James Pascaleff
- Office: 417 Fuld Hall
- Email: jpascale@ias.edu
I am a member of the Institute for Advanced Study for the Spring 2017 term. If you are looking for my main University of Illinois webpage, it is here.
Quantization of BCOV and the higher-genus B-model reading group
Meetings
Usual meeting time is Tuesday 3:15pm–4:30pm.
- Jan. 24, 2:30pm, Dilworth room. Preliminary meeting.
- Jan. 31, 3:15pm–4:30pm, S-101. James, Intro to BCOV theory.
- Feb. 14, 3:15pm–4:30pm, West Building Lecture Hall. James, Perturbative quantization and master equation.
- Feb. 28, 3:15pm–4:30pm, S-101. James, Perturbative quantization and master equation (cont'd).
- Mar. 7, 3:15pm–4:30pm, S-101. James again.
- Mar. 17, Si Li, BCOV theory and quantum B-model.
- Apr. 5, Mauricio Romo, BCOV equations.
- Apr. 13, Andrei Caldararu, Computing a categorical GW invariant.
- Apr. 13, Bohan Fang, Quantization of semisimple CohFTs.
- Apr. 18, Mauricio Romo, Derivation of the holomorphic anomaly equation.
Notes
These notes were taken by James. Note: some of the scanned notes may not display correctly in your browser; try downloading them.
- James, Perturbative quantization and master equation.
- Si Li, BCOV theory and quantum B-model.
- Mauricio Romo, BCOV equations.
- Andrei Caldararu, Computing a categorical GW invariant.
- Bohan Fang, Quantization of semisimple CohFTs.
- Mauricio Romo, Derivation of the holomorphic anomaly equations.
Readings
As this is a reading group, we should have some reading material. Please suggest things to add to this list.
- Kevin Costello, Renormalization and Effective Field Theory, Mathematical Surveys and Monographs, Volume 170, 2011.
- This book provides essential background to the papers of Costello and Li. A full-text PDF is available at http://www.ams.org/books/surv/170/. Note that you must access this link from the IAS network or else it will prompt you to log in (your university library may also have access).
- Si Li's homepage with links to his papers. Of particular interest is the sequence
- Si Li's thesis, Calabi-Yau geometry and higher genus mirror symmetry
- K. Costello and S. Li, Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
- S. Li, BCOV theory on the elliptic curve and higher genus mirror symmetry
- K. Costello and S. Li, Quantization of open-closed BCOV theory, I
- S. Li, Vertex algebras and and quantum master equation
- M. Bershadsky, S. Cecotti, H. Ooguri, C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Comm. Math. Phys. Volume 165, Number 2 (1994), 311-427.
- R. Dijkgraaf, Mirror Symmetry and Elliptic Curves. In: Dijkgraaf R.H., Faber C.F., van der Geer G.B.M. (eds) The Moduli Space of Curves. Progress in Mathematics, vol 129.
- R. Dijkgraaf, Chiral deformations of conformal field theories. Nuclear Physics B Volume 493, Issue 3, 2 June 1997, Pages 588–612
- K. Hori et al., Mirror Symmetry, Clay Math. Monographs Volume 1, 2003.
- Especially Chapters 14 (renormalization group flow) and 35 (mirror symmetry at higher genus).
- K. Cieliebak, K. Fukaya, J. Latschev, Homological algebra related to surfaces with boundary
- S. Hosono, BCOV ring and holomorphic anomaly equation.