External Lecturer:
Gregorio Malajovich
Course Type:
Seminar Series
Academic Year:
2018-2019
Period:
October
Duration:
10 h
Description:
Lecture 1: On counting solutions of polynomial systems
- Bézout's theorem
- Smale's 17-th problem
- Shortcomings of Bézout's theorem
- Sparse polynomial systems, and the mixed volume
Lecture 2: Differential forms
- Multilinear algebra over R
- Complex differential forms
- Kähler geometry
- The coarea formula, using bundles.
- Projective space
Lecture 3: Reproducing kernel spaces
- Spaces of complex fewnomials
- Metric structure on root space
- Unmixed systems
- Random analytic functions
Lecture 4: Mixed systems of equations
- Root density
- Affine and multi-homogeneous setting
- The semigroup of fewnomial spaces
Lecture 5: Exponential sums
- Legendre transform
- The momentum map
- Proof of Bernstein's theorem
Location:
TBC(to be checked)
Location:
A-135 on Thursday 24/10. A-133 otherwise.