Imperial College London

MissFrancescaCarocci

Faculty of Natural SciencesDepartment of Mathematics

Research Postgraduate
 
 
 
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Contact

 

f.carocci14 CV

 
 
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Location

 

669Huxley BuildingSouth Kensington Campus

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Summary

 

Summary

I am a PhD student at Imperial College London and part of The London School of Geometry and Number Theory. My supervisors are Richard Thomas and Cristina Manolache. I am interested in algebraic geometry; more specifically enumerative geometry and moduli problems, but also derived categories of coherent sheaves.

I am currently working on two projects.

  • I am studying a version of Donaldson-Thomas invariants which conjecturally give a mathematical definition of genus 0 Gopakumar-Vafa invariants. More precisely, I study local contributions of singular curves to the invariants using a technique involving Hitchin's spectral construction.
  • In a joint project with Cristina Manolache and Luca Battistella, we study genus 1 invariants arising from alternate compactifications of the moduli space of stable maps and their relations with Gromov-Witten invariants and Reduced Gromov-Witten invariants of Vakil-Zinger.