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Dhagash Mehta                                                                                                                                                               
Research Assistant Professor
email: dmehta [at] nd.edu
Dept of Chemical and Biomolecular Engineering
&
Dept of Applied and Computational Mathematics and Statistics

152B Hurley Hall
University of Notre Dame
Ph: (574) 631 6726
Fax: (574) 631 4822

I am a Research Assistant Professor at the Department of Applied and Computational Mathematics and Statistics, and Department of Chemical and Biomolecular Engineering at the University of Notre Dame. In Fall 2014, I was also a visiting research fellow at Simons Institute for Theory of Computing at Berkeley. Before joining U of Notre Dame, I was a Research Assistant Professor at Dept of Mathematics of North Carolina State University at Raleigh while also working at the Department of Chemistry of the University of Cambridge. Previously, I have held various research positions all around the globe.

News

3rd June 2016: My article, "Numerical Polynomial Homotopy Continuation Method to Locate All the Power Flow Solutions", with Hung Nguyen and Konstantin Turitsyn, has been accepted for publication in the Institute of Engineering and Technology (IET) journal of Generation, Transmission & Distribution.

1st June 2016: My article, "Kinetic transition networks for the Thomson problem and the Smale's 7th problem", with Jianxu Chen, Danny Z Chen, Halim Kusumaatmaja and David J Wales, is selected as the 'Editor's Suggestion' by the editors of the Physical Review Letters.

26th May 2016: My article, "Kinetic transition networks for the Thomson problem and the Smale's 7th problem", with Jianxu Chen, Danny Z Chen, Halim Kusumaatmaja and David J Wales, is now accepted for publication in Physical Review Letters.

20th May 2016: My new article, "Fixed Points of Belief Propagation - An Analysis via Polynomial Homotopy Continuation", with Christian Knoll, Franz Pernkopf and Tianran Chen, is now on arXiv.

18th May 2016: My new article, "Energy Landscapes of Machine Learning", with Andrew J Ballard, Jacob D Stevenson and David J Wales, is now submitted to journal. Preprint available on request.

5th May 2016: My article, "Reliable mixture critical point computation using polynomial homotopy continuation", with Hythem Sidky and Jonathan Whitmer, is now accepted for publication in American Industrial and and Chemical Engineering (AIChE) Journal.

10th April 2016: My new article, "Decomposing the parameter space of biological networks via a numerical discriminant approach", with Heather A Harrington, Helen M Byrne and Jonathan D Hauenstein, is now on arXiv.

28th January 2016: I am organizing a Tutorial Session on Recent Advances in Computational Methods for the Power Flow Equations, with Daniel Molzahn and Konstantin Turitsyn, at IEEE American Control Conference 2016.

28th January 2016: My article, "Recent Advances in Computational Methods for the Power Flow Equations", with Daniel K Molzahn and Konstantin Turitsyn, is now accepted for a Tutorial Session at IEEE American Control Conference 2016.

28th January 2016:
My new article, "Towards  Topologically Based Upper Bounds on the Number of Power Flow Solutions", with Daniel K Molzahn and Matthew Niemerg, is now accepted in a special session at IEEE American Control Conference 2016.

16th December 2015: My new article, "On the network topology dependent solution count of the algebraic load flow equations", with Tianran Chen, is on arXiv.

14th December 2015: My new article, 'Response to "Comment on 'Exploring the potential energy landscape of the Thomson problem via Newton homotopies' [J. Chem. Phys. 142, xxx (2015)]"', with Tianran Chen, John WR Morgan and David Wales, is accepted for publication in Journal of Chemical Physics.

10th December 2015: Submitted a new article, "Kinetic transition networks for the Thomson problem and Smale's 7th problem", with Jianxu Chen, Danny Z Chen, Halim Kusumaatmaja and David Wales, to a journal. Prepreint available on request.

19th November 2015: Submitted a new article, "Reliable mixture critical point computation using polynomial homotopy continuation", with Hythem Sidky and Jonathan Whitmer. Preprint available on request.

17th November 2015: Gave a talk at Department of Mathematics at Indiana University Purdue University Indianapolis.

