Graphical Designs and Graph Sparsifiers
[1]
Graphical designs and Gale duality
(with Catherine Babecki), Mathematical Programming, 200:2 (2023), 703-737.
[2] Random Walks, Equidistribution and Graphical Designs
(with Stefan Steinerberger), June 2022.
[3]
Spectrahedral Geometry of Graph Sparsifiers (with Catherine Babecki and Stefan Steinerberger),
June 2023.
[4]
Conformally rigid graphs (with Stefan Steinerberger),
February 2024. new
Algebraic Methods in Computer Vision
[1]
A QCQP Approach to Triangulation (with Chris Aholt and Sameer Agarwal),
Computer Vision - ECCV 2012 ,
Lecture Notes in Computer Science, 7572 (2012), 654-667.
[2]
A Hilbert scheme in computer vision (with Chris Aholt and Bernd Sturmfels),
Canadian Journal of Mathematics 65:5 (2013), 961-988.
[3]
The Euclidean distance degree of an algebraic variety (with
Jan Draisma, Emil Horobet, Giorgio Ottaviani and Bernd Sturmfels),
Foundations of Computational Mathematics 16:1 (2016), 99-149.
[4]
Counting real critical points of the distance to spectral matrix sets (with
Dimitriy Drusvyatskiy and Hon-Leung Lee), SIAM J. Matrix Analysis and Applications , 36:3 (2015),1360-1380.
[5]
The Euclidean distance degree of orthogonally invariant matrix varieties (with
Dimitriy Drusvyatskiy, Hon-Leung Lee and Giorgio Ottaviani),
Israel Journal of Mathematics, 221:1 (2017), 291-316.
[6]
Certifying the existence of epipolar matrices (with
Sameer Agarwal, Hon-Leung Lee and Bernd Sturmfels),
July 2014.
[7]
On the existence of epipolar matrices (with
Sameer Agarwal, Hon-Leung Lee and Bernd Sturmfels),
Int. J. Comput. Vis. 121:3 (2017), 403-415.
[8]
Ideals of the Multiview Variety,
(with Sameer Agarwal and Andrew Pryhuber)
IEEE Transactions on Pattern Analysis and Machine Intelligence,
43:4 (2021), 1279-1292.
[9]
On the local stability of semidefinite relaxations
(with Diego Cifuentes, Sameer Agarwal and Pablo A. Parrilo),
Mathematical Programming 193:2 (2022), 629-663.
[10]
Existence of two view chiral reconstructions
(with Andrew Pryhuber and Rainer Sinn), SIAM J. Applied Algebra and Geometry, 6:1 (2022),
41-76.
[11]
The chiral domain of a camera arrangement
(with Sameer Agarwal, Andrew Pryhuber, and Rainer Sinn), J. Mathematical Imaging and Vision,
64 (2022), 948-967.
[12]
An Atlas for the Pinhole Camera
(with Sameer Agarwal, Timothy Duff and Max Lieblich), Foundations of Computational Mathematics, (2022), published online.
[13]
The geometry of rank drop in a class of face-splitting matrix products: Part I
(with Erin Connelly, Sameer Agarwal and Alperen Ergur), Advances in Geometry, 24:3 (2024), 369-394.
[14]
Two Views of P3 ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, Tromso, Norway,
(2023) 7-12.
[15]
The geometry of rank drop in a class of face-splitting matrix products: Part II
(with Erin Connelly and Cynthia Vinzant), Advances in Geometry, 24:3, (2024), 395-420.
Extremal Graph Theory
[1]
Symmetric sums of squares over k-subset hypercubes
(with Annie Raymond, James Saunderson and Mohit Singh),
Mathematical Programming Series A, 167:2 (2018), 315-354.
[2]
Symmetry in Turán sums of squares polynomials from flag algebras
(with Annie Raymond and Mohit Singh), Algebraic Combinatorics 1:2 (2018), 249-274.
[3]
Simple graph density inequalities with
no sum of squares proofs (with Greg Blekherman, Annie Raymond and Mohit Singh),
Combinatorica, 40:4 (2020), 455-471.
[4]
Tropicalization of graph profiles
(with Greg Blekherman, Annie Raymond and Mohit Singh), Transactions of the AMS, 375 (2022), 6281-6310.
link to article
Lifts of Convex Sets
[1]
Theta bodies for polynomial ideals (with João Gouveia and Pablo A. Parrilo),
SIAM Journal of Optimization
20:4 (2010), 2097-2118.
