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Yisong Yang

I.Brief CV: Yisong Yang, born in May, 1958, professor. Fellow of American Mathematical Society, member of the London Mathematical Society

II.Education :
University of Massachusetts, U.S. Ph.D, 1988
Wuhan Institute of Physics and Mathematics (WIPM) of Chinese Academy of Sciences, Wuhan, P.R.ChinaM.Phil, 1985
Henan University, Kaifeng, P.R.ChinaB.Sc, 1982

III.Employment

IV.Research
2017.09-present, Courant Institute of Mathematical Sciences of New York University, Professor
2013.09-2015.08, New York University Shanghai, Professor
2012.05-present,Henan University, the "Hundred Talents" Distinguished experts of Henan Province
1995.09- present,New York University Tandon School of Engineering,Department of Mathematics, Professor
2008.09-2009.08,Yeshiva University, USA, Department of Mathematics, Professor
2001.09-2002.09,Institute for Advanced Study, Princeton, USA,Member
1999.07-1999.08,Institut des Hautes Etudes Scientifiques,Member
1994.09-1995.08,New York Institute of Technology, Department of Mathematics, Associate Professor
1993.09-1995.08,University of New Mexico, Department of Mathematics, Associate Professor
1993.09-1994.09,Institute for Advanced Study, Princeton, USA,Member
1992.09-1993.09,Carnegie Mellon University, USA, Department of Mathematics, Visiting Assistant Professor
1989.09-1992.08,University of New Mexico, Department of Mathematics, Assistant Professor
1988.09-1989.06, University of Minnesota, Institute of mathematics and Application, Postdoctoral Member

V.Teaching :( Current Course)
Mathematical Physics, Quantization, Partial Differential Equation in Theoretical Physics, Calculus of Variations, Nonlinear Analysis

VI.Research Field and Interests
Mathematical Physics, Partial Differential Equation, Nonlinear Analysis