30th October 2015: Gave talk at James Franck Institute at University of Chicago, Chicago, IL.

26th October 2015: Gave talk at Analysis Seminars Northwestern University, Evanston, IL.

6th October 2015: Gave talk at Algebra-Number Theory-Computational Mathematics seminars at Clemson University, Clemson, SC.

28th September 2015: My new article, "Recent Advances in Computational Methods for the Power Flow Equations", with Daniel K Molzahn and Konstantin Turitsyn, is submitted to the Tutorial Session at IEEE American Control Conference 2016.

25th September 2015:
My new article, "Towards  Topologically Based Upper Bounds on the Number of Power Flow Solutions", with Daniel K Molzahn and Matthew Niemerg, is submitted to a special session at IEEE American Control Conference 2016.

17th September 2015: Gave a talk at a very interesting workshop on Kinetic Networks: From Topology to Design, at Santa Fe Institute, Santa Fe, NM.

20th August 2015: My article with Tianran Chen, titled "Parallel degree computation for solution space of binomial systems with an application to the master space of N=1 gauge theories", is accepted for publication in Special Issue on Numerical Algebraic Geometry in Journal of Symbolic Computation.

7th August 2015: My article, with Markos Maniatis and Carlos Reyes, titled "Stability and symmetry breaking in a three Higgs-boson doublet model with lepton family symmetry O(2)xZ2", is accepted for publication in Physical Review D.

4th August 2015: My article, titled "Statistics of Stationary Points of Random Finite Polynomial Potentials", with Matthew Niemerg and Chuang Sun, is accepted for publication in Journal of Statistical Mechanics: Theory and Experiment.

25th July 2015: With Yan Fyodorov and Antonio Lerario, I am organizing a conference on Statistical Topology of Random Manifolds: Theory and Applications, at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, from 18-23 July 2015.

5th May 2015: My article with Tianran Chen, John W R Morgan and David Wales, titled 'Exploring the Potential Energy Landscape of the Thomson problem via Newton Homotopies', is now accepted for publication in Journal of Chemical Physics. Preprint can be available on request.

28th April 2015: My new article, titled "An index-resolved fixed-point homotopy and potential energy landscapes", with Tianran Chen, is now on arXiv.

19th April 2015: My article, titled 'Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis', with Noah Daleo, Florian Doerfler and Jonathan D Hauenstein, is accepted for publication in Chaos: An Interdisciplinary Journal of Nonlinear Science.

14th April 2015: My new article, titled "Statistics of Stationary Points of Random Finite Polynomial Potentials", with Matthew Niemerg and Chuang Sun, is now on arXiv.

9th April 2015: My article, titled "Communication: Newton homotopies for sampling stationary points of potential energy landscapes", with Tianran Chen, Jonathan Hauenstein and David Wales, is selected as a "Journal of Chemical Physics Editor's Suggestion for 2014". The article is available on arXiv here.

23rd March 2015: My new article, with Markos Maniatis and Carlos Reyes, titled "Stability and symmetry breaking in a three Higgs-boson doublet model with lepton family symmetry O(2)xZ2", is now on arXiv.

14-15th March 2015: Organized a special session, with Tianran Chen, on Homotopy Continuation Methods and Their Applications to Science and Engineering at the AMS Spring Central Sectional Meeting, Michigan State University, East Lansing, MI, USA.

26th February 2015: My new article with Tianran Chen, John W R Morgan and David Wales, titled 'Exploring the Potential Energy Landscape of the Thomson problem via Newton Homotopies', is submitted to a journal. Preprint can be available on request.

25th February 2015: My article with Crina Grosan, titled "A Collection of Challenging Optimization Problems in Science, Engineering and Economics", is accepted for publication in the proceedings of 2015 IEEE Congress on Evolutionary Computation (CEC2015) to be held at Sendai International Center, Sendai, Japan on 25-28th May, 2015. A preprint will be available on request.

23rd February 2015: My proceeding, with Souvik Chandra and Aranya Chakrabortty, titled "Equilibria Analysis of Power Systems Using a Numerical Homotopy Continuation Method", is now accepted for publication in the proceedings of 2015 IEEE Power and Energy Society General Meeting.

