP installments can be found at http://www.geometryandphysics.org.

At the boundary between physics and mathematics, one overarching goal is to develop a rigorous mathematical model for quantum field theory that accounts for the various non-rigorous physical constructions and phenomena. Among active endeavors toward this goal, the mathematical rigorization of Batalin-Vilkovisky quantization has seen significant progress in recent years. The following pair of events scheduled for two consecutive weeks in January 2016 focuses on two aspects of this rigorization.

Information of the conferences can be found at http://cgp.ibs.re.kr/conferences/MathematicalQuantumFieldTheory/.

  • Organizers: Gabriel C. Drummond-Cole (IBS-CGP), Owen Gwilliam (Max Planck Institute for Mathematics, Bonn), Calin Iuliu Lazaroiu (IBS-CGP), Wolfgang Lerche (CERN), Changzheng Li (IBS-CGP), Si Li (MSC, Tsinghua University), Jae-Suk Park (IBS-CGP & POSTECH)

The target space description of the topological B-model involves a deep interplay between deformation theory and the theory of quantization, forming a useful testing ground for old and new ideas in constructive field theory — in particular in its BV—BRST incarnation — and leading to rich problems in algebraic homotopy theory, derived algebraic geometry and analysis on manifolds.

The first workshop will focus on recent developments in this area and on approaches to remaining open problems.

The algebraic framework necessary to axiomatize BV quantization and renormalization uses homotopical algebra and derived geometry in a fundamental way. The development of homotopy-algebraic tools suited to this particular cluster of problems has borne fruit in a number of ways, and it has advanced the state of the art in mathematical axiomatization of BV-related aspects of quantum field theory. Moreover, these methods have enhanced field-theoretic interpretations of geometric invariants, such as the Witten genus and period integrals, and have motivated novel invariants, notably in the guise of factorization homology.

The second workshop will focus on foundational questions from this homotopical viewpoint, both in axiomatization and in application.

  • Conference 4 Number theory and quantum field theory; August 22 – 26, 2016.
  • Organizers: Philip Candelas (University of Oxford), Dmitry Kaledin (Steklov Mathematical Institute & Independent University of Moscow), Minhyong Kim (University of Oxford), Xenia de la Ossa (University of Oxford), Jae-Suk Park (IBS-CGP & POSTECH), Jeehoon Park (POSTECH)