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«Dr Dhagash Mehta Postal Add.: 152B, Hurley Hall, Dept of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, ...»

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Dr Dhagash Mehta

Postal Add.: 152B, Hurley Hall, Dept of Applied and Computational Mathematics and Statistics,

University of Notre Dame, Notre Dame, IN 46556, USA.

Email: dmehta@nd.edu; dhagashb@yahoo.com. Ph: +1-574-631-6726


Academic Positions

Aug 2014 - Present Research Assistant Professor in the Dept of Applied and Computational

Mathematics and Statistics in conjunction with the Dept of Chemical and Biomolecular Engineering at University of Notre Dame, South Bend, IN, USA.

Mentor: Associate Prof Jonathan Hauenstein, Assistant Prof Jonathan Whitmer and Prof Andrew Sommese.

Aug – Dec 2015 Fields Postdoc Fellowship at Fields Institute, Toronto, Canada.

Aug – Dec 2014 Visiting Research Fellow at the Simons Institute for the Theory of Computing, Berkeley, CA, USA.

Aug 2013- Aug 2014 Research Assistant Professor at the Dept of Mathematics, North Carolina State University, Raleigh, NC, USA Mentor: Assistant Prof Jonathan Hauenstein and Research Fellow at the Dept of Chemistry, The University of Cambridge, UK.

Mentor: Prof David J. Wales Oct 2010 - Aug 2013 Research Fellow at Physics Department in Syracuse University, USA.

Mentor: Prof Simon Catterall Jan 2009 - Oct 2010 Research Fellow at the Dept of Math. Physics, National University of Ireland Maynooth, Ireland.

Mentor: Dr Jon-Ivar Skullerud Education July 2011 Ph. D. Theoretical/Mathematical Physics, University of Adelaide, Australia.

Dissertation: Lattice vs. continuum: Landau gauge fixing and 't Hooft-Polyakov Monopoles Supervisors: Dr Lorenz von Smekal and Prof Anthony G Williams April-Dec 2007 Visiting Ph. D. Student, Imperial College London, UK.

Supervisor: Dr Arttu K Rajantie 2003- 2004 Part III of Mathematical Tripos, The DAMTP, University of Cambridge, UK.

Part III Thesis: Topological Defects in Lattice Gauge Theories and Their Extensions to Grand Unified Theories Part III Thesis Supervisor: Dr Arttu K Rajantie 2001 - 2003 M. Sc. Theoretical and Computational Physics, Sardar Patel Uni., India.

M.Sc. Thesis: Spatial/Spectral Resolution via Gravitational Microlensing Thesis Supervisor: Prof Ashwin R Jani 1998 - 2001 B. Sc. Physics, Gujarat University, India.

Other Research Experience Oct-Nov 2011 Visiting Research Fellow, Department of Physics, Harvard University.

May-July 2002 Summer Research Trainee, Physical Research Laboratory, Ahmedabad, India.

Dissertation: Signature of Chaos in Quantum Mechanical Systems Advisor: Dr Dilipsingh Angom External Fundings

PI: the Energy, Power, Controls and Networks program of NSF, titled “Collaborative Research:


Computational Methods for Stability Assessment of Renewable Integrated Power Systems”, 2015-16, US$ 54,186 (Single PI on this grant – part of a collaborative project: US$ 394,224).

2. Senior Investigator: National Science Foundation ACI 1440583: Symbolic-Numeric Approaches to Polynomials, 2014–2017, $149,995.

3. Australian Research Council DECRA Fellowship for three years worth of 395,220 AU$ (appx.

380,000 US$).

4. Japanese Society for the Promotion of Science (JSPS) Fellowship for two years worth of 11,888,000Yen (appx. 118,400 US$). Declined for personal reasons.

Awards and Achievements

1. Fields Postdoc Fellowship (Thematic Program on Computer Algebra) at Fields Institute, Toronto, CA, 2015.

2. DECRA Postdoctoral Fellowship by the Australian Research Council, 2014.

3. Visiting Research Fellow, Simons Institute for Theory of Computing, Berkeley, 2014.

4. Japanese Society for Promotion of Science Fellowship, 2013.

5. Society of Industrial and Applied Mathematics (SIAM) Travel Award, 2013.

6. Society of Industrial and Applied Mathematics (SIAM) Travel Award, 2011.

7. An Endeavor International Postgraduate Research Award (the prestigious Australian government research scholarships for international students), 2005-2009.

8. British Council Researchers Exchange Programme Award, 2007.

9. The D R Stranks Fellowships from the University of Adelaide, 2007.

10. Research Abroad Scholarships from the University of Adelaide, 2007.

11. The University Gold Medal for scoring the highest marks in the university in M.Sc. from the Sardar Patel University, Gujarat India, 2003.

12. The Prof. Joshi Endowment Prize by Dept. of physics of Sardar Patel University for getting the highest marks in theoretical subjects, 2002.

13. The Post-graduate Scholarships, the Sardar Patel University for scoring the highest marks in M.

Sc. (first year), 2002.

Research Spotlights

• My paper “Communication: Newton homotopies for sampling stationary points of potential energy landscapes” was a Journal of Chemical Physics Editor's Suggestion for 2014.

• My paper “Certifying Potential Energy Landscapes” was one of the 'Most Read Papers' of May 2013 in Journal of Chemical Physics.

• My paper "Supersymmetric lattice fermions on the triangular lattice: Superfrustration and criticality" was chosen by the editors of the New Journal of Physics as a 'Highlight of 2012'.

• My paper “Exact results for the star lattice chiral spin liquid”, highlighted as an Editor's Suggestion by the editors of Physical Review B.

Invited Speaker/Invited Contributor

• Workshop on Kinetic Networks: From Topology to Design, Santa Fe Institute, Sep 17-19, 2015.

• The 2015 IEEE Congress on Evolutionary Comp. (CEC2015), Sendai Japan, 25-28 May, 2015

• The Mini-Simposium on Applications of Numerical Algebraic Geometry at the SIAM Conference on Applied Algebraic Geometry 2011 at Raleigh, NC, USA, 6-9 Oct., 2011.

Conference Organizer Organizing a tutorial session on Recent Advances in Computational Methods for the Power • Flow Equations, with Daniel Molzahn and Konstantin Turitsyn, from 6-8 July, at IEEE American Control Conference 2016.

Organizing a conference on Statistical Topology of Random Manifolds: Theory and • Applications, with Yan Fyodorov and Antonio Lerario, from 18-23 July 2016, at International Center for Theoretical Physics, Trieste, Italy.

Organizer of a session on Homotopy Continuation Methods and Their Applications to Science • and Engineering, at Central Spring AMS Sectional Meeting, Michigan State University, East Lansing, MI, on 14-15 March 2015, with Tianran Chen.

Organizer of a session on Computational Algebraic Geometry and Its Applications to Science • and Engineering, at Fall Western AMS Section Meeting, San Fransisco, CA, on 25-26th August 2014, with Daniel Brake.

Organizer of a mini-symposium titled Applications of Computational and Numerical Algebraic • Geometry in Theoretical Physics, in SIAM Conference on Applied Algebraic Geometry 2013, Aug. 2013, Fort Collins, Colorado, USA, with Yang-Hui He.

Publications (Journal articles, peer-reviewed conference proceedings and preprints in chronological order according to the arXiv submission)

1. A network topology dependent upper bound on the number of equilibria of the Kuramoto model. Tianran Chen, Dhagash Mehta, Matthew Niemerg. ArXiv:1603.05905.

2. Investigating the maximum number of real solutions to the power flow equations: Analysis of lossless four-bus systems. Daniel K Molzahn, Matthew Niemerg, Dhagash Mehta, Jonathan D Hauenstein. ArXiv:1603.05908.

3. On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations.

Tianran Chen, Dhagash Mehta. ArXiv:1512.04987.

4. Kinetic transition networks of the Thomson problem and Smale's 7 th problem. Dhagash Mehta, Jianxu Chen, Danny Z Chen, Halim Kusumaatmaja, David Wales. Submitted to journal.

5. Response to "Comment on 'Exploring the potential energy landscape of the Thomson problem via Newton homotopies' [J. Chem. Phys. 142, xxx (2015)". Dhagash Mehta, Tianran Chen, John WR Morgan, David Wales. Accepted for publication (in press) in Journal of Chemical Physics.

6. Reliable mixture critical point computation using polynomial homotopy continuation. Hythem Sidky, Dhagash Mehta, Jonathan Whitmer. Submitted to journal.

7. Recent Advances in Computational Methods for the Power Flow Equations. Dhagash Mehta, Daniel K Molzahn and Konstantin Turitsyn. Acccepted for publication to the Tutorial Session at IEEE 2016 American Control Conference. ArXiv:1510.00073.

8. Towards Topologically Based Upper Bounds on the Number of Power Flow Solutions. Daniel K Molzahn, Dhagash Mehta, Matthew Niemerg. Accepted for publication for special session at IEEE 2016 American Control Conference. ArXiv:1509.09227.

9. An index-resolved fixed-point homotopy and potential energy landscapes. Tianran Chen and Dhagash Mehta. ArXiv:1504.06622. Submitted to journal.

10. Statistics of Stationary Points of Random Finite Polynomial Potentials. Dhagash Mehta, Matthew Niemerg, Chuang Sun. In press. Journal of Statistical Mechanics: Theory and Experiment. ArXiv:1504.02786.

11. Stability and symmetry breaking in a three Higgs-boson doublet model with lepton family symmetry O(2)xZ2. Markos Maniatis, Dhagash Mehta and Carlos Reyes. Physical Review D 92 (3), 035017.

12. Exploring the potential energy landscape of the Thomson problem via Newton homotopies.

Dhagash Mehta, Tianran Chen, John WR Morgan, David J Wales. The Journal of Chemical Physics 142 (19) 194113.

13. A collection of challenging optimization problems in Science, Engineering and Economics.

Dhagash Mehta and Crina Grosan. Invited contribution to 2015 IEEE Congress on Evolutionary Computation, Japan, 2015.

14. Parallel degree computation for solution space of binomial systems with an application to the master space of N=1 gauge theories. Tianran Chen, Dhagash Mehta. In press. Special issue on Numerical Algebraic Geometry in Journal of Symbolic Computation. ArXiv:1501.02237.

15. Certified Counting of Roots of Random Univariate Polynomials. Joseph Cleveland, Jeffrey Dzugan, Jonathan Hauenstein, Ian Haywood, Dhagash Mehta, Anthony Morse, Leonardo Robol, Taylor Schlenk. ArXiv:1412.1717. Submitted to journal.

16. Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis. Dhagash Mehta, Noah Daleo, Florian Doerfler, Jonathan D Hauenstein. Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (5), 053103.

17. Equilibria Analysis of Power Systems Using a Numerical Homotopy Method. Souvik Chandra, Dhagash Mehta, Aranya Chakrabortty. IEEE 2015 Power and Energy Society General Meeting.

18. Energy Landscape of the Finite-size Mean-field 2-spin Spherical Model and Topology Trivialization. Dhagash Mehta, Jonathan D. Hauenstein, Matthew Niemerg, Nicholas J. Simm, Daniel A. Stariolo. Physical Review E 91, 022133 (2015).

19. Exploring the Impact of Wind Penetration on Power System Equilibrium Using a Numerical Continuation Approach. Souvik Chandra, Dhagash Mehta, Aranya Chakrabortty. IEEE 2015 Special Session in American Control Conference.

20. Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams. Jonathan D Hauenstein, Rijun Huang, Dhagash Mehta and Yang Zhang. Journal of High Energy of Physics 1502 (2015) 136.

21. Numerical Polynomial Homotopy Continuation Method to Locate All The Power Flow Solutions. Dhagash Mehta, Hung D Nguyen, Konstantin Turitsyn. Submitted to journal.


22. Communication: Newton Homotopies for Sampling Stationary Points of Potential Energy Landscapes. Dhagash Mehta, Tianran Chen, Jonathan D Hauenstein, David J Wales. Journal of Chemical Physics 141 (12) 121104 (2014). (Selected for an Editor's Choice 2014).

23. Gauge fixing on the lattice via orbifolding. Dhagash Mehta, Noah Daleo, Jonathan D.

Hauenstein, Christopher Seaton. Physical Review D 90, 054504 (2014).

24. Experiments on the zeros of harmonic polynomials using certified counting. Jonathan Hauenstein, Antonio Lerario, Erik Lundberg, Dhagash Mehta. Journal of Experimental Mathematics vol 24 (2) 133 (2015).

25. An Inversion-Relaxation Approach for Sampling Stationary Points. Ciaran Hughes, Dhagash Mehta and David J Wales. Journal of Chemical Physics 140 (19), 194104 (2014).

26. Potential Energy Landscape of the Two-dimensional XY Model: Higher-index Stationary Points. Dhagash Mehta, Ciaran Hughes, Michael Kastner and David J Wales. Journal of Chemical Physics 140 (22), 224503 (2014).

27. Certification and Potential Energy Landscapes. Dhagash Mehta, Jonathan D Hauenstein and David J Wales. Journal of Chemical Physics 140 (22), 224114 (2014).

28. Enumerating copies in the first Gribov region on the lattice in up to four dimensions. Dhagash Mehta and Mario Schroeck. Physical Review D 89 9 094512 (2014).

29. Eigenvalue spectrum of lattice N=4 super Yang-Mills. David J. Weir, Simon Catterall, Dhagash Mehta. Published in Proceedings of Science (Lattice13) 2013.

30. Spectral functions of charmonium from 2 flavour anisotropic lattice data. Aoife Kelly, Jon-Ivar Skullerud, Chris Allton, Dhagash Mehta, Mehmet B. Oktay. Proceedings of Science (Lattice13) 2013.

31. Potential Energy Landscapes for the 2D XY Model: Minima, Transition States and Pathways.

Dhagash Mehta, Ciaran Hughes, Mario Schroeck, David J. Wales. Journal of Chemical Physics 139, 194503 (2013).

32. Exact Minimization of Higgs Potentials. Markos Maniatis and Dhagash Mehta. European Physical Journal Plus 129 (2014) 109.

33. Phase transitions and gluodynamics in 2-colour matter at high density. Tamer Boz, Seamus Cotter, Leonard Fister, Dhagash Mehta, Jon-Ivar Skullerud. European Physical Journal A49 (2013) 87.

34. Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces.

Brian Greene, David Kagan, Ali Masoumi, Dhagash Mehta, Erick Weinberg, Xiao Xiao.

Physical Review D 88 026005 (2013).

35. Energy Landscape of the Finite-size Mean-field 3-spin Spherical Model. Dhagash Mehta, Daniel A Stariolo, Michael Kastner. Physical Review E 87 (2013) 052143.

36. Communication: Certifying the potential energy landscape. Dhagash Mehta, Jonathan D.

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