Dimiter Vassilev ( CV.pdf )

Department of mathematics University of California, Riverside Office Phone: (951) 827-4610 Email: dvassilev@math.ucr.edu 

 Web Page: http://math.ucr.edu/~dvassilev

 

Education

Purdue University, West Lafayette, IN, Mathematics, M. S., May 1998, Ph.D., December 2000

 

Université Bordeaux I, Talence-Cedex, France, Mathematics, DEA, May 1994

University of Sofia, Sofia, Bulgaria, Mathematics, B.S., 1993

Positions

Visiting Assistant Professor, University of California, Riverside, CA, since June 2005

Visiting Assistant Professor, University of Arkansas, Fayetteville, January 2005 -May 2005

CRM-ISM Postdoctoral Fellowship, Montréal, PQ, January 2003 -December 2004

Visiting Assistant Professor, University of Arkansas, Fayetteville, AR, 2000 –2004

 

Teaching Experience

2005, University of California, Riverside, CA

2003, McGill University, Montréal, PQ

2000 – 2005, University of Arkansas, Fayetteville, AR

1995 –2000 Teaching Assistant, Purdue University, West Lafayette, IN

 

Papers

 

Quaternionic contact manifolds with a closed fundamental 4-form, with St. Ivanov, arXiv:0810.3888, 2008.

Conformal paracontact curvature and the local flatness theorem, with St. Ivanov and S.  Zamkovoy, MPIM2007-90, 2007.

Conformal quaternionic contact curvature and the local sphere theorem, with St. Ivanov, MPIM2007-79, 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 toHardy-Sobolev inequalities, submitted.

Strong unique continuation for generalized Baouendi-Grushin operators, with N. Garofalo, 21 pages, to appear in Comm. PDE.

Regularity near the characteristic boundary for sub-laplacian operators,  Pacific J Math.,  227 (2006), no. 2, 361--397.

 A note on the stability of local zeta functions, Proc. Amer. Math. Soc, 134 (2006), 81-91.

Overdetermined BVP, quadrature domains, and applications, with D. Khavinson and A. Solynin,  Comput. Methods Funct. Theory, 5 (2005),  19-48.

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, 411--448.

Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groupsp , with N. Garofalo, Math. Ann. 318 (2000), no. 3, 453--516.

 

Proceedings papers

 

Strong unique continuation for generalized Baouendi-Grushin operators, with N. Garofalo, Proceedings of the 4th ISAAC Congress, Toronto, 2003.

The non-linear Dirichlet problem and the CR Yamabe problem, with N. Garofalo, Boundary value problems for elliptic and parabolic operators (Catania, 1998) Matematiche (Catania) 54 (1999), suppl., 75–93.

 

 

Theses

Yamabe type equations on Carnot groups, Ph. D. thesis Purdue University, 2000, advisor Professor Nicola Garofalo

Opérateur à puissances bornées et decroissance de l’énergie locale, DEA thesis Université Bordeaux I, 1994, advisor Professor Vesselin Petkov

 

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 (CRM-ISM) Postdoctoral Fellowship

1999-2000, Purdue Research Foundation Grant

1998-1999, 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: nite type conditions, oscillatory integrals, multiplier ideals

Symmetry properties of solutions to non-linear 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, Sub-Elliptic PDE’s and Geometric Analysis, Dartmouth College, March, 2005

Stability results for local zeta functions associated to elliptic equations, CMS Winter 2004 Meeting, Symposium on Harmonic Analysis, McGill University, Montréal, December 2004

Regularity near the characteristic boundary for sub-laplacian operators, AARMS-CRM Workshop on Singular Integrals and Analysis on CR Manifolds, Dalhousie University, Halifax, May 2004

Unique continuation for some sub-Laplace operators, ISAAC 2003, Special Session on Harmonic Analysis and Partial Differential Equations, York University, Toronto, August 2003

Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-laplacians, 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, University of Arkansas, 2000

Symmetry properties of positive entire solutions of Yamabe type equations on groups of Heisenberg type, Special Session on Non-linear Eigenvalue Problems and Applications, Joint Mathematics Meetings, Washington, DC, 2000.

 

Seminar Talks

On the analysis and geometry of some nonlinear partial differential equations, Colloquium, University of New Mexico, March, 2007.

The Yamabe equation - applications in analysis and conformal geometry, Colloquium, Texas Tech University, March, 2007.

Conformal geometry and function theory on quaternionic contact manifolds, Analysis Seminar, Concordia University and McGill University, February 2007.

Pseudo-Einstein structures on quaternionic contact manifolds, Differential Geometry Seminar, University of California Riverside, October 2006.

Lp estimates and asymptotic behavior of finite energy solutions to some non-linear equations, Geometry Seminar, University of California Riverside, January 2006.

Stability results for local zeta functions associated to elliptic equations, Functional Analysis Seminar, University of California Riverside, December 2005.

Asymptotic behavior and Lp space regularity of solutions to non-linear elliptic equations related to sharp Hardy-Sobolev inequalities and applications, Analysis Seminar, McGill University, November 2005.

Some overdetermined BVP and applications to sharp inequalities and droplet shapes, Functional Analysis Seminar, University of California Riverside, November 2005.

The Yamabe equation on groups of Iwasawa type, Geometry Seminar, University of California Riverside, November 2005
.

Free boundary problems of 2-D bubble and droplet shapes, Analysis Seminar, University of Arkansas, January 2005.

On the shape of bubbles and some related problems, Séminaire d’analyse non-linéaire et systémes dynamiques, Université de Montréal, March 2004.

Stability results for local zeta functions, Analysis Seminar, University of Arkansas, September 2003.

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, Purdue University, February 2003.

Overdetermined boundary value problems, quadrature domains and applications, Analysis Seminar, McGill University, January 2003.

Review and extensions of some overdetermined BVPs, Analysis Seminar, University of Arkansas, November 2002.

On strong unique continuation for generalized Grushin operators, Analysis Seminar, University of Arkansas, February 2002.

On Some Groups of Step Two, Analysis Seminar, University of Arkansas, September 2000.

 Yamabe type equations on groups of Heisenberg type, Geometry Seminar, University of Chicago, February 2000.

Power Bounded Operators and Local Energy Decay for the Wave Equation with Time-Dependent Potential, University of Delaware, April, 1995.

 

Working Seminar Talks

Short-time existence of the Ricci flow, CIRGET, Université du Québec à Montréal, Fall 2003

Eigenvalue problems for surfaces after Hersch, Li-Yau, Bourguignon-Li-Yau and Gromov, Université du Québec à Montréal, Spring 2003

The Yamabe problem, Geometry Seminar, University of Arkansas, 2002

Boundary regularity for solutions of stochastic PDEs, Game Theory Seminar, University of Arkansas, 2001

 

Student Involvment

The frequency function of an elliptic differential equation and applications, Graduate Students Analysis Seminar, University of New Mexico, March, 2007.

UC LEADS advisor, 2006.

Brownian motion and minimal surfaces, Graduate Students Seminar Talk, University of Arkansas, 2004

Advisor in the ISM Undergraduate Summer Scholarship program, Study of the shape of a bubble in a viscous incompressible uid with a source at innity, 2003

Introduction to MAPLE, πµε-club Talk, University of Arkansas, 2002

The contraction principle and the existence of solutions of PDEs, Graduate Students Seminar Talk, University of Arkansas, 2001

 

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, Washington Elementary Schools, FAyettevile, AR

2004 Midwest Geometry Conference, Fayetteville, Arkansas, co-organizer