How to edit?
- Read a documentation page for wiki math markup or go to the page of any problem and click source to see how other people write.
Status of problems
- Problems with solutions appear in bold.
- Problems with partial solutions, hints, discussion are in italics.
- The other posted problems have a wiki page with the statement of the problem only.
Many problems have no wiki page at all… If you solved a problem (completely or partially), have an idea or a hint, or simply want to promote the discussion by posting the problem statement to the wiki, then add the problem and create its page and see your wikidot karma improve.
Exercises by day
- Mon, June 18:
- Convex Algebraic Geometry: Newton Polytopes and Sums of Squares, Motzkin Form, Sums of Squares on a Lemniscate, Convex Hulls of Planar Curves, Conical Hull of a Compact Convex Set, Nonnegative and SOS cones
- Tropical Exercises: Minkowski sums, Non-constant coefficients.
- Computational algebraic geometry: Every system = a system of quadrics, Gamma exceptional set, …
- Tue, June 19:
- Wed, June 20:
- Lifts of convex sets: Lemniscate of Gerono
- Thu, June 21:
- Lifts of Convex Sets: Cross Polytopes, Rank of a Slack Matrix, Vanishing Ideals of Finitely Many Points, Birkhoff Polytope and Permutahedron
- Groebner Fans and Tropical Varieties: Principal Ideals, Term Orders and Weights, Tropical Varieties and Gfan
- Semidefinite and Polynomial Optimization: Explicit Example of Semidefinite Duality, Univariate Nonnegative Polynomial
- Fri, June 22:
- Mon, June 25:
- Mixed Volume and Bernstein's Theorem: Newton polygons with no common slopes, Mixed volume computation, MV(P,P,...,P), Mixed volume is symmetric, Mixed Volume is multi-linear, Mixed volume and containment, Bezout Bound, Mixed volume formula in dimension 2, Criterion for non-zero mixed volume
- Convex Algebraic Geometry: Dual Faces, Maximal Faces of the Nonnegative Cone, Exposed Extreme Rays of the Nonnegative Cone
- Primary Decomposition: Intersection of primary ideals
- Tues, June 26:
- Thu, June 28:
- Fri, June 29:
- Mon, July 02:
- Tues, July 03: