
Dhagash Mehta
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. 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.
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
AlgebraNumber TheoryComputational 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. 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 Higgsboson doublet model
with lepton family symmetry O(2)xZ_{2}",
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 1823 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
indexresolved fixedpoint 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 Higgsboson doublet model
with lepton family symmetry O(2)xZ_{2}",
is now on arXiv. 1415th 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 2528th 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
13, 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
2528th 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 FiniteSize Meanfield 2spin 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
Threeloop 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. 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 "Gaugefixing
on the lattice via Orbifolding", is now accepted
for publication in Physical Review D. 26th June 2014: My new article with Noah S Daleo, Jonathan D Hauenstein and Christopher Seaton, titled "Gaugefixing 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
TwoDimensional XY Model: HigherIndex
Stationary Points", is accepted for publication in
Journal of Chemical Physics. 
Conferences
