Jan Manschot

Assistant Professor in Theoretical Physics



Contact details

School of Mathematics

Trinity College

Dublin 2

Ireland


Hamilton Building

Office: 2.5

Telephone: +353 1 896 8516

Email: manschot AT maths.tcd.ie


Teaching


Hamilton Institute Workshop


Research interests

My research deals with fundamental aspects of gauge theory, gravity and string theory. I am in particular interested in the quantum spectra of non-perturbative objects of these theories, such as instantons, monopoles, black holes and D-branes. Two directions of my past and current research are:

  1. Bound states of fundamental constituents: supersymmetric gauge and gravity theories have a rich spectrum of so-called Bogomolny'i-Prasad-Sommerfield bound states of their fundamental constituents. Figure 1 below portrays schematically a bound state of three black holes with electric-magnetic charges γi. The degrees of freedom associated with the bound state can be described by the representation theory of quivers. Figure 2 below shows the quiver associated to the black hole bound state. An up-to-date Mathematica package for computations of BPS indices and topological invariants of quiver moduli spaces is available at CoulombHiggs .

  2. Partition functions of Yang-Mills theory and supergravity: Partition functions contain crucial information about quantum spectra and are indispensable tools to address questions about entropy, phase transitions, symmetries and dualities of the physical theories. These symmetries and dualities imply interesting number theoretic properties for the partition functions. Supersymmetric quantum spectra typically depend discontinuously on external parameters J (a phenomena also known as wall-crossing). This is captured by partition functions through sums over an indefinite lattice. See Figure 3 below.




Figure 1: Multi-center black hole


Figure 2: Quiver


Figure 3: Indefinite lattice

Recent preprints and publications:

  1. with G. Korpas, "Donaldson-Witten theory and indefinite theta functions", arXiv:1707.06235

  2. with S. Alexandrov, S. Banerjee, B. Pioline, "Multiple D3-instantons and modular forms II", arXiv:1702.05497

  3. with S. Mozgovoy, "Intersection cohomology of moduli spaces of sheaves on surfaces", arXiv:1612.07620

  4. with S. Alexandrov, S. Banerjee, B. Pioline, "Indefinite theta series and generalized error functions", arXiv:1606.05495

  5. with S. Alexandrov, S. Banerjee, B. Pioline, "Multiple D3-instantons and modular forms I", arXiv:1605.05945

  6. with K. Bringmann, and L. Rolen, "Identities for generalized Appell functions and the blow-up formula", arXiv:1510.00630

  7. with M. Z. Rolón, "The asymptotic profile of χy-genera of Hilbert schemes of points on K3 surfaces", arXiv:1411.1093

  8. "Sheaves on P2 and Generalized Appell Functions", arXiv:1407.7785

  9. with B. Pioline and A. Sen, "Generalized quiver mutations and single centered indices", arXiv:1309.7053

  10. with K. Bringmann, "Asymptotic formulas for coefficients of inverse theta functions, arXiv:1304.7208

See for a more complete list for example: scholar.google.com


Selection of presentations:

  1. "Gauge theory and generalised Appell functions, Number Theory and Physics, 24 May 2016, Paris, pdf

  2. "Sheaves on Surfaces and Generalised Appell Functions, GEOQUANT 2015, Madrid, pdf

  3. "BPS bound states and Quivers", 11 June 2015, ZMP colloquim, DESY pdf

  4. "Gauge Theory and Generalised Appell Functions", 28 May 2015, IQF, Dublin pdf

  5. "Black Hole Bound States", 20 March 2014, Quantum Gravity in Paris pdf

  6. Lecture Course "Quivers and BPS Bound States", 12 - 17 January 2014, Les Diablerets Winter School , Notes , Exercices

Past activities:

Indefinite Theta Functions and Applications in Physics & Geometry, June 6 - June 9, 2017


Last update: 22 September 2017