Mathematical issues in model building:
- sheaves for heterotic strings
- G4-form flux in F-theory
- biased landscape counting
- M5-brane instantons intrinsically
- geometric transitions in compact models
Moduli stabilization issues:
- dynamical stringy realization of gauge mediation without any prior fixing of some moduli by hand
- dynamical realization of large extra dimensions (LVS) without light scalars
- dynamical realization of inflation
- stabilization of IIB/F-theory & other moduli taking mutual conditions for fluxes/branes/instantons into account
- universal predictions for certain classes of string models
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