26th January 2015: My REU students (Joseph Cleveland, Jeffrey Dzugan, Anthony Morse and Taylor Schlenk) presented a poster, titled 'Counting The Number of Real Roots of Random Polynomials', at Joint Mathematics Meeting 2015. Their poster has been selected as an Outstanding Presentation at the meeting!

17th January 2015: My article with Souvik Chandra and Aranya Chakrabortty, titled "Exploring the Impact of Wind Penetration on Power System Equilibrium Using a Numerical Continuation Approach", is now accepted in proceedings of the 2015 American Control Conference to be held at Chicago, IL, from July 1-3, 2015. 

16th January 2015: My new article with Crina Grosan, titled "A Collection of Challenging Optimization Problems in Science, Engineering and Economics", is submitted to 2015 IEEE Congress on Evolutionary Computation (CEC2015) to be held at Sendai International Center, Sendai, Japan on 25-28th May, 2015. A preprint will be available on request.

13th January 2015: My article with Jonathan D Hauenstein, Matthew Niemerg, Nicholas J Simm and Daniel Stariolo, titled "Energy Landscape of the Finite-Size Mean-field 2-spin Spherical Model and Topology Trivialization", is  accepted for publication in Physical Review E.

12th January 2015: My new article with Tianran Chen, titled "Parallel degree computation for solution space of binomial systems with an application to the master space of N=1 gauge theories", is on arXiv.

24th December 2014: My article with Jonathan D Hauenstein, Rijun Hung and Yang Zhang, titled "Global Structure of Curves from Generalized Unitary Cut of Three-loop Diagrams", is accepted for publication in Journal of High Energy Physics.

17th December 2014: Final exam of my class of ACMS 20620 (Applied Linear Algebra) today!

5th December 2014: My new article, titled 'Certified counting of roots of random univariate polynomials', with Joseph Cleveland, Jeffrey Dzugan, Jonathan D Hauenstein, Ian Haywood, Anthony Morse, Leonardo Robol and Taylor Schlenk, is now on arXiv. This paper is an outcome of my REU project with my REU students.

3rd December 2014: My new article, titled 'Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis', with Noah Daleo, Florian Doerfler and Jonathan D Hauenstein, is now on arXiv.

1st December 2014: Submitted a new proceeding, titled "Equilibria Analysis of Power Systems Using a Numerical Homotopy Continuation Method", with Souvik Chandra and Aranya Chakrabortty, to 2015 IEEE Power and Energy Society General Meeting.

25th October 2014: Organized a special session on Computational Algebraic Geometry and its Applications to Science and Engineering at AMS Fall Western Sectional Meeting, San Francisco State University, San Francisco, CA, with Daniel Brake.

13th October 2014: Enjoying the workshop on Solving Polynomial Equations at Simons Institute for Theory of Computing, Berkeley, CA.

1st October 2014:
My new paper with Jonathan D Hauenstein, Matthew Niemerg, Nicholas J Simm and Daniel A Stariolo, titled "Energy Landscape of the Finite-Size Mean-field 2-spin Spherical Model and Topology Trivialization", is on arXiv.

30th September 2014:
My new paper with Souvik Chandra and Aranya Chakrabortty, titled "Exploring the Impact of Wind Penetration on Power System Equilibrium using a Numerical Computation Approach", is submitted to a special session in American Control Conference 2015. A preprint is available here.

29th September 2014: The article with Tianran Chen, Jonathan D Hauenstein and David J Wales, titled "Newton homotopies for sampling stationary points of potential energy landscapes", is now published online in the Communications in Journal of Chemical Physics and is available here.

17th September 2014: My article with Tianran Chen, Jonathan D Hauenstein and David J Wales, titled "Newton homotopies for sampling stationary points of potential energy landscapes", is accepted for publication in the Communications in Journal of Chemical Physics.

12th September 2014: My article, Experiments on the zeros of harmonic polynomials using certified counting, with Jonathan D Hauenstein, Antonio Lerario and Erik Lundberg, has been accepted for publication in Journal of Experimental Mathematics.

