I am an associate professor in the Department of Physics and Astronomy at James Madison University.

My research is in mathematical physics, and my main interests are in quantum field theory and string theory.  My recent research interests include two-dimensional conformal field theory in its relation to geometry and the landscape of string vacua, soliton form factors, and aspects of string duality. 

I studied at Cornell and at Duke and have been a postodoc at the Enrico Fermi Institute at the University of Chicago, at the Max Planck Institute for Gravitational Physics (the Albert Einstein Institute), the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M, and most recently in the
Department of Mathematics at Harvard.  More information of this sort may be found in my  CV .

String theory is a branch of modern theoretical physics with the broad and ambitious aim of reconciling two indubitable experimental facts:  the remarkable success of general relativity to describe large scale phenomena such as planets, stars, and galaxies, and the success of quantum mechanics, embodied by local quantum field theory, to describe the microscopic dynamics of (seemingly) fundamental particles such as quarks, electrons, and photons.  There are, by now, many sources where one might learn more about string theory; one of my favorite places is the incredibly beautiful introductory chapter of the classic GSW text.  An introduction to some central features of my work may be found here.

• Contact
  
  • the best way to reach me is by email: the invocation is melnikix  at  JMU  dot  EDU  .
    
  • my office is 2154 in the Physics and Chemistry Building.
  • my office telephone number is 540 568 5141 .
    

  
  

• the day-to-day life
  
  • I am on educational leave through August 2024. I will be spending this time at the University of Paris and at the Max Planck Institute for Gravitational Physics. If you would like to contact me, please use the email address above!
    

• current research interests
  • quantum field theory in two dimensions
  • solitons and non-perturbative phenomena in quantum field theory
    
  • supersymmetric sigma models
  • worldsheet-exact results in heterotic compactifications (massless spectra, Yukawa couplings, etc)
    
  • stringy geometry: resolution of singularities in geometry and conformal field theory, extensions of mirror symmetry
  • superconformal field theory
  • conformal perturbation theory and moduli space geometry
  • string duality
    
    
• some future research directions and exciting questions
  

• most of my papers are on SPIRES ; a few more from my younger days are listed in the CV
  
  
• here are some representation theory lecture notes from a course at A&M in the spring of 2014.
  
  
• I recently finished a book on (0,2) quantum field theory in two dimensions.  You can take a look here.
  
  
  
• conferences, past and future
  
  • I co-organized several workshops on (0,2) theories.  These were lots of fun and led to new collaborations and discussions.   Here you can find a little bit about them:
    
    • (0,2) mirror symmetry and quantum cohomology (August 2010 at the AEI)
    • (0,2) mirror symmetry and heterotic Gromov-Witten invariants (March 2010, BIRS in Banff, CA)
    • Topological heterotic strings (June 2011, ESI in Vienna, Austria)
    • Heterotic Strings and (0,2) QFT (April 2013, at the Mitchell Institute)
    • GLSM2020 (on Zoom)  (August 2020)
    • GLSM@30, planned for May 2023 at the Simons Center for Geometry and Physics
      
      
  • Here are a few sets of slides of talks I have given
    
    • (0,2) mirror map from STRINGS 2010
      
    • heterotic fluxes from STRING MATH 2012
    • hybrid models from STRING PHENO 2013
    • (0,2) overview from FRG Mirror Symmetry Workshop at Brandeis University
    • (0,2) overview from GLSM2020 Zoom conference
      
      
      
      
• friendly collaborators
  I have been very lucky to work with many wonderful people over the years.  I learned lots of string theory and geometry from Paul Aspinwall, Dave Morrison, and Ronen Plesser, as well as my fellow grads at Duke, Carina Curto and Sven Rinke;  there I also had a chance to meet Anda Degeratu, who has cleared up much geometric confusion over the years, as well as Eric Sharpe - a constant source of many fun discussions, questions, and answers.  At Chicago I had the opportunity to work with Emil Martinec, Sav Sethi, and especially with Jock McOrist .  During my time at AEI I had the pleasure of working with Ruben Minasian and Stefan Theisen.  At A&M I really enjoyed working with Andy Royston, and we have since renewed our collaboration, together with Costis Papageorgakis.
  

• I am living in Harrisonburg, VA together with Adrienne, and our daughter Athena. 
  
  
• I like to bike, run, and climb.