PIMS - UCalgary Geometric Analysis Seminar Series: Luda Korobenko

  • Date: 02/04/2022
  • Time: 14:00
Lecturer(s):
Luda Korobenko, Reed College
Location: 

Online

Topic: 

Hypoellipticity via Sums of Squares

Description: 

Abstract: Many results on hypoellipticity of second order operators rely on the assumption that the operator can be written as a sum of squares of vector fields (e.g. Hormander's bracket condition, and Christ's hypoellipticity theorem for infinitely degenerate operators). For operators that are not sub elliptic and not sums of squares, hypoellipticity has been only proved in some very special cases, for example, when L=L_1+g(x)L_2 and L_1 and L_2 are subelliptic.
In this talk I will address the question of hypoellipticity for a general divergence form operator, whose matrix is comparable, but not necessarily equal, to a diagonal matrix of a special form. The idea is to find sharp sufficient conditions which guarantee that a smooth positive matrix can be written as a sum of squares of positive dyads with sufficient degree of smoothness. Interestingly, this question has not been completely resolved even for scalar positive functions.

 

Speaker Bio: I work in the area of Real Analysis, more precisely, degenerate elliptic PDEs, studying properties of solutions to such equations and associated metric measure spaces. I received my PhD from the University of Calgary in 2013, and I have been an Assistant Professor at Reed College since 2017 after completing postdoc appointments at the University of Pennsylvania, and at McMaster University.

 

 

Other Information: 

This seminar is available via Zoom. Registration is required

 

Time: 2–3pm PST (3–4pm MDT) 

-------

 

This seminar series will promote mathematical and physical topics employing the use and creation of geometric analysis techniques. Some of the main themes the seminar will explore are 1) PDEs on manifolds, 2) geometric flows, 3) inverse problems for PDEs and geometric settings, and 4) the introduction of microlocal techniques to a broader geometric and analysis audience.

 

The series will run on Friday afternoons 2–3pm PST (3–4pm MDT), starting January 14, 2022 and ending around April 8, 2022.

 

See more information and other dates in the series or contact Tracey Balehowsky, tracey.balehowsky@ucalgary.ca