Mathematics

CURRICULUM VITAE

PDF files: [ CV ] [ CV with publications ] [ Research statement ] [ Teaching statement ]

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EDUCATION

• Purdue University, West Lafayette, Indiana USA

  Ph.D., Mathematics, May 2008

  Advisor: Professor Rodrigo Bañuelos

  Thesis: "Dirichlet and Neumann heat kernel properties."

• Wrocław University of Technology, Wrocław, POLAND

  M.S., Mathematics, June 2003

  Advisor: Professor Tadeusz Kulczycki

  Thesis: "Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes."

HONORS AND AWARDS

• Purdue University: A. H. Ismail Interdisciplinary Doctoral Travel Grant, 2006.
• Purdue University: Gerald R. MacLane Memorial Award, Outstanding Graduate Student in Mathematics, 2004.
• Polish Mathematical Society: The Best Student's Paper in Probability and Applied Mathematics, First Award, 2003.

NSF SUPPORT

• Proposal submitted to Analysis program, 2010; pending

TEACHING EXPERIENCE

• University of Illinois at Urbana-Champaign, Urbana, Illinois
  • Graduate level Applied Stochastic Processes
  • Matrix Algebra using Mathematica
  • Ordinary Differential Equations, Probability
• Purdue University, West Lafayette, Indiana
  • Instructor: Calculus, Algebra
  • Recitation: Calculus, Calculus and Analytic Geometry

CONFERENCE CO-ORGANIZED

• AMS special session on "Sharp spectral estimates in analysis, geometry, and probability" (Spring 2010 Southeastern Section Meeting). Program

CONFERENCE PRESENTATIONS

• The method of rotations and tight frames: sharp upper bounds for sums of eigenvalues. Nonlocal operators and partial differential equations, Bedlewo POLAND, 2010.
• The method of rotations and tight frames: sharp upper bounds on Laplace eigenvalues. Queen Dido Conference, Carthage TUNISIA, 2010.
• Sums of Dirichlet eigenvalues: minimizing with equilateral triangles. AMS Spring Southeastern Sectional Meeting, Kentucky US, 2010.
• Sharp bounds for eigenvalues of triangles. AMS Fall Central, Texas US, 2009.
• Isoperimetric bounds for Neumann eigenvalues of triangles. Low Eigenvalues of Laplace and Schrödinger Operators, Oberwolfach GERMANY, 2009
• Isoperimetric bounds for eigenvalues of triangles. Symposium on Inverse Problems Honoring Alberto Calderón, Rio de Janeiro BRAZIL, 2007.
• Sharp estimates for eigenvalues of triangles. International Conference on Stochastic Analysis and Its Applications, Seattle US, 2006.
• Intrinsic ultracontractivity for relativistic stable processes. Analysis and Probability related to solvable Lie groups, Zakopane POLAND, 2002.

SEMINAR TALKS

• The method of rotations and tight frames: sharp upper bounds on Laplace eigenvalues, Analysis Seminar, Washington Univ. at St. Louis, Oct. 2010.
• Sharp bounds for eigenvalues of triangles, Analysis Seminar, Syracuse University, Dec. 2009
• Sharp bounds for eigenvalues of triangles, Differential Geometry Seminar, University of California Irvine, Oct. 2009.
• Sharp integrability condition of an exit time for stable processes from unbounded domains, Probability Seminar at University of Virginia, Feb. 2008.
• Neumann heat kernel monotonicity, Joint Differential Equations and Stochastic Analysis Seminar, University of Illinois at Urbana-Champaign, Nov. 2007.
• Expected exit time for symmetric stable processes from unbounded domains, Lisbon PORTUGAL, invited for one week by Prof. Pedro Freitas, Sep. 2007.
• Isoperimetric bounds for eigenvalues of triangles, Scattering and Spectral Theory Seminar, Purdue University, Sep. 2007.
• Sharp integrability condition for an exit time for stable processes from unbounded domains, Probability Seminar, Purdue University, Sep. 2007.
• Estimates for the first eigenvalue of triangles and other planar domains, Wrocław POLAND, June 2006.
• Intrinsic ultracontractivity for a relativistic process, Karpacz POLAND, 2003.