VII.R & D project(chaired or co-chaired)
1.The Faddeev Knots and the SkyrmeSolitons，NSF DMS-0406446New York Institute of Technology,    2005.08    124000 dollars,    chaired
2.Elliptic problems in field theories，NFS DMS-9972300    New York Institute of Technology,    1999.07，69936dollars,    chaired
3.Applications of Elliptic PDE's to Gauge Theory, Topology, and Physics，NFS DMS-9505170，    New York Institute of Technology,    1995.07，    202550dollars,co-chaired
4.Nonlinear Problems Arising from Theoretical Physics，NFS DMS-9596041，    New York Institute of Technology,    1994.08    20000dollars,    chaired
5.Nonlinear Problems Arising from Theoretical Physics，NFS DMS-9400243    University of New Mexico,    1994.06，    20000dollars,    chaired
6.Partial Differential Equation in Quark Confinement Mechanism （11471100），general program,    Henan University,    2015.01    750,000 RMB    chaired
7.Vortex of Solutions in Partial Differential Equation of Field Theory（11471099），    general program,    Henan University,    2015.01，    700,000 RMB        co-chaired
VIII.Selected Papers and Publications(published)
1.Determination of gap solution and critical temperature in doped graphene superconductivity. Z. Angew. Math. Phys. 68 (2017), no. 2, 68:34. With Xu.
2.Critical pull-in curves in MEMS actuators in presence of Casimir force. ZAMM Z. Angew. Math. Mech. 96 (2016), no. 12, 1406–1422. withMcLellan, Luciano and Xu.
3.Magnetic impurity inspired Abelian Higgs vortices. J. High Energy Phys. 2016, no. 2, 046. with Han.
4.Resolution of Chern-Simons-Higgs vortex equations. Comm. Math. Phys. 343 (2016), no. 2, 701–724.  with Han, Lin.
5.Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds. Nuclear Phys. B 904 (2016), 470–493.  with Chen.
6.Relativistic Chern-Simons-Higgs vortex equations. Trans. Amer. Math. Soc. 368 (2016), no. 5, 3565–3590. wiht Han.
7.Explicit Integration of Friedmann's Equation with Nonlinear Equations of State, Journal of Cosmology and Astroparticle Physics 05 (2015) 020 [with S. Chen and G. W. Gibbons].
8.Existence Theorems for Vortices in the Aharony--Bergman--Jaferis--Maldacena Model, Communications in Mathematical Physics 333 (2015) 229--259 [with X. Han].
9.Chern--Simons Vortices in the Gudnason Model, Journal of Functional Analysis 267 (2014) 678--726 [with X. Han, C. S. Lin, and G. Tarantello].
10.Existence of Multiple Vortices in Supersymmetric Gauge Field Theory,Proceedings of Royal Society(London) A 468 (2012) 3923--3946 [with S. X. Chen
11.Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods, Communications in Mathematical Physics 313 (2012) 445--478[with Elliott H. Lieb].
12.Electrically and Magnetically Charged Vortices in the Chern-Simons-Higgs Theory, Proceedings of the Royal Society(London) A 465 (2009) 3489--3516 [with R. Chen, Y. Guo, and D. Spirn].
13.Existence of Faddeev Knots in General Hopf Dimensions, Surveys in Differential Geometry 13 (2009) 149--221 [with F. B. Hang and F. H. Lin].
14.Energy Splitting, Substantial Inequality, and Minimization for the Faddeev and Skyrme Models, Communications in Mathematical Physics 269 (2007) 137--152 [with F. H. Lin].
15.Prescribing Zeros and Poles on a Compact Riemann Surface for a Gravitationally Coupled Abelian Gauge Field Theory, Communications in Mathematical Physics 249 (2004) 579--609.
16.Existence of Energy Minimizers as Stable Knotted Solitons in the Faddeev Model, Communications in Mathematical Physics 249 (2004) 273--303 [with F. H. Lin].
17.Cosmic Strings in a Product Abelian Gauge Field Theory, Nuclear Physics B 885 (2014) 25--33.
18.Existence of Optical Vortices,SIAM Journal of Mathematical Analysis 46 (2014) 484--498 [with R. Zhang].
19.Existence of Dyons in Minimally Gauged Skyrme Model via Constrained Minimization, Journal of Functional Analysis 262 (2012) 3602--3625 [with Z. F. Gao].
20.Existence of Hyperbolic Calorons,Proceedings of the Royal Society(London) Series A 471 (2015) 2176 [with L. Sibner and R. Sibner].
21.Friedmann's Equations and Chebyshev's Theorem, Journal of Cosmology and Astroparticle Physics 12 (2014) 035 [with S. Chen, G. W. Gibbons, and Y. Li].
22.Exact Kink Solitons in Skyrme Crystals, Physical Review D 89 (2014) 025007 [with S. Chen and Y. Li].
23.AbelianHopfions and a Fractionally Powered Topological Lower Bound, Nuclear Physics B 875 (2013) 388--407 [with E. Radu and D. H. Tchrakian].
