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
Michaelmas Term: Mechanics I (MA1241)
Hilary term: Mechanics II (MA1242) , Calculus on Manifolds (MA2322)
Projects in theoretical physics and/or mathematics: MA4492, MA4491
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 nonperturbative objects of these theories, such as instantons, monopoles, black holes and Dbranes. Two directions of my past and current research are:
Bound states of fundamental constituents: supersymmetric gauge and gravity theories have a rich spectrum of socalled Bogomolny'iPrasadSommerfield bound states of their fundamental constituents. Figure 1 below portrays schematically a bound state of three black holes with electricmagnetic charges γ_{i}. 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 uptodate Mathematica package for computations of BPS indices and topological invariants of quiver moduli spaces is available at CoulombHiggs .
Partition functions of YangMills 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 wallcrossing). This is captured by partition functions through sums over an indefinite lattice. See Figure 3 below.



Recent preprints and publications:
with G. Korpas, "DonaldsonWitten theory and indefinite theta functions", arXiv:1707.06235
with S. Alexandrov, S. Banerjee, B. Pioline, "Multiple D3instantons and modular forms II", arXiv:1702.05497
with S. Mozgovoy, "Intersection cohomology of moduli spaces of sheaves on surfaces", arXiv:1612.07620
with S. Alexandrov, S. Banerjee, B. Pioline, "Indefinite theta series and generalized error functions", arXiv:1606.05495
with S. Alexandrov, S. Banerjee, B. Pioline, "Multiple D3instantons and modular forms I", arXiv:1605.05945
with K. Bringmann, and L. Rolen, "Identities for generalized Appell functions and the blowup formula", arXiv:1510.00630
with M. Z. Rolón, "The asymptotic profile of χ_{y}genera of Hilbert schemes of points on K3 surfaces", arXiv:1411.1093
"Sheaves on P2 and Generalized Appell Functions", arXiv:1407.7785
with B. Pioline and A. Sen, "Generalized quiver mutations and single centered indices", arXiv:1309.7053
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:
"Gauge theory and generalised Appell functions, Number Theory and Physics, 24 May 2016, Paris, pdf
"Sheaves on Surfaces and Generalised Appell Functions, GEOQUANT 2015, Madrid, pdf
"BPS bound states and Quivers", 11 June 2015, ZMP colloquim, DESY pdf
"Gauge Theory and Generalised Appell Functions", 28 May 2015, IQF, Dublin pdf
"Black Hole Bound States", 20 March 2014, Quantum Gravity in Paris pdf
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
Journées de Physique Mathématique Lyon "BPS states, Hitchin Systems and Quivers", 35 September 2014
Last update: 22 September 2017