Miroslav Rapcak

Bio:

I am currently a senior research fellow at the Department of Theoretical Physics in CERN. Previously, I was a postdoctoral fellow at The Berkeley Center for Theoretical Physics. I received my PhD in 2019 from the University of Waterloo working at Perimeter Institute for Theoretical Physics under the supervision of Davide Gaiotto.

I am interested in mathematical aspects of string theory and quantum field theory. My current research focuses mostly on discovering new applications of supersymmetric gauge theories and string theory leading to novel insights in geometric representation theory. I am also interested in applications of representation theory of algebras in holography, knot theory, geometric Langlands program and other areas. In the past, I worked on integrability of defects in conformal field theories and construction of classical solutions in bosonic string field theory.

Contact information:

• Email: miroslav[dot]rapcak[at]gmail[dot]com

• Address: Building 4, Meyrin site, Switzerland 

• Office: 4/2-069

• Phone: +33 7 80 76 41 09

Publications:

• Butson, Rapcak: Perverse coherent extensions on Calabi-Yau threefolds and representations of cohomological Hall algebras, (2023), [arXiv:2309.16582] 

• Gaiotto, Rapcak, Zhou: Deformed Double Current Algebras, Matrix Extended W_\infty Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection, (2023), [arXiv2309.16929] 

• Aganagic, LePage, Rapcak: Homological Link Invariants from Floer Theory, (2023), [arXiv:2305.13480] 

• Rapcak: Branes, Quivers and BPS Algebras, (2021), [arXiv:2012.04118] 

• Gaiotto, Rapcak: Miura operators, degenerate fields and the M2-M5 intersection, (2020), [arXiv:2012.04118] 

• Budzik, Rapcak, Rojas, Conformal Defects from String Field Theory, JHEP 01 (2021) 120, [arXiv:2009.06567] 

• Rapcak, Soibelman, Yang, Zhao, Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds, (2020), [arXiv:2007.13365] 

• Rapcak, On Extensions of gl(1|1) Kac-Moody algebras and Calabi-Yau Singularities,  JHEP 01 (2020) 042, [arXiv:1910.00031] 

• Rapcak, Soibelman, Yang, Zhao, Cohomological Hall algebras, vertex algebras and instantons, Commun.Math.Phys. 376 (2019) 3, 1803-1873, [arXiv:1810.10402] 

• Prochazka, Rapcak, W-algebra modules, free fields, and Gukov-Witten defects,  JHEP 05 (2019) 159, [arXiv:1808.08837] 

• Prochazka, Rapcak, Webs of W-algebras, JHEP 11 (2018) 109, [arXiv:1711.06888] 

• Gaiotto, Rapcak, Vertex Algebras at the Corner,  JHEP 01 (2019) 160, [arXiv:1703.00982] 

• Rapcak, Nonintegrability of NS5-like Interface in N=4 Supersymmetric Yang-Mills, (2015), [arXiv:1511.02243]  

• Kudrna, Rapcak, Schnabl, Ising model conformal boundary conditions from open string field theory, (2014), [arXiv:1401.7980] 

Selected talks:

2023

• July: Branes, Quivers and BPS Algebras, Fields and Strings seminar, LMU, Munich, Germany

• February: Knot Homologies from Landau Ginsburg Models, String-Theory Seminar, Oxford, UK

2022

• November: Knot Homologies from Landau Ginsburg Models, Berkeley String-Math Seminar, Berkeley, USA, [slides], [video] 

• November: Algebras of Operators on Intersecting M2- and M5-branes, String Theory Journal Club, CERN, Switzerland

• November: Knot Homologies from Landau Ginsburg Models, Physical Mathematics Seminar, University of Geneva, Switzerland

• November: Coherent Sheaves, Quivers and Affine-Yangian Representations, Seminar on Combinatorics and Lie Theory and Topology, University of Pisa, Italy

• June: Knot Homologies from Landau Ginsburg Models, Enumerative Invariants, Quantum Fields and String Theory Correspondences, Mittag-Leffler institute, Sweden

• February: Branes, Quivers and BPS algebras, Uppsala, Sweden

• January: Branes, Quivers and BPS algebras, Caltech, Pasadena, USA

2021

• December: W_\infty and Melted Crystals of DT and PT, M-seminar, Kansas State University, Manhattan, [slides]

• November: W_\infty and Melted Crystals of DT and PT, Quantum Field Theories and Quantum Topology Beyond Semisimplicity, BIRS, Banff, Canada, [slides]

