**Office: Blocker 601H**

Office hours: Tues. 10:30-11:30, Wed. 10-11 or by appointment

**E-mail: **jml@math.tamu.edu

TAMU math dept homepage

Fall 2015 teaching: Math 623, Fall 15:

Differential Geometry II

Meeting: MWF 12:40-1:30pm Blocker 202

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:My CV (last updated 9/15)

Geometry seminar, meeting Mondays 3-4 Blocker 220 and Fridays 4-5pm Blocker 628.

Working seminar for post-docs and graduate students meeting Wednesdays, Blocker 624,

3-4pm

Everyone is welcome to the seminars, graduate students

are particularly encouraged to attend.

TAMU seminar calendar

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.

Survey articles

PAPERS/PREPRINTS in past 5 years

On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication (with N. Ryder) Permanent vs determinant: an exponential lower bound assuming

symmetry and a potential path towards Valiant's conjecture (with N. Ressayre)On minimal free resolutions and the method of shifted partial derivatives in complexity theory (with K. Kefremenko, H. Schenck and J. Weyman) Abelian Tensors (with Mateusz Michalek) Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group (with S. Kumar, Discrete Math. 2015) Complexity of linear circuits and geometry (with F. Gesmundo, G. Hauenstein and C. Ikenmeyer, to appear in FOCM) Geometric Complexity Theory: an introduction for geometers (Ann. U. Ferrara 2015)

Computer aided methods for lower bounds on the border rank (with G. Hauenstein and C. Ikenmeyer, Exper. Math. 2013)

Explicit tensors of border rank at least 2n-2 (J. Pure. Appl. Alg. 2015)

New lower bounds for the rank of matrix multiplication (SICOMP, 2014)

Padded polynomials, their cousins, and geometric complexity theory (with H. Kadish, Communications in Algebra 2014) New lower bounds for the border rank of matrix multiplication (with G. Ottaviani, Theory of Computing 2015) On the third secant variety (with J. Buczynski, JAC 2014) On the geometry of Tensor Network States (with Y. Qi and K. Ye, QIC, 2012) Equations for secant varieties of Veronese and other varietites (with G. Ottaviani, Annali di Matematica Pura e Applicata, 2013) Fubini-Griffiths-Harris rigidity of homogeneous varieties (with C. Robles, IMRN 2013) Determinental equations for secant varieties and the Eisenbud-Koh-Stillman conjecture (with J. Buczynski and A. Ginesky, J.London Math. Soc. 2013)

Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program (with L. Manivel and N. Ressayre, CMH 2013) P versus NP and geometry ( J. Symb. Comp.2010, MEGA 2009 special issue)

Ranks of tensors and a generalization of secant varieties (with J. Buczynski, LAA special issue on tensors 2013) An overview of mathematical issues arising in the Geometric complexity theory approach to VP \neq VNP (with P. Buergisser, L. Manivel and J. Weyman, SIAM J. Comp. 2011) Holographic algorithms without matchgates (with Jason Morton and Serguei Norine, LAA special issue on tensors 2013) On the ranks and border ranks of symmetric tensors (with Z. Teitler, FOCM 2010) Maple file to be read with billards article below (also click here for text version) On the Debarre-deJong and Beheshti-Starr conjectures on varieties with too many lines (with O. Tommasi, Mich. Math. J. 2010) Lines on hypersurfaces (with C. Robles, J. London Math. Soc. 2010) On secant varieties of compact Hermitian symmetric spaces (with J. Weyman, J. Pure Appl. Alg. 2009) Fubini's theorem in codimension two (with C. Robles, Crelle 2009) Fubini-Griffiths-Harris rigidity and Lie algebra cohomology (with C. Robles, (Asian Math. J. 2013)

all articles (since 2006)

Books:An introduction to Geometric Complexity Theory (to appear in the Newsletter of the EMS) Exterior differential systems, Lie algebra cohomology, and the rigidity of homogeneous varieties (2008) Differential geometry of submanifolds of projective space (2006) Exterior differential systems and billiards (2006) Representation theory and projective geometry (with L. Manivel), 2004

Tensors: Geometry and Applications.

AMS GSM 128. Click here to see table of contents and preface, and to order.

Click here for corrections and additionsCartan For Beginners: Differential geometry via moving frames and exterior differential systems (with T. Ivey)

AMS GSM 61 . To see the table of contents, preface, and selected pages click here

To order the book from the AMS, click here.

to see corrections to text, click here

math reviews of all published papersLuke Oeding, PhD May 2009, Defining equations of the varietyof principal minors solved a conjecture of Holtz and Sturmfels.

PhD students:

Current students: Cameron Farnsworth, Fulvio Gesmundo, Younghui Guan, and Curtis Porter.

Graduated students:

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.

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, thesis: Nongenericity of variations of Hodge structure for hypersurfaces of high degree,

published in Duke. Math. J.

New to the area? Here are some Brazos Valley links

Now available:

## Sungbook: A Collection of Korean Short Stories

available at Amazon (both paperback and kindle):