24.Solutions to the Master Equations Governing Fractional Vortices, Journal of Differential Equations 254 (2013) 1437--1463 [with C. S. Lin and G. Tarantello].
25.Exact Kink Solitons in a Monopole Confinement Problem, Physical Review D 86 (2012) 085030 [with S. X. Chen and Y. Li].
26.Sharp Existence and Uniqueness Theorems forNon-Abelian Multiple Vortex Solutions, Nuclear Physics B 846 (2011) 650--676 [with C. S. Lin].
27.Dynamics of Electrostatic MEMS Actuators, Journal of Mathematical Physics 53 (2012) 022703 [with R. Zhang and L. Zhao].
28.Electrically Charged Solitons in Gauge Field Theory, ActaMathematicaScientia (invited survey article dedicated to the memory of Guoping Li and Xinmou Wu) 30 (2010) 1975--2005.
29.On a Vegetation Pattern Formation Model Governed by a Nonlinear Parabolic System, Nonlinear Analysis 14 (2013) 507--525 [with KaloyanMarinov and Tianze Wang].
30.Existence of Dyons in the Coupled Georgi--Glashow--Skyrme Model, Annales de Henri Poincare 12 (2011) 329--349 [with Fanghua Lin].
31.Non-Abelian Multiple Vortices in Supersymmetric Field Theory,Communications in Mathematical Physics 304 (2011) 433--457 [with Chang-Shou Lin].
32.Charged Cosmological Dust Solutions of the Coupled Einstein and Maxwell Equations, Discrete and Continuous Dynamical Systems (in honor of Louis Nirenberg) 28 (2010) 567--589 [with Joel Spruck].
33.Phase Transition Solutions in Geometrically Constrained Magnetic Domain Wall Models, Journal of Mathematical Physics 51 (2010) 023504 [with S. X. Chen].
34.Proof of the Julia--Zee Theorem, Communications in Mathematical Physics 291(2009) 347--356 [with Joel Spruck].
35.Steady State Solutions for Nonlinear Schroedinger Equation Arising in Optics,Journal of Mathematical Physics 50 (2009) 053501 [with R. F. Zhang] [Corrigendum]. (This article was one of the top 20 most downloaded articles in the months of May and June, 2009, of the journal.)
36.]Universal Growth Law for Knot Energy of Faddeev Type in General Dimensions,Proceedings of the Royal Society A 646 (2008) 2741--2757 [with F. H. Lin].
37.Existence of Knots of Minimum Energy and Topological Growth Laws in the Faddeev Model, Topology and Physics (in memory of Xiao-Song Lin), Nankai Tracts in Mathematics 12 (2008) pp. 242--259 [with F. H. Lin].
38.Spherically Symmetric Self-Dual Yang-Mills Instantons on Curved Backgrounds in All Even Dimensions, Physical Review D 77 (2008) 044017 [with E. Radu and D. H. Tchrakian].
39.A System of Elliptic Equations Arising in Chern-Simons Field Theory, Journal of Functional Analysis 247 (2007) 289--350 [with C. S. Lin and A. C. Ponce].
40.Analysis on Faddeev Knots and SkyrmeSolitons: Recent Progress and Open Problems,  in Perspectives in Nonlinear Partial Differential Equations (in honor of HaimBrezis), Contemporary Mathematics 446, pp. 319--344, American Mathematical Society, 2007 [with F. H. Lin].
41.Geometry, Topology, and Gravitation Synthesized by Cosmic Strings, Pure and Applied Mathematics Quarterly 3 (2007) 737--772 (in honor of Robert Gulliver, Robert Hardt, and Leon Simon).
42.Generalized Bernstein Property and Gravitational Strings in Born--Infeld Theory, Nonlinearity 20 (2007) 1193--1213 [with L. Sibner and R. Sibner].
43.Nonlinear Nonlocal Elliptic Equations Modeling Electrostatic Actuation, Proceedings of the Royal SocietyA 463 (2007) 1323--1337 [with F. H. Lin].
44.Moduli Space of BPS Walls in Supersymmetric Gauge Theories, Communications in Mathematical Physics 267 (2006) 783--800 [with N. Sakai].
45.Static Knot Energy, Hopf Charge, and Universal Growth Law, Nuclear Physics B 747 (2006) 455--463 [with F. H. Lin].
46.Faddeev Knots, SkyrmeSolitons, and Concentration-Compactness, Proceedings of the 23rd International Conference on Differential Geometry Methods in Theoretical Physics, Nankai Tracts in Mathematics 10 (2006) pp. 313--322 [with F. H. Lin].
47.Existence of Static BPS Monopoles and Dyons in Arbitrary $(4p-1)$-Dimensional Spaces, Letters in Mathematical Physics 77 (2006) 249--263 [with X. Q. Wang].
48.Mathematical Analysis of the Multiband BCS Gap Equations in Superconductivity, Physica D 200 (2005) 60--74.
49.Existence of 2D Skyrmions via Concentration-Compactness Method, Communications on Pure and Applied Mathematics 57 (2004) 1332--1351 [with F. H. Lin].
50.The Faddeev Knots as Stable Solitons: Existence Theorems, Science in China Series A 47 (2004) 187--197 [with F. H. Lin].