8th September 2014: Awarded 100K core hours of Class C computational allocation at Fermilab Lattice QCD clusters as the only PI.

26th August 2014: Teaching started. I am teaching ACMS 20620 (Applied Linear Algebra) this semester.

22nd August 2014: Joined Dept of Applied and Computational Mathematics and Statistics at the University of Notre Dame!

22nd August 2014: My article with Noah S Daleo, Jonathan D Hauenstein and Christopher Seaton, titled "Gauge-fixing on the lattice via Orbifolding", is now accepted for publication in Physical Review D.

15th August 2014:
My new article with Jonathan D Hauenstein, Rijun Hung and Yang Zhang, titled "Global Structure of Curves from Generalized Unitary Cut of Three-loop Diagrams", is on arXiv.

12th August 2014: My new article with Hung D Nguyen and Konstantin Turitsyn, titled "Numerical Polynomial Homotopy Continuation Method to Locate All The Power Flow Solutions", is on arXiv.

7th August 2014: Submitted a new article with Tianran Chen, Jonathan D Hauenstein and David J Wales, titled "Newton homotopies for sampling stationary points of potential energy landscapes", to journal.

30th July 2014:
My REU students presented their poster at the Undergraduate Research Symposium at North Carolina State University. Today is also the last day for the REU program.

26th June 2014: My new article with Noah S Daleo, Jonathan D Hauenstein and Christopher Seaton, titled "Gauge-fixing on the lattice via Orbifolding", is on arXiv.

24th June 2014: My new article with Jonathan D Hauenstein, Antonio Lerario andErik Lundberg, titled "Experiments on the zeros of harmonic polynomials using certified counting" is on arXiv.

3rd June 2014: My article with Markos Maniatis, titled "Exact minimization of the Higgs potentials", is published in European Journal of Physics Plus.

26th May 2014: My REU students have arrived! Looking forward to work with them.

23rd May 2014: My article with Jonathan D Hauenstein and David J Wales, titled "Certification and the Potential Energy Landscape", is accepted for publication in Journal of Chemical Physics.

18th May 2014: My article with Ciaran Hughes, Michael Kastner and David J Wales, titled "Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points", is accepted for publication in Journal of Chemical Physics.

9th May 2014: My article with Mario Schroeck, titled "`Enumerating copies in the first Gribov region on the lattice in up to four dimensions", is accepted for publication in Physical Review D.

29th April 2014:
My article with Ciaran Hughes and David J Wales, titled "An Inversion-Relaxation Approach for Sampling Stationary Points of Spin Model Hamiltonians", is accepted for publication in Journal of Chemical Physics.

3rd March 2014:
My article with Mario Schroeck, titled "Enumerating Copies in the First Gribov Region on the Lattice in up to four Dimensions", submitted on arXiv. The arXiv version is here.

3rd December 2013:
My article with Aoife Kelly, Jon-Ivar Skullerud, Chris Allton and Mehmet B Oktay, "Spectral functions of charmonium from 2 flavour anisotropic lattice data", is accepted in Proceedings of Science (LATTICE13). The arXiv version is here.

14th November 2013: My article with Simon Catterall and David J Weir, "Eigenvalue spectrum of lattice N=4 super Yang-Mills", is accepted in Proceedings of Science (LATTICE13). The arXiv version is here.

1st November 2013: My paper with Ciaran Hughes, Mario Schroeck and David J Wales, "Potential energy landscapes for the 2D XY model: Minima, transition states, and pathways", is accepted for publication in Journal of Chemical Physics. The arXiv version is here.

15th September 2013: My article with Jonathan D Hauenstein and Yang-Hui He, "Numerical elimination and moduli space of vacua", is published in Journal of High Energy Physics. The arXiv version is here.

4th August 2013: Successfully organized a mini-symposium on Applications of Computational and Numerical Algebraic Geometry to Theoretical Physics at Society for Industrial and Applied Mathematics (SIAM) Algebraic Geometry 2013, at Fort Collins, Colorado, with Yang-Hui He.

5th July 2013: Markos Maniatis and myself uploaded an article, "Exact Minimization of Higgs Potentials", on arXiv.






Conferences