Program Schedule

Week 3 Schedule







9:30-10:30AM Sturmfels 1 Wampler 2 Sturmfels 2 Sturmfels 3 Sturmfels 4
10:30-11AM Break Break Break Break Break
11AM-12PM Dickenstein 1 Maclagan 1 Maclagan 2 Maclagan 3 Maclagan 4
12-2PM Lunch Lunch Free Lunch Lunch
2-3PM Wampler 1 Dickenstein 2 Free Dickenstein 3 Dickenstein 4
3-3:30PM Break Break Free Break Break
3:30-5:30PM Problem Session Problem Session Free Problem Session Problem Session

All Lectures will be held in Room 1116 in Klaus Advanced Computing Building.

The exercises are posted on t-square and some solutions are on

Guest Lecturer Visit Times and Preliminary Lecture Titles:

Alicia Dickenstein: Computational algebra and biochemical reaction networks

  1. Chemical reaction netwoks with mass action kinetics. Definitions,examples and main properties.
  2. Reversible and weakly reversible networks. Complex balanced and detailed balanced steady states.
  3. Invariants. Enzymatic networks. Motifs. Multistationarity.
  4. Chemical reaction networks with toric steady states.

Diane Maclagan:

1. Groebner Complex and Non-Constant Coefficient Tropical Varieties.
2. Fundamental Theorem of Tropical Geometry.
3. Tropical Implicitization.
4. Tropical Implicitization via Geometric Tropicalization.

Bernd Sturmfels:

1. Convex Algebraic Geometry.
2. The Central Curve in Linear Programming.
3. The Entropic Discriminant.
4. Non-negative Polynomials versus Sums of Squares.

Charles Wampler: Applications of Numerical Algebraic Geometry I,II

Week 1:

Pablo Parrilo:   

1. Intro to Convex Geometry.
2. Semidefinite Optimization.
3. Sums of Squares and Semidefinite Optimization.
4. Polynomial Optimization.

Rekha Thomas:

1. Intro to Groebner Bases.
2. Cone Factorizations I.
3. Theta Bodies.
4. Cone Factorizations II.

Anton Leykin: Intro to Computational Algebra and Numerical Algebraic Geometry I-III.

Josephine Yu:

1. Polytopes and Tropical Hypersurfaces.
2. Groebner Fan and Constant Coefficient Tropical Varieties.

Greg Blekherman: What is Convex Algebraic Geometry?

Week 2:

Mike Stillman: Primary Decomposition I-V.

Thomas Kahle: Binomial Primary Decomposition.

Anton Leykin:

4. Singular Solutions: End Games and Deflation.
5. Numerical Irreducible and Primary Decomposition.

Josephine Yu:

3. Tropical Varieties, Mixed Volume, Bernstein's Theorem.
4. Elimination.
5. Resultants.

Greg Blekherman:

2. Cones of Nonnegative Polynomials and Sums of Squares: Duals, Faces, Boundary.
3. Dual Cone to Sums of Squares and Positive Gorenstein Ideals.
4. Real Waring Rank.

First Set of Exercises is posted here. 

Social Activities:

Saturday 6/23/2012: There will be a picnic at Piedmont Park starting at 10:30AM. Bring frisbees, soccer balls, etc. We have reserved the double-decker bandstand pavilion. The map of Piedmont park is available here.

Wednesday 6/27/2012: We will take an excursion to Stone Mountain. The bus will pick you up from the dorms at 6:30PM.