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Steven Flores

Ph.D., Postdoctoral Researcher

Email: firstname.lastname(at)helsinki.fi

Mailing Address:
Department of Mathematics and Statistics
PL 68
FIN-00014 University of Helsinki
Finland

Visiting Address:
Gustaf Haellstroemin katu 2b, Helsinki
Room A412

 

Research Interests: 

My research focuses on two-dimensional statistical mechanics models whose observables exhibit a conformal invariant scaling limit at criticality. Such models include percolation, Ising and Potts models, random cluster models, loop-gas models, various random walks, and more, and they frequently arise in material science and polymer science. Because they are complicated enough to accurately simulate real-world phenomena yet simple enough for tractable calculations to be possible, these models are both practical and fascinating to study. As such, they have attracted intense interest from physicists and mathematicians for decades. Together, this community has used rigorous methods in probability and analysis, non-rigorous but convincing methods from theoretical physics, and computer simulation to contribute new results to this current and evolving field.

In my recent work, I study how clusters in percolation, Potts models, and random cluster models span and interconnect distant parts of the system domain to form crossing patterns and pinch-point configurations. To investigate these properties, I use conformal field theory, Schramm Loewner evolution, computer simulation, and other methods to either predict or rigorously determine these properties.

Curriculum Vitae: (Link)

Publications:

  • (Link) S. M. Flores, "Correlation functions in two-dimensional critical systems with conformal symmetry," thesis dissertation.
  • (Link) J. J. H. Simmons, P. Kleban, S. M. Flores, and R. M. Ziff, "Cluster densities at 2-D critical points in rectangular geometries," J Phys. A: Math. Theor. 44 (2011) 385002 (Preprint).
    • (Link) Figure 5 selected for the cover of J. Phys. A: Math. Theor. 44, Issue 38.
  • (Link) S. M. Flores and P. Kleban, and R. M. Ziff, "Cluster pinch-point densities in polygons," J. Phys. A: Math. Theor. 45 (2012), 505002 (Preprint) .
    • (Link) Selected for the 2012 highlights edition of J. Phys. A.
    • (Link) Figure 27 selected for the cover of J. Phys. A: Math. Theor. 45, Issue 50.
  • (Link) S. M. Flores and P. Kleban, "A solution space for a system of null-state differential equations, Part I," Commun. Math. Phys., Vol. 333, Issue 1 (2015), 389-434 (Preprint).
  • (Link) S. M. Flores and P. Kleban, "A solution space for a system of null-state differential equations, Part II," Commun. Math. Phys., Vol. 333, Issue 1 (2015), 435-481 (Preprint).
  • (Link) S. M. Flores and P. Kleban, "A solution space for a system of null-state differential equations, Part III," Commun. Math. Phys., Vol. 333, Issue 2 (2015), 597-667 (Preprint).
  • (Link) S. M. Flores and P. Kleban, "A solution space for a system of null-state differential equations, Part IV," Commun. Math. Phys., Vol. 333, Issue 2 (2015), 669-715 (Preprint).
  • (Link) S. M. Flores, R. M. Ziff, and J. J. H. Simmons, "Percolation crossing probabilities in hexagons: a numerical study," J. Phys. A: Math. Theor. 48 (2015) 025001 (Preprint).
    • (Link) Selected for the publisher’s pick feature of J. Phys. A.
    • (Link) Figure 4 selected for the cover of J. Phys. A: Math. Theor. 48, Issue 2.
  • S. M. Flores, J. J. H. Simmons, and P. Kleban, "Multiple-SLE connectivity weights for rectangles, hexagons, and octagons," (Preprint).
  • S. M. Flores, J. J. H. Simmons, P. Kleban, and R. M. Ziff, "Partition functions and crossing probabilities for critical systems in polygons," in preparation.

Presentations:

  • (Link) "Pinch-point Densities for Percolation in Polygons," Advances in Percolation and Related Topics, University of Michigan, May 2012.
  • (Link) "Correlation Functions in Two-Dimensional Critical Systems with Conformal Symmetry," thesis defense, University of Michigan, May 2012.
  • (Link) "Lattice-model Crossing Probabilities and a System of PDEs for Multiple SLE," University of Helsinki, September 2014 and Aalto University, October 2014.
  • (Link) "A Solution Space for a System of BPZ Equations: Rigorous Results and Applications," Australian National University, July 2015.

 

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