• September: M5-branes in Toric 3-folds and Vertex Operator Algebras, Mathematical Physics Seminar, Purdue university, [notes] 

• August: Branes, Quivers and BPS Algebras, Summer School on Algebraic Geometry in High-Energy Physics, Fields Institute for Research in the Mathematical Sciences and the Pacific Institute for the Mathematical Sciences, [lecture 1] [lecture 2] [lecture 3] [lecture 4] 

• July: The Miura Operator at the M2-M5 intersection, Quantum Fields, Geometry and Representation Theory 2021, ICTS-TIFR Bangalore, [slides], [video] 

• May: The Miura Operator at the M2-M5 intersection, BIMSA, Beijing, [slides] 

• May: M5-M2 Systems and the Affine Yangian, QFT, Strings and Beyond, ETH Zurich, [slides] 

• February: Miura Operators, Degenerate Fields and the M2-M5 Intersection, SCGP physics group meeting, Simons Center for Geometry and Physics

2020:

• November: Miura Operators, Degenerate Fields and the M2-M5 Intersection, Informal String-Math Seminar, UC Berkeley, [slides], [video] 

• November: Affine Yangian and Pandharipande-Thomas Box Counting, Algebraic geometry and moduli seminar, ETH Zurich, [slides]

• June: W-algebras and Coulomb-Branch Algebras from the M-theory Perspective, FZU, Academy of Sciences, Prague 

• June: W-algebras, Coulomb Branch Algebras and M-theory, MFF UK, Prague

• April: Extensions of Kac-Moody Algebras and Calabi-Yau Singularities, QMAP seminar, UC Davis

2019:

• December: Extensions of Kac-Moody algebras and Calabi-Yau singularities, Geometric Representation Theory and Quantum Field Theories, TSIMF, China

• October: Extensions of Kac-Moody algebras and Calabi-Yau singularities, Caltech, Pasadena, USA

• September: Extensions of Kac-Moody algebras and Calabi-Yau singularities, String-Math Seminar, UC Berkeley, USA

• July: Extensions of Kac-Moody algebras and Calabi-Yau singularities, Physics Institute of the Academy of Sciences, Prague, Czech Republic

• July: The Vertex Algebra Vertex, Integrable Systems and Quantum symmetries, CVUT Prague, Czech Republic

• April: Different Constructions of Corner VOAs, Vertex Algebras in Mathematics and Physics, University at Albany, USA

• February: COHA and AGT for Spiked Instantons, Cohomological Hall algebras in Mathematics and Physics, Perimeter Institute, Canada, [video] 

• January: Vertex Algebras for Divisors in Toric 3 - folds, Non-Local Aspects of Holomorphic and Topological Field Theory (IHES, France), [video] 

2018:

• October: The Vertex Operator Algebra Vertex, Simons Center for Geometry and Physics, Stony Brook, USA, [video] 

• October: The Vertex Operator Algebra Vertex, Princeton University, Princeton, USA

• October: The Vertex Operator Algebra Vertex, Harvard University, Cambridge, USA

• September: The Vertex Operator Algebra Vertex, Yale University, New Haven, USA

• July: Representation Theory of Vertex Operator Algebras and Gukov-Witten Defects, IST Austria, Klosterneuburg, Austria

• July: Representation Theory of Vertex Operator Algebras and Gukov-Witten Defects, Group 32, Prague, Czech Republic, [slides]

• March: The Vertex Algebra Vertex, National Taipei University (Taipei, Taiwan)

• February: The Vertex Operator Algebra Vertex, Kavli IPMU (Kashiwa, Japan)

2017:

• November: Vertex Operator Algebras via Topological Vertex Like Construction, UC Davis, Davis, USA

• November: Vertex Operator Algebras via Topological Vertex Like Construction, California Institute of Technology, Pasadena, USA

• October: Vertex Operator Algebras via Topological Vertex Like Construction, UC Berkeley, Berkeley, USA

• July: Vertex Algebras at the Corner, String Math 2017, Hamburg, Germany, [video] 

• June: Vertex Algebras at the Corner, Strings 2017, Tel Aviv, Israel, [video], [poster] 

• June: Vertex Algebras at the Corner, Physics Institute of the Academy of Sciences, Prague, Czech Republic

• June: Vertex Algebras at the Corner, International Conference on Integrable Systems, Prague, Czech Republic