Office: Blocker 601H
Office hours: Tues. and Thurs.
10-11am
E-mail: jml@math.tamu.edu
TAMU
math dept homepage
Supported
by NSF grant DMS-1405368
Teaching Fall 2016: Geometry and complexity
theory Math
662
Meeting: MWF 10:20 - 11:10 Bloc 624
Fall 2014 I served as Chancellor's Professor at
the Simons
Institute for the Theory of Computing,
UC Berkeley,
and co-organized (with P. Burgisser, K. Mulmuley
and B. Sturmfels) of the semester long program Algorithms
and Complexity in Algebraic Geometry
During
the semester I gave a course on Geometry
and Complexity Theory, and have notes
for the course.
Honors combined ScB and MS, Mathematics, Brown University, 1986 (MS thesis director, K. Nomizu)
PhD., Mathematics, Duke University, 1990 (director R. Bryant)
Habilitation., Mathematics, Universite Toulouse, 1997 (directeur, C. Simpson)
I organize and co-organize:
Geometry seminar, meeting Fridays 4-5pm Blocker 628.
Working seminar for post-docs and graduate students meeting Tuesdays, Blocker 506A,
9:30-10:30am
Everyone is welcome to the seminars, graduate students
are particularly encouraged to attend.
TAMU seminar calendar
My CV (last updated 10/16)
My travel plans
I am on the editorial board of Foundation of Computational Mathematics, Differential Geometry and its Applications, and Linear Algebra and its Applications.
**DGA special issue on geometry and complexity theory**
The journal Differential Geometry and its Applications http://ees.elsevier.com/dga/ will be having a special thematic issue dedicated to geometry and complexity theory. I encourage you to submit an article for consideration.
I am trying to put together a high quality issue that will increase the visibility of this emerging area. Moreover, having an issue dedicated to the geometry and complexity will increase the visibility of each individual article as well, as previously, articles in the area have been appearing in a wide range of publications. The deadline for submissions is Dec. 31, 2016.
If you submit through the DGA webpage, be sure to include in your cover letter that it is for the thematic issue. If you have any questions about the thematic issue, please do not hesitate to contact me at jml@math.tamu.edu.
PAPERS/PREPRINTS in past 5 years
The geometry of rank decompositions of matrix multiplication I: 2x2 matrices (with L. Chiantini, C. Ikenmeyer and G. Ottaviani)
On the complexity of the permanent in various computational modes (with C. Ikenmeyer)
The method of shifted partial derivatives cannot separate the permanent from the determinant (with K. Efremenko, H. Schenck, and J. Weyman)
A 2n^2-log_2(n)-1 lower bound for the border rank of matrix multiplication (with M. Michalek)
Padded polynomials, their cousins, and geometric complexity theory (with H. Kadish, Communications in Algebra 2014)
Determinental equations for secant varieties and the Eisenbud-Koh-Stillman conjecture (with J. Buczynski and A. Ginesky, J.London Math. Soc. 2013)
Survey articles
Books:
Geometry and complexity theory: to be published spring 2017 by Cambridge University press. Click here to see a draft copy
Tensors: Geometry and Applications.
AMS GSM 128. Click here to see table of contents and preface, and to order.
Click here for corrections and additions
Cartan For Beginners: Differential geometry via moving frames and exterior differential systems,
Second Edition (with T. Ivey) AMS GSM 175
http://bookstore.ams.org/gsm-175
Slides of recent talks:
Complexity theory and geometry (Berlin Mathematical School colloquium 2/15)
Perm v. det: an exponential lower bound assuming symmetry (Innovations in Theoretical Computer Science 1/16)
math reviews of all published papers
PhD students:
Current students: Kashif Bari, Fulvio Gesmundo, and Yao Wang
Graduated students:
Cameron Farnsworth, August 2016, THE POLYNOMIAL WARING PROBLEM AND THE DETERMINANT
Yonghui Guan, August 2016, EQUATIONS FOR CHOW VARIETIES, THEIR SECANT VARIETIES AND
OTHER VARIETIES ARISING IN COMPLEXITY THEORY
Curtis Porter, August 2016 THE LOCAL EQUIVALENCE PROBLEM FOR 7-DIMENSIONAL, 2-NONDEGENERATE CR
MANIFOLDS WHOSE CUBIC FORM IS OF CONFORMAL UNITARY TYPE
Yang Qi, PhD August 2013 Geometry of Feasible Spaces of Tensors
determined defining equations for the third secant variety of a triple Segre product and closedness of tensor network states
Ke Ye, PhD August 2012, IMMANANTS, TENSOR NETWORK STATES AND THE GEOMETRIC
COMPLEXITY THEORY PROGRAM determined symmetry groups of immanents, and closedness of tensor network states
Ming Yang, PhD Sept. 2012, On partial and generic uniqueness of block term tensor decompositions in signal processing, solving questions originating in signal processing.
Luke Oeding, PhD May 2009, Defining equations of the varietyof principal minors solved a conjecture of Holtz and Sturmfels.
Frederic Holweck, PhD fall 04, Dual varieties, simple singularities and simple Lie algebras
Here is a summary of his results in English
E. Allaud, PhD spring 03, Nongenericity of variations of Hodge structure for hypersurfaces of high degree,
New to the area? Here are some Brazos Valley links
Now available:
by Suil Kang (Author)
available at Amazon (both paperback and kindle):
Various links
tamuwebmail