2007 IMA PI Summer Program for Graduate Students
Applicable Algebraic Geometry
Texas A&M University in College Station, Texas
23 July- 10 August, 2007
Schedule
All lectures and problem sessions will be held in Blocker 165, the computer labs will be held in Blocker 131 and Blocker 125 , and the refreshements will be in Blocker 112.
The Summer Graduate Program begins with registration at 8:30 AM on Monday, 23 July 2007 in Blocker hall just outside of room 165.
Week 1
Frank Sottile: Introduction to algebraic geometry and Gröbner bases Some notes
Thorsten Theobald: Introduction to real algebraic geometry and sums of squares.
            Some notes. Exercises for Part 1.
Monday
23 July		 Tuesday
24 July		 Wednesday
25 July		 Thursday
26 July		 Friday
27 July
9:00--10:30 Orientation Sottile 2
Gröbner bases		 Sottile 3
Resultants		 Sottile 4
Solving polynomials		 Sottile 5
Structure of Varieties
10:30--11:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
11:00 -- 12:30 Sottile 1
Ideals and varieties		 Theobald 2
Eigenvalue techniques		 Theobald 3
Real roots in
the multivariate case		 Theobald 4
Global optimization
and sums of squares		 Theobald 5
Semidefinite programming
12:30 -- 2:00 Lunch Lunch Lunch Lunch Lunch
2:00 -- 3:30 First Steps in
Computer Algebra		 Computer Lab
Singular		 Problem Session Problem Session Computer Lab
SeDuMi
3:30 -- 4:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
4:00 -- 5:15 Theobald 1
Real roots of
univariate polynomials 		Seminar
James Ruffo		 Seminar
Hal Schenck		 Seminar
John Keyser		 Seminar
J. Maurice Rojas
Evening Picnic
Week 2
Frank Sottile: Projective Varities and Toric varieties
Thorsten Theobald: Optimization and tropical geometry.
Monday
30 July		 Tuesday
31 July		 Wednesday
1 August		 Thursday
2 August		 Friday
3 August
9:00--10:30 Sottile 6
Projective varieties		 Sottile 7
Toric ideals		 Sottile 8
Hilbert Function
and Degree		 Sottile 9
Toric varieties		 Sottile 10
Bernstein's theorem;
homotopy methods
10:30--11:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
11:00 -- 12:30 Theobald 6
Algebraic certificates
and Positivstellensätze		 Theobald 7
Constrained
optimization		 Theobald 8
Tropical geometry		 Theobald 9
Algebraic techniques		 Theobald 10
Amoebas and
deformations
12:30 -- 2:00 Lunch Lunch Lunch Lunch Lunch
2:00 -- 3:30 Problem Session Problem Session Computer Lab Computer Lab Problem Session
3:30 -- 4:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
4:00 -- 5:15 Seminar
Luis Garcia		 Seminar
Laura Matusevich		 Seminar
Frank Sottile		 Seminar
Josephine Yu
Evening Ice Skating
Week 3
Seth Sullivant: Algebra and Probability
Serkan Hosţen: Algebra and Statistical Inference
Monday
6 August		 Tuesday
7 August		 Wednesday
8 August		 Thursday
9 August		 Friday
10 August
9:00--10:30 Sullivant 1
Statistical Models are
Semi-Algebraic Sets		 Sullivant 2
Conditional Independence		 Sullivant 3
Graphical Models		 Sullivant 4
Phylogenetic Models
10:30--11:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
11:00 -- 12:30 Hosten 1
Log-linear and
Hierarchical Models		 Hosten 2
Maximum Likelihood
Estimation		 Hosten 3
Complexity of
Markov Bases of
Hierarchical Models		 Hosten 4
The maximum
likelihood degree		 Sullivant 5
Gaussian
Bayesian Networks
12:30 -- 2:00 Lunch Lunch Lunch Lunch Lunch
2:00 -- 3:30 Cancelled Computer Lab Question Session Computer Lab Hosten 5
Parametric Inference
3:30 -- 4:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
4:00 -- 5:15 Seminar
Darbha Swaroop		 Seminar
Thorsten Theobald		 Seminar
Serkan Hosţen		 Seminar
Seth Sullivant
Evening Conference Dinner
Café Eccell
This summer graduate program is supported by the Participating Institutions of the Institute for Mathematics and its Applications, by the US National Science Foundation, and by the Texas A&M University.
Modified since: 18 July 2007.