## Time |
## Monday |
## Tuesday |
## Wednesday |
## Thursday |
## Friday |

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 http://aga2012.wikidot.com.**

**Guest Lecturer Visit Times and Preliminary Lecture Titles:**

Alicia Dickenstein: Computational algebra and biochemical reaction networks

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