Google Scholar profile

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. new

[3] Spectrahedral Geometry of Graph Sparsifiers (with Catherine Babecki and Stefan Steinerberger), June 2023. new

[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 (with Erin Connelly, Sameer Agarwal and Alperen Ergur), January 2023. new

[14] Two Views of P3, June 2023. new

[15] Lines, Quadrics and Cremona Transformations in Two-View Geometry (with Erin Connelly and Cynthia Vinzant), August 2023. new

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.