[2] Convex Hulls of Algebraic Sets , (with João Gouveia), chapter in the "Handbook of Semidefinite, Cone and Polynomial Optimization", International Series in Operations Research & Management Science, Vol. 166, Miguel Anjos and Jean-Bernard Lasserre (eds), Springer, 2012.
[3]
A new hierarchy of semidefinite programming relaxations for cycles in binary
matroids and cuts in graphs (with João Gouveia, Monique Laurent
and Pablo A. Parrilo), Mathematical Programming, Series A, 133:1-2 (2012), 203-225.
[4]
Lifts of convex sets and cone factorizations (with João Gouveia and Pablo A. Parrilo), Mathematics of Operations Research 38 (2013), 248-264.
[5]
Polytopes of minimum positive semidefinite rank
(with João Gouveia and Richard Robinson),
Discrete & Computational Geometry 50:3 (2013), 679-699.
[6]
Which nonnegative matrices are slack matrices? (with João Gouveia,
Roland Grappe, Volker Kaibel, Kanstanstin Pashkovich and Richard Robinson),
Linear Algebra and its Applications 439 (2013), 2921-2933.
[7]
Approximate cone factorizations and lifts of polytopes (with
João Gouveia and Pablo A. Parrilo),
Isaac Newton Institute preprint NI13069-POP,
Mathematical Programming, 151:2 (2015),
613-637.
[8]
Worst-case results for positive semidefinite rank (with
João Gouveia and Richard Robinson),
Mathematical Programming Series B, 153:1 (2015) 201-212.
[9]
Positive semidefinite rank (with
Hamza Fawzi, João Gouveia, Pablo A. Parrilo and Richard Z. Robinson),
Math Programming Series B , 153:1 (2015), 133-177.
[10]
Four dimensional polytopes of minimum positive semidefinite rank, (with
João Gouveia, Kanstanstin Pashkovich and Richard Z. Robinson),
J. Combin. Theory Ser. A 145 (2017), 184--226.
[11]
Spectrahedral lifts of convex sets
Proceedings of the International Congress of Mathematicians -- 2018 Rio de Janeiro, 3 (2018),
3807--3830.
[12]
The slack realization space of a polytope
(with João Gouveia, Antonio Macchia and Amy Wiebe),
SIAM J. Discrete Math., 33:3, (2019) 1637-1653.
[13]
Projectively unique polytopes and
toric slack ideals (with João Gouveia, Antonio Macchia and Amy Wiebe), J. Pure and Applied Algebra, 224:5 (2020), 106-229.
[14]
Lifting for simplicity: concise descriptions of convex sets
(with Hamza Fawzi, Joao Gouveia, Pablo A. Parrilo, and James Saunderson), SIAM Review,
64:4 (2022) published online
Toric Ideals and Integer Programming
[1] An algebraic geometry
algorithm for scheduling in presence
of setups and correlated demands (with Sridhar R. Tayur and
N.R.Natraj), Mathematical Programming, 69 (1995), 369-401.
[2] Groebner bases and
triangulations of the second hypersimplex
(with Jesus de Loera and Bernd Sturmfels), Combinatorica
15 (1995), 409-424.
[3] A geometric Buchberger
algorithm for integer programming,
Mathematics of Operations Research, 20 (1995),
864-884.
[4] Groebner bases in integer programming
(with Serkan Hosten),
OPTIMA Mathematical Programming Society Newsletter,
48 (1995).
[5] Test sets and inequalities for integer
programs (with Robert Weismantel)
Proceedings of the 5th International IPCO conference, Vancouver ,
LNCS 1084 (1996) 16-30.
[6] Variation of cost
functions in integer programming
(with Bernd Sturmfels), Mathematical Programming
77 (1997), 357-387.
[7] Truncated Groebner bases
for integer programming (with Robert Weismantel), Applicable
Algebra in Engineering, Communication and Computing 8 (1997), 241-257.
[8] Applications to integer programming,
in Applications of Computational Algebraic Geometry,
D.A. Cox and B. Sturmfels eds.,
AMS Proceedings of Symposia in Applied Mathematics, 53
(1997), 119-142.
[9] Groebner bases in
integer programming,
Handbook of Combinatorial Optimization Vol. 1,
D.-Z. Du and P.M.Pardalos eds., Kluwer Acad. Publ.,
Boston, MA (1998) 533-572.
[10] Groebner bases and integer programming
(with Serkan Hosten), Groebner Bases and
Applications, B.Buchberger and F.Winkler eds.,
Cambridge University Press, London Math. Soc. Lecture Notes Series
251 (1998), 144-158.