51.Gauged Harmonic Maps, Born--Infeld Electromagnetism, and Magnetic Vortices, Communications on Pure and Applied Mathematics 56 (2003) 1635--1665 [with F. H. Lin].
52.On Pokrovskii's Anisotropic Gap Equations in Superconductivity Theory, Nonlinearity 16 (2003) 2061--2073.
53.Rigorous Proof of Isotope Effect by Bardeen--Cooper--Schrieffer Theory, Journal of Mathematical Physics 44 (2003) 2004--2025.
54.MultipleInstantons Representing Higher-Order Chern--PontryaginClasses,II, Communications in Mathematical Physics 241 (2003) 47--67 [with L. Sibner and R. Sibner].
55.Existence of Solutions to the Efros Self-consistency Equation in All Dimensions,Proceedings of the Royal Society A 459 (2003) 853--861.
56.The Uniqueness and Approximation of a Positive Solution of the Bardeen--Cooper--Schrieffer Gap Equation, Journal of Mathematical Physics 41 (2000) 6007--6025 [with J. B. McLeod].
57.Classical Solutions in the Born--Infeld Theory, Proceedings of the Royal Society A 456 (2000) 615--640.
58.]Abelian Gauge Theory on Riemann Surfaces and New Topological Invariants, Proceedings of the Royal Society A 456 (2000) 593--613 [with R. Sibner and L. Sibner].
59.On a System of Nonlinear Elliptic Equations Arising in Theoretical Physics, Journal of Functional Analysis 170 (2000) 1--36.
60.Strings of Opposite Magnetic Charges in a Gauge Field Theory, Proceedings of the Royal Society A 455 (1999) 601--629.
61.Sigma Models Coupled with Abelian Gauge Fields, Journal of Mathematical Physics 39 (1998) 5824--5831 [with D. O'Keeffe and D. H. Tchrakian].
62.Chern--Simons Solitons and a Nonlinear Elliptic Equation, Helvetica PhysicaActa 71 (1998) 573--585.
63.Coexistence of Vortices and Anti-vortices in an Abelian Gauge Theory, Physical Review Letters 80 (1998) 26--29.
64.String-like Defects and Fractional Total Curvature in a Gauged Harmonic Map Model, Advances in Nonlinear Partial Differential Equations and Related Areas (edited by Y. Li et al), pp. 334--378, World Scientific Publishing, 1998.
65.The Lee--Weinberg Magnetic Monopole of Unit Charge: Existence and Uniqueness, Physica D 117 (1998) 215--240.
66.Dually Charged Particle-like Solutions in the Weinberg--Salam Theory, Proceedings of the Royal SocietyA 454 (1998) 155--178.
67.Nonlinear Problems in Field Theories, Proceedings of International Workshop on Mathematical and Physical Aspects of Nonlinear Field Theories, Lecture Notes Series 42, pp. 1--26, 1998, Seoul National University (edited by D. Chae).
68.Multiple Instantons Representing Higher-Order Chern--Pontryagin Classes, Communications in Mathematical Physics 188 (1997) 737--751 [with J. Spruck and D. H. Tchrakian].
69.The Relativistic Non-AbelianChern--Simons Equations, Communications in Mathematical Physics 186 (1997) 199--218.
70.The Existence of Solitons in Gauged Sigma Models with Broken Symmetry: Some Remarks, Letters in Mathematical Physics 40 (1997) 177--189.
71.Topological Solitons in the Weinberg--Salam Theory,Physica D 101 (1997) 55--94.
72.Cosmic Strings and Criticality, Proceedings of the Royal Society A 453 (1997) 581--591.
73.A Necessary and Sufficient Condition for the Existence of Multisolitons in a Self-DualSigma Model, Communications in Mathematical Physics 181 (1996) 485--506.
74.Topological and Nontopological Self-Dual Chern--Simons Solitons in a Gauged Sigma Model, Physical Reviews D 54 (1996) 5245--5258 [with K. Arthur and D. H. Tchrakian].
75.Mathematical Theory of Self-Dual Cosmic Strings: Existence and Obstructions,InternationalJournal of Modern Physics A11 (1996) 203--227 [invited review article].
76.Skyrme Models with Self-Dual Limits, Journal of Mathematical Physics 37 (1996) 2569--2584 [with K. Arthur, G. Roche, and D. H. Tchrakian].
77.The Existence of Generalized Self-Dual Chern--Simons Vortices, Letters in Mathematical Physics 36 (1996) 403--413 [with D. H. Tchrakian].
78.Existence Theorems for Periodic Non-relativistic Maxwell--Chern--Simons Solitons, Journal of Differential Equations 127 (1996) 571--589 [with J. Spruck].
79.Prescribing Topological Defects for the Coupled Einstein and Abelian Higgs Equations,Communications in Mathematical Physics 170 (1995) 541--582.
80.Regular Stationary Solutions of the Cylindrically Symmetric Einstein-Matter-Gauge Equations, Journal of Mathematical Analysis and Applications195 (1995) 160--190 [with J. Spruck].
