Familiarity with graduate level mathematics in topics such as numerical linear algebra, optimization, or algebraic geometry.

This course offers an introduction to both theoretical and computational methods for working with such models.

It is aimed at graduate students from across the mathematical sciences (Mathematics, EECS, Statistics, Physics, etc).

**Consultants:**
Qingchun Ren
and
Jose Rodriguez
will help with the course.

One of them will
be available for your questions on
Fridays between 11am and 1pm.

Homework 1 is due Monday, January 27.

Homework 2 is due Monday, February 3.

Homework 3 is due Monday, February 10.

Homework 4 is due Wednesday, February 19.

Homework 5 is due Monday, February 24.

Homework 6 is due Monday, March 3.

Homework 7 is due Monday, March 10.

especially if you collaborate with another students whose background is different from yours.

Term papers are posted below, next to the names of the students and their presentation dates.

Bates-Hauenstein-Sommese-Wampler: Numerically Solving Polynomial Systems with Bertini, SIAM, 2013.

Blekherman-Parrilo-Thomas: Semidefinite Optimization and Convex Algebraic Geometry, SIAM, 2013.

Cox-Little-O'Shea: Using Algebraic Geometry, Springer, 2005.

Landsberg: Tensors: Geometry and Applications, American Mathematical Society, 2012.

Sottile: Real Solutions to Equations from Geometry, American Mathematical Society, 2011.

Auditors interested in a particular topic are welcome to attend just that week. Enrolled students will attend all weeks.

Jan 22-24: Gröbner Basics

Jan 27-31: Elimination

Feb 3-7: Decomposing Varieties

Feb 10-14: Sparse Polynomial Systems

Feb 19-21: Semidefinite Programming

Feb 24-28: Nonnegative Polynomials and Sums of Squares

Mar 3-7: Invariant Theory and Tensors

Mar 10-14: Representation Theory and Tensors

Mar 17-21: Tropical Algebra

Mar 31-April 2: Nash Equilibria

April 4: Shamil Shakirov: Nonlinear algebra in physics

April 7: Jose Rodriguez: Numerical algebraic geometry

April 9: Qingchun Ren: Phylogenetics

April 11: Bernd Sturmfels: Get real

April 14-18: No Lectures

April 21: Ralph Morrison: Commuting tropical matrices

Joe Kileel: The calibrated trifocal variety

April 23: Andrew Lampinen: Minimal embedding dimension bounds for receptive fields

Kaie Kubjas and Zvi Rosen: Completion of rank one probability matrices

April 25: Jacob Emmert-Aronson and Moor Xu: Quintic spectrahedra

Frank Ban: Permanent versus determinant

April 28: Marco Vivero Avila: Retrosynthetic analysis via weighted graphs

Elina Robeva: Orthogonal tensor decomposition

April 30: Weiqiao Han: Singularities and genus of the k-ellipse

Danny Hermes: Principal components analysis in non-Euclidean spaces

May 2: Eric Lee and Madhusudan Manjunath: Steady states in metabolism

Emmanuel Tsukerman: Dimension of Gram spectrahedra

May 5: Matt Xuan: Duality and optimization

Bo Lin: Almost toric hypersurfaces