[11] The associated primes
of initial ideals of lattice ideals (with Serkan Hosten),
Mathematical Research Letters, 6 (1999), 83-97.
[12] Standard pairs and group
relaxations in integer programming (with Serkan Hosten),
Journal of Pure and Applied Algebra, 139
(1999), 133-157.
[13] Algebraic methods in
integer programming, Encyclopedia of
Optimization (eds: C. Floudas and P. Pardalos), Kluwer Academic
Publishers, Dordrecht, 2001
[14] Gomory Integer Programs (with
Serkan Hosten), Mathematical Programming, Series B,
96 (2003), 271 - 292.
[15]
Toric initial ideals of $\Delta$-normal configurations:
Cohen-Macaulayness and degree bounds (with Edwin O'Shea),
Journal of Algebraic Combinatorics, 21
(2005), 247 - 268.
[16] The structure of group
relaxations
Discrete Optimization (eds: K. Aardal, G. Nemhauser, R. Weismantel),
Handbooks in Operations Research and Management Science,
12, Elsevier, 2005.
[17]
The circuit ideal of a vector configuration (with Tristram
Bogart and Anders Jensen), Journal of Algebra, 309:2 (2007), 518-542.
[18]
Small Chvatal rank (with Tristram Bogart and Annie Raymond),
Mathematical Programming Series B, 124:1-2 (2010), 45-68.
Toric Hilbert Schemes
[1] Combinatorics of the toric Hilbert
scheme (with Diane Maclagan), Discrete and Computational
Geometry 27 (2002), 249-264.
[2] Algorithms for the toric Hilbert
scheme (with Mike Stillman and Bernd Sturmfels), a chapter in
Computations in Algebraic Geometry with Macaulay 2 (eds:
D. Eisenbud, D. Grayson, M. Stillman and B. Sturmfels), Algorithms and
Computation in Mathematics Vol 8, Springer 2002, 179-213
[3]
The toric Hilbert scheme of a rank two lattice
is smooth and irreducible (with Diane Maclagan),
Journal of Combinatorial Theory, Series A, 104:1 (2003), 29-48.
Groebner bases, Groebner fans and Tropical Varieties
[1] Computing Groebner
fans of toric ideals (with Birk Huber),
Experimental Mathematics 9 (2000)
321-331.
[2]
The Hilbert zonotope and a polynomial
time algorithm for universal Groebner bases (with
Eric Babson and Shmuel Onn), Advances in Applied Math
30 (2003) 529-544.
[3] Computing tropical varieties (with Tristram Bogart, Anders Jensen,
David Speyer and Bernd Sturmfels), Journal of Symbolic
Computation, 42:1-2 (2007), 54-73.
[4]
The generic Groebner walk (with Komei Fukuda, Anders Jensen and
Niels Lauritzen), Journal of Symbolic
Computation, 43:3 (2007), 298-312.
[5] Computing Groebner fans (with Komei Fukuda and Anders
N. Jensen), Mathematics of Computation,
76 (2007), 2189-2212.
[6] Nice initial
complexes of some classical ideals (with Aldo Conca and Serkan
Hosten), Contemporary Math., 423
(2007), 11-42.
Algebraic Combinatorics and Representation Theory
[1]
Symmetric iterated Betti numbers (with Eric Babson and Isabella
Novik), Journal of Combinatorial Theory,
Series A, 105 (2004), 233 - 254.
[2]
Reverse lexicographic and lexicographic shifting (with Eric
Babson and Isabella Novik), Journal of Algebraic Combinatorics,
23:2 (2006), 107 - 123.
[3] Moduli spaces of graded representations of finite
dimensional algebras (with Eric Babson and Birge Huisgen-Zimmermann),
Contemporary Math., 419 (2006), 7-27.
[4]
Moduli of McKay quiver representations I: the coherent component
(with Alastair Craw and Diane Maclagan), Proceedings
of the London Math. Society (3), 95:1 (2007),
179-198.
[5]
Moduli of McKay quiver representations II: Groebner basis techniques
(with Alastair Craw and Diane Maclagan),
Journal of Algebra, 316:2 (2007), 514-535.
Other Topics
[1] Creating weekly timetables for
maximizing employee preferences (with Caleb Z. White, Youngbae
Lee, Yoonsoo Kim and Patrick Perkins), The UMAP Journal,
25:1 (2004), 5 - 24.