81.Vortex Condensation in the Chern--Simons Higgs Model: An Existence Theorem, Communications in Mathematical Physics 168 (1995) 321--336 [with L. A. Caffarelli].
82.Topological Solutions in the Self-Dual Chern--Simons Theory: Existence and Approximation, Annales de l'Institut Henri Poincare -- Analyse non Lineaire 12 (1995) 75--97 [with J. Spruck].
83.The Existence of Ginzburg--Landau Solution on the Plane by a Direct Variational Method, Annales de l'Institut Henri Poincare -- Analyse non Lineaire 11 (1994) 517--536.
84.Obstructions to the Existence of Static Cosmic Strings in an Abelian Higgs Model, Physical Review Letters 72 (1994) 10--13.
85.Self-Duality of the Gauge Field Equations and the Cosmological Constant, Communications in Mathematical Physics 162 (1994) 481--498.
86.A Nonlinear Elliptic Equation Arising from Gauge Field Theory and Cosmology, Proceedings of the Royal Society A 446 (1994) 453--478 [with X. Chen, S. Hastings, and J. B. McLeod].
87.The Critical Temperature and Gap Solution in the Bardeen--Cooper--Schrieffer Theory of Superconductivity, Letters in Mathematical Physics 29 (1993) 133--150 [with Q. Du].
88.An Equivalence Theorem for String Solutions of the Einstein-Matter-Gauge Equations, Letters in Mathematical Physics 26 (1992) 79--90.
89.On the Existence of Multivortices in a Generalized Bogomol'nyi System, Zeitschrift fur angewandteMathematik und Physik 43 (1992) 677--696.
90.The Existence of a Class of Cosmic String Solutions with Infinite Energy, Proceedings of the Royal Society of Edinburgh A 122 (1992) 301--315.
91.The Existence of Non-Topological Solitons in the Self-Dual Chern--Simons Theory,Communications in Mathematical Physics 149 (1992) 361--376 [with J. Spruck].
92.On Multivortices in the Electroweak Theory. I: Existence of Periodic Solutions,Communications in Mathematical Physics 144 (1992) 1--16 [with J. Spruck].
93.On Multivortices in the Electroweak Theory. II: Existence of Bogomol'nyi Solutions, Communications in Mathematical Physics 144 (1992) 215--234 [with J. Spruck].
94.Symmetric Superconducting States in Thin Films, SIAM Journal on Applied Mathematics 52 (1992) 614--629 [with S. Wang].
95.Abrikosov's Vortices in the Critical Coupling, SIAM Journal on Mathematical Analysis 23 (1992) 1125--1140 [with S. Wang].
96.Solutions of the Generalized Bogomol'nyi Equations via Monotone Iterations, Journal of Mathematical Physics 33 (1992) 4239--4249 [with S. Wang].
97.Vacuum Decay of Non-Abelian Vortices, Mathematical Methods in the Applied Sciences 15 (1992) 79--88.
98.A Generalized Self-Dual Chern--Simons Higgs Theory, Letters in Mathematical Physics 23 (1991) 179--191.
99.Existence of the Massive Vortices, Journal of Mathematical Physics 32 (1991) 1395--1399.
100.On the BardeenCooperSchrieffer Integral Equation in the Theory ofSuperconductivity, Letters in Mathematical Physics 22 (1991) 27--37.
101.On the Abelian Higgs Models with Sources, Journal de MathematiquesPuresetAppliquees 70 (1991) 325--344.
102.The Computation of Superconductivity in Thin Films, Journal of Computational Physics 89 (1990) 257--275 [with S.-Y. Lin].
103.Vortices on Asymptotically Euclidean Riemann Surfaces, Nonlinear Analysis 15 (1990) 577--596.
104.Self-Dual Monopoles in a Seven-Dimensional Gauge Theory, Letters in Mathematical Physics 20 (1990) 285--290.
105.Blow-Up of the Yang--Mills Fields, Journal of Mathematical Physics 31 (1990) 1237--1239.
106.Ginzburg--Landau Equations for Superconducting Films and the MeissnerEffect, Journal of Mathematical Physics 31 (1990) 1284--1289.
107.Boundary Value Problems of the Ginzburg--Landau Equations, Proceedings of the Royal Society of Edinburgh A 114 (1990) 355--365.
108.Convergence of the Pseudospectral Method for the Ginzburg--Landau Equation, Journal of Mathematical Analysis and Applications 147 (1990) 556--568.
109.Existence of Solutions for a Generalized Yang--Mills Theory, Letters in Mathematical Physics 19 (1990) 257--267.
110.On the Ginzburg--Landau Wave Equation, Bulletin of the London Mathematical Society 22 (1990) 167--170.
111.A Comparison of the Eigenvalues of Two Sturm--Liouville Problems, Canadian Mathematical Bulletin 33 (1990) 386--390.
112.Existence, Regularity, and Asymptotic Behavior of the Ginzburg--Landau Equations, Communications in Mathematical Physics 123 (1989) 147--161.
113.Generalized Skyrme Models on Higher Dimensional Riemannian Manifolds, Journal of Mathematical Physics 30 (1989) 824--828.

