



Dimiter Vassilev ( CV.pdf )
Department
of mathematics
Web Page: http://math.ucr.edu/~dvassilev
Education 


Université
Bordeaux I, 
Positions 
Visiting Assistant
Professor,
Visiting Assistant
Professor,
CRMISM Postdoctoral
Fellowship,
Visiting Assistant
Professor,

Teaching Experience 
2005,
2003,
2000 – 2005,
1995 –2000 Teaching
Assistant,

Papers 

Quaternionic contact manifolds with a closed fundamental 4form, with St. Ivanov, arXiv:0810.3888, 2008. Conformal quaternionic contact curvature and the local sphere theorem, with St. Ivanov, MPIM200779, 2007. Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, with St. Ivanov and I. Minchev, to appear in JEMS, 2007. Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem, with St. Ivanov and I. Minchev, International Centre for Theoretical Physics preprint IC/2006/117, 2006. Lp estimates and asymptotic behavior for finite energy solutions of extremals toHardySobolev inequalities, submitted. Strong unique continuation for generalized BaouendiGrushin operators, with N. Garofalo, 21 pages, to appear in Comm. PDE. Regularity near the characteristic boundary for sublaplacian operators, Pacific J Math., 227 (2006), no. 2, 361397. A note on the stability of local zeta functions, Proc. Amer. Math. Soc, 134 (2006), 8191. Overdetermined BVP, quadrature domains, and applications, with D. Khavinson and A. Solynin, Comput. Methods Funct. Theory, 5 (2005), 1948. Symmetry properties of positive entire solutions of Yamabe type equations on groups of Heisenberg type , with N. Garofalo, Duke Math. J. 106 (2001), no. 3, 411448. Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of subLaplacians on Carnot groupsp , with N. Garofalo, Math. Ann. 318 (2000), no. 3, 453516. 



Proceedings
papers 

Strong unique
continuation for generalized BaouendiGrushin
operators,
with N. Garofalo, Proceedings of the 4th ISAAC
Congress,
The nonlinear Dirichlet
problem and the CR Yamabe problem, with N. Garofalo, Boundary value problems for elliptic and
parabolic operators ( 


Theses 
Yamabe
type equations on Carnot groups, Ph. D. thesis Opérateur à puissances
bornées et decroissance
de l’énergie locale, DEA thesis Université 
Awards 
February 2007  October 2007, The National Academies Twinning Program grant, The Yamabe equation on the quaternionic sphere, $7,150 supplement. February 2005 February 2007, The National Academies Twinning Program grant, The Yamabe equation on the quaternionic sphere, PI, $17, 750. January 2003 December 2004, Centre de Recherches Mathématiques Institut des Sciences Mathématiques (CRMISM) Postdoctoral Fellowship 19992000, Purdue Research Foundation Grant 19981999, Purdue Research Foundation Grant 1994, European Community Tempus Fellowship at Université Bordeaux I 
Current Interests 
Entire solutions of the Yamabe equation on groups of Heisenberg type and the related Obata problem on the boundaries of rank one symmetric spaces; Sasakian geometry Stability of local zeta functions and applications: ﬁnite type conditions, oscillatory integrals, multiplier ideals Symmetry properties of solutions to nonlinear PDEs, Quadrature domains and overdetermined boundary value problems Boundary layers on domains in Carnot groups

Conference Talks 
Towards an Obata Theorem on the quaternionic sphere, Special Session on Geometry of Riemannian Manifolds with Additional Structures, AMS Meeting, Miami, FL April 2006
The geometry of the Yamabe equation on groups of Heisenberg type, Workshop on
Minimal surfaces, SubElliptic PDE’s and Geometric
Analysis,
Stability results for
local zeta functions associated to elliptic equations, CMS Winter 2004
Meeting, Symposium on Harmonic Analysis,
Regularity near the
characteristic boundary for sublaplacian
operators, AARMSCRM Workshop on Singular Integrals and Analysis on CR
Manifolds, Unique continuation for some subLaplace operators, ISAAC 2003, Special Session on Harmonic Analysis and Partial Differential Equations, York University, Toronto, August 2003 Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of sublaplacians, Special Session on Geometry and Analysis in Carnot Carathéodory Spaces, AMS Regional Meeting, University of Notre Dame, Notre Dame, 2000. Yamabe
type equations on groups of Heisenberg type,
Arkansas Spring Lecture Series,
Symmetry properties of
positive entire solutions of Yamabe type equations
on groups of Heisenberg type, Special Session on Nonlinear Eigenvalue Problems and Applications, Joint Mathematics
Meetings, 
Seminar Talks 
On the analysis and
geometry of some nonlinear partial differential equations, Colloquium,
University of New Mexico, March, 2007.
Conformal geometry and
function theory on quaternionic contact manifolds,
Analysis Seminar,
PseudoEinstein
structures on quaternionic contact manifolds,
Differential Geometry Seminar, Lp
estimates and asymptotic behavior of finite
energy solutions to some nonlinear equations, Geometry Seminar,
Stability results for
local zeta functions associated to elliptic equations, Functional Analysis
Seminar,
Some overdetermined
BVP and applications to sharp inequalities and droplet shapes, Functional
Analysis Seminar,
Free boundary problems of
2D bubble and droplet shapes, Analysis Seminar, On the shape of bubbles and some related problems, Séminaire d’analyse nonlinéaire et systémes dynamiques, Université de Montréal, March 2004.
Stability results for
local zeta functions, Analysis Seminar, The sharp constant in the Sobolev type embedding on a Carnot group, Geometry Seminar, Université du Québec à Montréal, March 2003. Overdetermined
boundary value problems, quadrature
domains and applications, PDEs Seminar, Overdetermined
boundary value problems, quadrature
domains and applications, Analysis Seminar,
Review and extensions of
some overdetermined BVPs,
Analysis Seminar,
On strong unique
continuation for generalized Grushin operators,
Analysis Seminar,
On Some Groups of Step
Two, Analysis Seminar, Yamabe type equations on groups
of Heisenberg type, Geometry Seminar,
Power Bounded Operators
and Local Energy Decay for the Wave Equation with TimeDependent Potential, 
Working Seminar Talks 
Shorttime existence of the Ricci ﬂow, CIRGET, Université du Québec à Montréal, Fall 2003 Eigenvalue problems for surfaces after Hersch, LiYau, BourguignonLiYau and Gromov, Université du Québec à Montréal, Spring 2003
The Yamabe
problem,
Geometry Seminar,
Boundary regularity for
solutions of stochastic PDEs, Game Theory Seminar, 
Student Involvment 
The frequency function of
an elliptic differential equation and applications, Graduate Students
Analysis Seminar, UC LEADS advisor, 2006.
Brownian motion and
minimal surfaces,
Graduate Students Seminar Talk, Advisor in the ISM Undergraduate Summer Scholarship program, Study of the shape of a bubble in a viscous incompressible ﬂuid with a source at inﬁnity, 2003
Introduction to
MAPLE, πµεclub
Talk,
The contraction principle
and the existence of solutions of PDEs, Graduate Students
Seminar Talk, 
Courses 
Linear Algebra with Applications, Discrete Mathematics, Calculus I, II and III, Survey of Calculus, Differential Geometry, Real Analysis, Differential Equations with Applications, Differential Equations 
Service/Outreach 
Referee and MathSciNet Reviewer
How to measure the
distance to far away things,
2004 Midwest Geometry
Conference,