1.AMS Invited Hour Address, 2001, Williams College, Williamstown, Massachusetts

2.Institut Henri Poincare Gauthier-Villars Prize, 1996, Paris, France (with Joel Spruck)

3.Othmer Senior Faculty Fellow, 2006 - 2009, Polytechnic University

4.Efroymson Faculty Award for Excellence, 1991, University of New Mexico

5.University Graduate Fellowship, 1986 - 1987, University of Massachusetts

1. "Vortices on Riemann Surfaces"  - Special Session on Geometry and Topology of Moduli Spaces (The 858th AMS Conference, Albuquerque, April 1990).

2. "Global Bifurcation in the Bardeen-Cooper-Schrieffer Energy Gap Equation"  - Special Session on Quantum and Statistical Mechanics (The 2nd International SIAM Conference, Washington D. C., July 1991).

3. "Multivortices in the Electroweak Theory"   - Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory (AMS-IMS-SIAM), Seattle, July 1991.

4. "The Self-Dual Chern-Simons Solitons"  - Special Session on Nonlinear Partial Differential Equations (The 868 AMS Conference, Philadelphia, October 1991).

5. "Nonlinear Elliptic PDEs in the Salam-Weinberg Theory" - First Applied Mathematics Symposium of Young Researchers (Beijing, July 1992).

6. "The Self-Dual Cosmological Equations"  - Special Session on Nonlinear Elliptic Problems in Geometry and Physics (The 881st AMS Conference, Washington D. C., April 1993).

7. "The Minimization of Ginzburg-Landau Energy: How Much do we Know?"  - One-hour invited talk at Workshop on Recent Progress and Applications of the Ginzburg-Landau Equations (Carnegie-Mellon University, Pittsburgh, June 1993).

8. "Vortices in the Theory of Superconductivity" - One-hour invited talk at Joint Summer Research Conference on the Mathematics of Superconductivity (AMS-IMS-SIAM, Seattle, July 1993).

9. "Gravitational Vortices and Two-Dimensional Nonlinear Elliptic Equations" - 45-minute invited talk at Japan-America Mathematical Institute Workshop on Nonlinear Partial Differential Equations, Pattern Formation, Singularities, and Related Topics (Johns Hopkins University, Baltimore, March, 1994).

10. Prescribing Topological Defects for the Coupled Einstein and Abelian Higgs Equations" -Special Session on Gauge Theory and Applications, (The 892nd AMS Conference, Brooklyn, New York, April, 1994).

11. "Gauged Harmonic Maps from ${\bf R}^2$ to $S^2$" - Special Session on Partial Differential Equations (The 910th AMS Conference, Courant Institute, New York, April, 1996).

12. "Particle-like Solitons in the Weinberg--Salam Theory and the Calculus of Variations"  -First North-America Tianyuan Mathematics Conference (MSRI, Berkeley, California, June, 1997).

13. "A Tale of Vortices and Anti-vortices" - Special Session on Concentration Phenomena in Partial Differential Equations (The 927th AMS Conference, University of Wisconsin, Milwaukee, October, 1997).

14. "Nonlinear Problems in Field Theories": Lecture I, "Self-dual Cosmic Strings"; Lecture II, "Electroweak Solitons and Nonlinear Analysis"; Lecture III, "Relativistic Chern-Simons Equations" - A series of three one-hour invited lectures at the  International Workshop on Mathematical and Physical Aspects of Field Theories  held at Seoul National University, Seoul, Korea, Feb. 23-25, 1998.

15. "Born-Infeld Theory and Nonlinear Elliptic Problems" - Special Session on Elliptic and Parabolic Equations, International Conference on Differential Equations and Dynamical Systems, Kennesaw, Georgia, May, 2000.

16. "Instantons, Characteristic Classes, and Nonlinear Elliptic Equations" - Special Session on Nonlinear Partial Differential Equations (The 959th AMS Conference, Columbia University, New York, November, 2000).

17. "Nonlinear Problems in Born-Infeld Theory" - 50-minute invited lecture at the international conference  A Week End in Nonlinear Analysis, University of Rome, II, Italy, March 8 - 9, 2001.

18. "Harmonic Maps, Gauge Fields, and Magnetic Vortices"  - AMS hour invited address (The 971st AMS Conference, Williams College, Williamstown, October 13 - 14, 2001).

19. "Born-Infeld Electromagnetism, Generalized Bernstein Problems, and Nonlinear PDEs" - Prairie Analysis Seminar, Kansas State University, Manhattan, October 19 - 20, 2001.

20. "Harmonic Representation of Topological Classes and a Vortex Equation" - International Conference on Diffusion-Reaction Equations, National Center of Theoretical Sciences, Taiwan, May 26 - 30, 2004.

21. "Geometry, Topology, and Gravitation Synthesized by Cosmic Strings"
- 45-minute invited talk at Nonlinear Partial Differential Equations and Calculus of Variations (an
international conference dedicated to the 60th birthday of Professors R. Gulliver, R. Hardt, and L. Simon), Center of Mathematical Sciences, Zhejiang University, Hangzhou, China, June 20 - 23, 2005.

22. "Mathematics of the BCS Gap Equations in Superconductivity" - 45-minute invited talk at Workshop on Ginzburg-Landau Theory and Related Topics, Morningside Center of Mathematics, Chinese Academy of Science, Beijing, China, June 28 - 30, 2005.

23. "Faddeev Knots and SkyrmeSolitons" - 45-minute invited talk at International Conference on Differential Geometry Methods in Theoretical Physics XXIII, Nankai Institute of Mathematics, Tianjin, China, August 20 - 26, 2005.

24. "Faddeev Knots, SkyrmeSolitons, and Concentrated-Compactness" - 45-minute invited talk
at Special Session on Geometric Analysis and Calculus of Variations,  First Joint American Mathematical Society and Taiwanese Mathematical Society Conference, Tunghai University, Taiwan, December 14 - 18, 2005.

25. "Topics in Mathematical Physics - Harmonically Representing Topological Classes" - a series of four invited lectures at the Graduate Summer School, Fudan University, Shanghai, China, June 2006.

26. "Relativistic Chern-Simons Equations and Variational Methods" -- 20-minute invited talk at the Special Session on Nonlinear Differential Equations and Applications (The 1020th AMS Conference, University of Cincinnati, Cincinnati, October 21--22, 2006).

27. "Some Nonlinear Elliptic Problems in Mathematical Physics" -- One-hour invited talk at the conference Geometric Analysis and Nonlinear Elliptic PDEs (on the occasion of the 60th birthday of Professor Joel Spruck), Johns-Hopkins University, Baltimore, October 27--29, 2006.

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